DesCalc Metric Aisc

METAL BUILDING SOFTWARE

CALCULATIONS MANUAL

(METRIC VERSION)

SEPTEMBER 5, 2000

METAL BUILDING SOFTWARE FARGO, NORTH DAKOTA

METAL BUILDING DESIGN is a program of Metal Building Software, Inc. (MBS) of Fargo, North Dakota. This program is to serve as a computational aid for the building designer. The building designers should familiarize themselves with the computations used in the program. The building designer is responsible for checking the computations produced by the program. Every effort has been made to ensure the accuracy of this program and MBS will not accept responsibility for any mistake, error, or misrepresentation in or as a result of the usage of this program.

This Manual is an updating and electronic representation of the material in the MBS Hand Calculations Manual.

This version of the manual is in Metric Units.

REVISION 1.0

Copyright 2000 by Metal Building Software, Inc.

1. INTRODUCTION The design of metal buildings includes: load generation, apply those loads to frame and components, structural analysis to calculate internal actions, and use the internal actions with the design code to select the members. This entire process is carried out by a series of computer programs that are inter-connected to operate as a single program. The program output is typically reviewed by the design engineer and either approved as is, or the output is modified and then approved. As the design engineer approves the design they are either approving all the steps taken by the computer program or if they differ with some of the steps, their differences will not significantly effect the program output. The objective in this manual is to illustrate all the steps taken by a computer program in the design of metal buildings. The illustration begins with drawings of the designed building. This is followed by the calculations that include reference to building codes and structural design codes. The building design is illustrated with a sample building that contains a number of features common to metal buildings. This building does not contain all possible building features. This manual will be enlarged, as other building features are included. Following the section on the sample building, the next section illustrates the application of building loads according to the 1996 MBMA recommendations. The remaining sections provide detailed calculations for each of the building design topics. Currently, designers are using either the 86 AISI code with the 89 addendum or using the 96 AISI code. These calculations illustrate the 86-89 code. The Appendix contains some of the reference material used in the design.

2. FEATURES OF THE SAMPLE BUILIDNG A three dimensional view of the sample building is shown on the next page. The building features are listed below the drawing and referenced to the drawing. As calculations reference the sample building it is necessary to know the building dimensions. These building dimensions are available on the erection drawings. The erection drawings are on the follow pages. Those drawings include: - Anchor Bolt Plan ............................................... 2-3 - Anchor Bolt Details ........................................... 2-4 - Anchor Bolt Reactions....................................... 2-5 - Roof Plan ........................................................... 2-6 - Rigid Frame Elevation....................................... 2-7 - Right Endwall .................................................... 2-8 - Left Endwall ...................................................... 2-9 - Back Sidewall .................................................. 2-10 - Front Sidewall.................................................. 2-11 - Erection Details ......................................... 2-12, 13

Calculations Manual 06/06 MBS, Inc. Page 2-1


FEATURES OF THE SAMPLE BUILDING

(Roof Purlins Were Removed To Better See The Framing)

1. Interior Frame With Interior Column 2. Rigid Frame In Endwall 3. Portal Frame In Sidewall 4. X Bracing In Sidewall 5. Bypass Girts In This Sidewall 6. Flush Girts In This Endwall 7. Bypass Girts In This Endwall 8. Framed Opening 9. Walk Door 10. X Bracing In Roof 11. Post And Beam Endwall 12. Sliding Door

3. LOADS ON METAL BUILDINGS 3.1 Wind Load Site Conditions.................................................................................. 3-1 3.2 Main Wind Framing............................................................................................. 3-1 A. Used for Wind Loads on .......................................................................... 3-1 B. Design Wind Pressure.............................................................................. 3-1 C. Transverse Wind ...................................................................................... 3-1 D. Summary of Transverse Wind ................................................................. 3-3 E. Longitudinal Wind ................................................................................... 3-3 F. Summary of Longitudinal Wind .............................................................. 3-4 3.3 Components and Cladding Wind Loads .............................................................. 3-5 A. Used for Wind Loads on .......................................................................... 3-5 B. Design Wind Pressure.............................................................................. 3-5 C. Panels ....................................................................................................... 3-5 D. Component Wind Loads by Design Program .......................................... 3-5 3.4 Seismic Loads ...................................................................................................... 3-6 A. Seismic Site Conditions ........................................................................... 3-6 B. Seismic Base Shear .................................................................................. 3-6 C. Seismic Coefficients for Longitudinal Load............................................ 3-6 D. Transverse Seismic Load on Rigid Frame ............................................... 3-6 3.5 Design Load Combinations.................................................................................. 3-6 A. MBMA 96 Code Requirements ............................................................... 3-6 B. General Rigid Frame Design Loads for MBMA 96 ................................ 3-7 C. Rigid Frame Design Loads for Crane and Seismic, MBMA 96 .............. 3-8

3. LOADS ON METAL BUILDINGS 3.1 WIND LOAD SITE CONDITIONS

Code: MBMA 96, Closed Building, Category II, V = 85 mph = 38.0 mps See Appendix A for the MBS description of the MBMA design loads. It contains the table referenced below as MBMA(96).

3.2 MAIN WIND MBMA (96) FRAMING

A. Used for Wind Loads on: - Interior Rigid Frames - Endwall Frames - X bracing in Roof, Sidewall, and Endwall

B. Design Wind Pressure, p

( )( ) ( )

( )[ ]aTableMBMAImpsV

mheighteaveBuildingHmkNHVq

GCqIp

w

pw

1.1.4.10.38

0.8,/,9.2010447.000256.0 2722

==

==⋅⋅=

⋅⋅=

]828.0[/83.0

/83.09.20108

477.03800256.0

2

2722

WindBasicmkN

mkNq

==

=⎟⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛⋅=

C. Transverse Wind Coefficients, (GCp)

a. Interior and end zone wind coefficients

From Table MBMA-1, roof slope < 2.11:12, enclosed building Load 1 Interior Zone: C1 = 0.25, C2 = -1.00, C3 = -0.65, C4 = -0.55 [D1] Load 2 Interior Zone: C1 = 0.65, C2 = -0.60, C3 = -0.25, C4 = -0.15 [D2] Load 1 End Zone: C1 = 0.50, C2 = -1.40, C3 = -0.80, C4 = -0.70 [D3] Load 2 End Zone: C1 = 0.90, C2 = -1.00, C3 = -0.40, C4 = -0.30 [D4]


Wind design loads are the sum of the external and internal wind pressures as shown below.

External wind +

internal pressure External wind +

internal suction

From the above coefficients, it can be seen that the external wind coefficients are: C1 = 0.40, C2 = -0.80, C3 = -0.45, C4 = -0.30 and the internal pressure is + 0.20. Many building codes report the external and internal wind coefficients and the

designer is to calculate the net wind loads. The MBMA code reports the net wind coefficient on each building surface as in Table MBMA-1.

b. Width of end zone, see Table MBMA-1 End zone width = the larger of 20 feet and 2 times the edge strip width.

m

widthstripEdge

0.391.0363,2.13004.0

2.3840.0,0.33010.0

===⋅≥=⋅=⋅=≤

05.3,1.62

0.632,1.628.320==⋅=

=⋅==≥ama

widthzoneEnd

c. Wind coefficients for end frame based on interior zone and end zone, Ceff


( ) ( )

endeff

endeff

CCaLFor

LaLaCCCC

aLFor

=⋅>

−⋅⋅⋅−+=

⋅≤

2

42

2intint

( ) ( ) 965.05.705.35.705.344 22 =−⋅⋅=−⋅⋅

LaLa

Wind load 1 C1 = ( ) 49.0965.025.050.025.0 =⋅−+

C2 = ( ) 39.1965.000.140.100.1 −=⋅−−− C3 = ( ) 79.0965.065.080.065.0 −=⋅−−− C4 = ( ) 69.0965.055.070.055.0 −=⋅−−− Note the calculated coefficients are nearly equal to the end coefficients. For

simplicity, the end and interior coefficients will not be combined for the MBMA 96 code. For other wind codes where the end zone width is much smaller the coefficients will be combined.

D. Summary of Transverse Wind

Rigid Frames only at interior locations Wind_1 = [D1], Wind_2 = [D2] Rigid Frames located at endwall Wind_1 = [D3], Wind_2 = [D4] Endwall Rafter Wind_1 = [D3], Wind_2 = [D4] Bracing Wind = [D3]

E. Longitudinal Wind a. Wind coefficients, roof and sidewall bracing

From Table MBMA(96)-2

C1 = ( )90.065.0 C2 = 83.0− C3 = ( )30.015.0 −−

- The values in ( ) are at the edge of the endwall over a distance ‘a’. - A single wind coefficient based on the interior and edge loading and the interior and

end zone width is:


( )

( ) 18.030

30.00.320.323015.03

70.030

90.00.320.323065.01

=⋅⋅+⋅−⋅

=

=⋅⋅+⋅−⋅

=

C

C

b. Roof and Sidewall bracing, line 34 of roof input

C1 = 2/581.083.070.0 mkN=⋅ C2 = 2/689.083.083.0 mkN=⋅ C3 = 2/149.083.018.0 mkN=⋅

c. Wind coefficients, Interior rigid frame

Table MBMA-3 Load 1 C1 = - 0.70, C2 = -1.00, C3 = -0.65, C4 = -0.70 Load 2 C2 = - 0.30, C2 = -0.65, C3 = -0.25, C4 = -0.30 Note load 1 has greater loads than load 2. However, load 1 needs to be applied from

the left and right ends of the building in order to obtain a symmetrical frame. The design wind coefficients are: Load 1: C1 = - 0.70, C2 = -1.00, C3 = -0.65, C4 = -0.70 Load 2: C1 = - 0.70, C2 = -0.65, C3 = -1.00, C4 = -0.70

d. Rigid frame in endwall and endwall rafter Similar values from Table MBMA-3. Load 1: C1 = - 0.70, C2 = -1.40, C3 = -0.80, C4 = -0.70 Load 2: C1 = - 0.70, C2 = -0.80, C3 = -1.40, C4 = -0.70

F. Summary for Longitudinal Wind - Roof Design Input File:

- the wind loads from Section b. are on the wind pressure/suction line. - Rigid Frame Design Input File, “Wind Coefficients” line:


- For frames only at interior locations - Use coefficients from Section c. - For frames located at endwall - Use coefficients from Section d. - Endwall Design Input File, “Wind Coefficients” line:

- The Wind_1 roof coefficients from Section d, however, a single longitudinal wind load is used and the maximum suction is used on both roof surfaces.

3.3 COMPONENTS AND CLADDING A. Used for Wind Loads on:

- Panels, girts, purlins, endwall columns, endwall roof extensions, sidewall roof extensions

B. Design Wind Pressure, p: The design wind pressure by building component and openings is given in Tables

MBMA(96)-2 and MBMA-4. Appendix A contains a description of the data. C. Panels

Example wall panel exterior wind coefficients are 1.2, -1.2, and (-1.4), the –1.4 is for wind loading on the end zone, a distance 'z' on the endwall and 2 times 'z' on the sidewall. If roof design parameter 17 is set to '2' the program will check the panels for the wind suction on the edge zone, else it will use the interior zone wind loading.

D. Component Wind Loads by Design Program Unless noted, C from Table MBMA(96)-2, Roof Slope, RS < 2.11:12 (10 degrees).

a. Sidewall Design (Line 14) Wall girt: C = 1.0, -1.1

p = 1.0 · 0.828 = 0.828 kN/m² p = -1.1 · 0.828 = -0.911 kN/m²

Wall panel: C = 1.2, -1.2 p = 1.2 · 0.828 = ±0.994 kN/m²

Door jamb: same as endwall columns

b. Endwall Design (Line 30) Endwall columns: C = 1.0, -1.0

p = 1.0 · 0.828 = ±0.828 kN/m² Endwall panel: C = 1.2, -1.2

p = 1.2 · 0.828 = ±0.994 kN/m²

c. Roof Design (Line 34) Purlins: C = -1.2

p = -1.2 · 0.828 = ±0.994 kN/m² Gable Extensions: C = -1.8

p = -1.8 · 0.828 = -1.490 kN/m²


Panels: C = -1.3 p = -1.3 · 0.828 = -1.076 kN/m²

3.4 SEISMIC LOADS - See Appendix B for the MBS description of ASCE 7-98 Seismic Code. A. Seismic Site Conditions From Code Figure 9.4.1.1(a) the spectral response acceleration for a building in central

Alabama is 0.25. From Code Table 9.4.1.2.a for Ss = 0.25 and Site Class C, the Fa = 1.2. B. Seismic Base Shear

RW

RWV

RWSF

V sa

⋅=⋅⋅⋅⋅=

⋅⋅⋅⋅=

24.025.02.1322.1

2.1 32

C. Seismic Coefficient for Longitudinal Load for bracing 0.5=R

WWRWV ⋅=⋅=⋅= 048.0524.024.0

The seismic coefficient is on the “Basic Loads” line of the roof design input file. It is 0.048.

D. Transverse Seismic Load on Rigid Frame for moment resisting frames 0.4=R

)()( wallsroof WWW += ( )SLFLCLDLWidthSpacingBayW roof +++⋅⋅=)(

psfofloaddeadroofDL 0.2= 0.3ofloadcollateralCL = (roof design parameter 32 for other than 2psf) psfloaddeadframeFL 2== 0.30, usepsfloadsnowSL ∴<= psfSpacingBayHeightEaveW wall 222)( ⋅⋅⋅= (roof despar 33 for other than 2psf)

( )

k

W

7.182.15.17

222

2425023210025

=+=

⋅⋅⋅++++⋅⋅=

Seismic force at eave on frame kRW 12.147.1824.024.0 =⋅=⋅= One half of this force (0.56) is applied at each eave line on the frame. See “Basic

Loads” line in the rigid frame input file.

3.5 SNOW LOADS


A. Flat roof snow load is: (Flat roof includes 1:12 roof slope) - See Appendix C for the MBS description of ASCE 7-98 Snow Loads. gtef pICCp ⋅⋅⋅⋅= 70.0 from Table 7-2, for a partially exposed roof in exposure C. ,

,,

0.1=eC from Table 7-3 for a heated structure without special thermal condition. 0.1=tC from Table 7-4 for a category II building 0.1=I from Figure 7-1 for a central Alabama location. psfpg 10=

psfp f 71011170.0 =⋅⋅⋅⋅= B. Minimum Roof Snow Load Minimum Pf is I · Pg = 1 · 10 = 10psf. Therefore, use a roof snow of 10psf. Enter the

10psf as the roof snow load on the building data entry screen. 3.6 DESIGN LOAD COMBINATIONS A. ASCE 7-98 Code Requirements

Section 2.4.1 of the ASCE 7-98 Code lists the following design load combinations: 1. D 2. D + (Lr or S) 3. D + (Lr or S) + (W or 0.7 E) 4. 0.6 D + W 5. 0.6 D + 0.7 E where: D = dead load, Lr = roof live load, S = snow, W = wind, and E = earthquake. The reference to loads from flood, soil, temperature, and rain were omitted from the

above list. Section 2.4.3 on load reduction states that when two or more loads are used with dead

load that the two or more loads should be multiplied by 0.75. Also, the design loads using the 0.75 can not have the one-third stress increase when wind load is present. However, since the one-third stress increase is used for all the loads involving wind, this design load is multiplied by 4/3. This results in a design load of 1.33 · D + L + W.

B. Rigid Frame Design Loads for ASCE7-98 The MBS program can use either the default design load combinations or use design load

combinations set specifically for each building code. PE 7-99-6 and 4-00-11 provide instructions on setting the rigid frame design loads as desired by the user.

The design load combination for the rigid frame using the ASCE-7 98 Code are shown on

the next page. The need for each design load is described below the list of loads.


*(20)DESIGN LOADS: * --------------------Load_Coefficients------------------- *Load Live/ Live -Wind_1- -Wind_2- Long_Wind -Seismic-- *No Id Dead Coll Snow Right Lt Rt Lt Rt 1 2 Long Tran 18 1 1.00 1.00 1.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 2 1.00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 3 1.33 1.00 1.00 .00 1.00 .00 .00 .00 .00 .00 .00 .00 4 1.33 1.00 1.00 .00 .00 1.00 .00 .00 .00 .00 .00 .00 5 1.33 1.00 1.00 .00 .00 .00 1.00 .00 .00 .00 .00 .00 6 1.33 1.00 1.00 .00 .00 .00 .00 1.00 .00 .00 .00 .00 7 .60 .00 .00 .00 1.00 .00 .00 .00 .00 .00 .00 .00 8 .60 .00 .00 .00 .00 1.00 .00 .00 .00 .00 .00 .00 9 .60 .00 .00 .00 .00 .00 1.00 .00 .00 .00 .00 .00 10 .60 .00 .00 .00 .00 .00 .00 1.00 .00 .00 .00 .00 11 .60 .00 .00 .00 .00 .00 .00 .00 1.00 .00 .00 .00 12 .60 .00 .00 .00 .00 .00 .00 .00 -1.00 .00 .00 .00 13 .60 .00 .00 .00 .00 .00 .00 .00 .00 1.00 .00 .00 14 .60 .00 .00 .00 .00 .00 .00 .00 .00 -1.00 .00 .00 15 .60 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 .70 16 .60 .00 .00 .00 .00 .00 .00 .00 .00 .00 .00 -.70 17 .60 .00 .00 .00 .00 .00 .00 .00 .00 .00 .70 .00 18 .60 .00 .00 .00 .00 .00 .00 .00 .00 .00 -.70 .00

Design Loads Comments 1 ASCE Load 2 2 ASCE Load 1

3 thru 6 ASCE Load 3 with 4 transverse wind loads and loads ‘L’ and ‘W’ are multiplied by 4/3 to permit the 1/3 stress increase for wind.

7 thru 10 ASCE Load 4 with 4 transverse wind loads 11 thru 14 ASCE Load 4 with 2 longitudinal wind

loads. Diagonal bracing forces from longitudinal wind are also included. One for longitudinal wind from either direction.

15 & 16 ASCE Load 3 and 5, transverse seismic to the right and left. Snow load is added if the snow loads exceeds 30 psf.

17 & 18 Same as 15 and 16 only it is longitudinal seismic from either direction.


4. RIGID FRAME DESIGN 4.1 Introduction.......................................................................................................... 4-1 4.2 Composition Of Frame ........................................................................................ 4-1 A. Program Output: Design Summary Report.............................................. 4-1 B. Program Output: Member, Segment, and Splice ID ................................ 4-3 4.3 Loads On Interior Frame...................................................................................... 4-2 A. Dead, Live, and Collateral ....................................................................... 4-2 B. Wind_1 From Left ................................................................................... 4-2 4.4 Frame Analysis .................................................................................................... 4-4 4.5 Some Basic Load Reactions................................................................................. 4-4 4.6 Statics Check On Basic Load Reactions.............................................................. 4-4 A. Dead Load................................................................................................ 4-4 B. Collateral Load......................................................................................... 4-4 C. Live Load ................................................................................................. 4-5 D. Wind_1 From Left ................................................................................... 4-5 4.7 Internal Actions for Stress Check At Top Of Columns ....................................... 4-5 A. Program Output: Section Properties Report ............................................ 4-5 B. Sign Convention For Internal Actions ..................................................... 4-6 C. Dead Load................................................................................................ 4-6 D. Live Load ................................................................................................. 4-7 E. Wind_1 From Left ................................................................................... 4-7 4.8 Stress Check At Top Of Column ......................................................................... 4-7 A. Program Output: Actions and Stress Report............................................ 4-7 B. Member Plates ......................................................................................... 4-8 C. Shear Check ............................................................................................. 4-8 D. Member Unbraced Length ....................................................................... 4-9 E. Program Output: Unbraced Length Report.............................................. 4-9 F. Cb For Outside Flange, The Compression Flange ................................... 4-9 G. Actions For Outside Flange Stress Check ............................................... 4-9 H. Special Program For Stress Check......................................................... 4-10 I. Outside Flange Unity Check.................................................................. 4-10 J. Inside Flange Unity Check..................................................................... 4-12 4.9 Check Interior Column ...................................................................................... 4-14 A. Calculations............................................................................................ 4-14 B. Program Output: Interior Column Design Report ................................. 4-14

4.10 Check Number and Diameter Of Anchor Bolts................................................. 4-15 A. Calculations............................................................................................ 4-15 B. Program Output: Base Plate and Anchor Bolt Design........................... 4-16 4.11 Check Base Plate Thickness .............................................................................. 4-16 4.12 BEP Thickness ................................................................................................... 4-17 A. Calculations............................................................................................ 4-18 B. Program Output: Bolted End Plate Design ............................................ 4-21 4.13 BEP: Flange To End Plate Weld........................................................................ 4-22 4.14 Stiffener At Column To Rafter Splice ............................................................... 4-22 A. Calculations............................................................................................ 4-22 B. Program Output: Stiffener Report.......................................................... 4-24 4.15 Stiffener Above Interior Column....................................................................... 4-24 4.16 Interior Column Connection To Rafter Uplift ................................................... 4-25 A. Flange Bending From Tension in Bolts ................................................. 4-25 B. Total Tension Stress In Flange .............................................................. 4-27 4.17 Design of Interior Column Cap Plate................................................................. 4-27 A. Calculations............................................................................................ 4-27 B. Program Output: Interior Column Cap Plate ......................................... 4-27 4.18 Check Size Of Flange Brace .............................................................................. 4-28 A. Calculate Force In Flange Brace............................................................ 4-28 B. Member Stress Check ............................................................................ 4-28 C. Program Output: Flange Brace Report .................................................. 4-31 4.19 Check Flange Brace To Purlin Connection ....................................................... 4-30 4.20 Weld Of Web To Flange.................................................................................... 4-32 A. Calculations............................................................................................ 4-32 B. Program Output: Web to Flange Weld .................................................. 4-32 4.21 Check Web At Top Of Sidewall Column .......................................................... 4-33 A. Calculations............................................................................................ 4-33 B. Program Output: Special Segment Report............................................. 4-33 4.22 Check Flange At Top Of Sidewall Column....................................................... 4-33 4.23 Check Area Reduction in Tension Flange ......................................................... 4-33 A. Calculations............................................................................................ 4-33 B. Program Output: Influence of Holes in Tension Flange........................ 4-34

4.24 Calculating Live Load Deflection...................................................................... 4-34 A. Calculations............................................................................................ 4-34 B. Program Output: Deflection Report....................................................... 4-35 4.25 Calculating Drift Ratio....................................................................................... 4-35

4. RIGID FRAME DESIGN

4.1 INTRODUCTION

Based on the entered building data and options set by the designer the program prepares a preliminary design of the rigid frame. This design is in the rigid frame design input file. The program then designs the rigid frame in the output file. If the designer wants to change the program output, they can revise the input file and rerun the design. Consider the designed rigid frame to be satisfactory to the designer. This chapter will provide those calculations that will verify the program output. As the calculations are described it is often necessary to refer to the MBS program output. Portions of the program output are included where they are referenced. The program output is placed in boxes to separate it from the calculations.

4.2 COMPOSITION OF FRAME

Frame outside dimensions: see the erection drawing frame cross section on Pg. 2-5. For the size of web and flange plate, see the design summary as shown below.

A. Program Output: Design Summary Report

=============================================================================== Calc_Manual Design Summary Report 8/31/00 7:08am =============================================================================== MEMBERS: Mem Seg| Flange |Web_Depth| Plate_Thickness | Max_UCV | Max_UCO | Max_UCI Id Id | Len Wid|Strt End| Web O-flg I-flg|Id Ld Ucv|Id Ld Uco|Id Ld Uci --- --- ---- --- ---- ---- ----- ----- ----- -- -- ---- -- -- ---- -- -- ---- 1 1 7795 164 400 600 3.0 6.0 6.0 6 9 0.69 6 2 0.66 5 13 0.80 2 2 3232 164 600 571 5.0 6.0 6.0 7 1 0.33 7 2 0.50 7 2 0.44 2 3 8000 164 571 500 5.0 6.0 6.0 17 1 0.23 13 1 0.48 14 6 0.36 3 4 3000 164 500 660 5.0 6.0 8.0 20 1 0.49 20 1 0.62 20 1 0.66 4 5 2999 164 660 500 5.0 6.0 8.0 21 1 0.49 21 1 0.62 21 1 0.66 5 6 8000 164 500 571 5.0 6.0 6.0 24 1 0.23 28 1 0.48 27 9 0.37 5 7 3233 164 571 600 5.0 6.0 6.0 34 1 0.33 34 3 0.50 34 3 0.44 6 8 7795 164 600 400 3.0 6.0 6.0 35 6 0.68 35 3 0.66 36 12 0.80 No. Cycles For Plate Optimization= 9 LOAD COMBINATIONS: 1 - DL+CO+LL 2 - DL+WL1 3 - DL+WR1 6 - DL+LW1 9 - DL-LW2 12 - DL+CO+LL+WL2/2 13 - DL+CO+LL+WR2/2


The first two columns refer to the Member ID and Segment ID. The “M” and “S” numbers for the frame are shown on the following page. This design graphic is available from the rigid frame design program.

4.3 LOADS ON INTERIOR FRAME

A. DEAD, LIVE, COLLATERAL

( )( )( ) ( )( )( ) kNcolumneriorW

mkNcollateralWkNrafterleftW

kNkgcolumnleftWmkNroofonW

mkNW

D

D

D

D

D

l

34.281.9239int/75.01.05.7

50.581.912243994.181.98.19/90.012.05.7

/5.460.05.7

=⋅==⋅=

=⋅+==⋅=

=⋅==⋅=

B. WIND_1 FROM LEFT

mkNWmkNW

mkNWmkNW

/42.3828.055.05.74/04.4828.065.05.73

/21.6828.00.15.72/55.1828.025.05.71

=⋅⋅==⋅⋅==⋅⋅==⋅⋅=


B. Program Output: Member, Segment, and Splice ID

4.4 FRAME ANALYSIS

The program uses the stiffness method of analysis to determine the frame reactions. An example of a check on the program output with other software is given in Appendix C.

4.5 SOME BASIC LOAD REACTIONS The reactions report provides the basic load reactions shown below.

Load H1 V1 H2 V2 V3 DL 1.8 10.7 1.8 10.7 22.9 CL 1.1 5.2 1.1 5.2 12.2 LL 6.4 31.1 6.4 31.1 73.0

WL1 -23.4 -49.5 14.8 -22.7 -81.7

4.6 STATICS CHECK ON BASIC LOAD REACTIONS

A. DEAD LOAD Member + Interior Column Wt = (1518 + 239) · 9.81 / 1000 = 17.2 kN Length of roof slope = 15000/cos 5 = 15019 mm Sum of load = 15.0 · 7.5 · 2 · 0.12 + 17.2 = 44.2 kN Sum of reaction = 10.7 + 10.7 + 22.9 = 44.3 kN, Okay B. COLLATERAL LOAD Sum of load = 15.0 · 2 · 7.5 · 0.10 = 22.5 kN Sum of reactions = 5.21 + 5.21 + 12.2 = 22.6 kN, Okay


C. LIVE LOAD Sum of load = 30 · 4.5 = 135.0 kN Sum of reactions = 31.1 + 31.1 + 73.0 = 135.2 kN, Okay D. WIND_1 FROM LEFT Vertical load = 6.21 · 15 + 4.04 · 15 = 153.8 kN Vertical reaction = 49.5 + 22.7 + 81.7 = 153.9 kN, Okay Horizontal load = 1.55 · 8 + 3.42 · 8 - (6.21 - 4.04) · 15 ·tan 5 = 37.9 kN Horizontal reaction = 23.4 + 14.8 = 38.2 kN, Okay

4.7 INTERNAL ACTIONS FOR STRESS CHECK POINT AT TOP OF COLUMN

The program provides stress checks at many points on the frame. These points are numbered from the lower left corner, moving clockwise around the frame. The location of stress check points, plate composition, and section properties are reported. That part of the Section Properties Report for the left column is shown below: A. Program Output: Section Properties Report

=============================================================================== Calc_Manual Section Properties 9/ 4/00 6:32pm =============================================================================== IM SN ID X Y WD WT FW TO TI AREA IXX SXO SXI RX RY RTO RTI cm cm mm mm mm mm mm cm2 cm4 cm3 cm3 mm mm mm mm -- -- -- ---- ---- ---- ---- --- ---- ---- ---- ---- --- --- --- --- --- --- 1 1 1 42 0 400 3.0 164 6.0 6.0 32 9711 471 471 213 37 43 42 1 1 2 44 144 440 3.0 164 6.0 6.0 33 11917 527 527 213 37 43 42 1 1 3 45 289 480 3.0 164 6.0 6.0 34 14386 585 585 213 36 42 42 1 1 4 47 433 520 3.0 164 6.0 6.0 35 17128 644 644 213 35 42 42 1 1 5 49 578 560 3.0 164 6.0 6.0 36 20153 705 705 213 35 42 42 1 1 6 51 722 600 3.0 164 6.0 6.0 38 23469 767 767 213 34 41 41

The internal actions for the top of the first column (ID=6) are given below. The hand calculations match the P, V, and M shown in this report.


=============================================================================== Calc_Manual Actions & Stress Report 9/ 4/00 6:32pm =============================================================================== | ACTIONS(kN,kN-)|CALC. STRESS(MN/m2)|ALLOW STRESS(MN/m2)| UNITY CHECKS Sn Id | Axl Shr Mom | Axl Shr B-o B-i| Axl Shr B-o B-i| Shr O-f I-f | P V M | Fa Fv Fbo Fbi| Fa Fv Fbo Fbi| Ucv Uco Uci -- -- ---- ---- ------ ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- LOAD COMBINATION :28 DL 1 6 9.0 -1.7 12.1 2 1 16 -16 137 14 207 164 0.07 0.05 0.11 LOAD COMBINATION :29 LL 1 6 31.2 -6.0 43.1 8 3 56 -56 137 14 207 164 0.23 0.19 0.39 LOAD COMBINATION :30 WL1 1 6 -49.6 11.5 -123.4 -13 6 -161 161 276 19 218 276 0.33 0.74 0.63

X0 = 420 mm , X1 = 510 mm , Y1 = 7220 mm Slope of C.G. line = (510 - 420) mm in 7220 mm = 1.25 : 100 B. Sign Convention For Internal Actions

C. Dead Load [ ] = program output Fy = Reaction - Column Wt = 10.7 - 198 · 9.81 / 1000 = 8.8 kN [9.0] Fx = Reaction = 1.8 kN [1.7]


M = 1.8 · 7.22 - 10.7 · (0.51 - 0.42) = 12.0 kN [12.0] D. Live Load Fy = Reaction = 31.1 kN [31.2] Fx = Reaction = 6.4 kN M = 6.4 · 7.22 - 31.1 · (0.51 - 0.42) = 43.4 kN-m [43.1]

Resolve X and Y forces to be parallel and normal to the C.G. line for the member. Shear = 6.4 + 31.1 · 1.25 / 100 = 6.0 kN [6.0]

E. Wind_1 From Left Fy = Reaction = -49.5 kN [-49.6] Fx = Reaction - Wind Load = 23.4 - 1.55 · 7.22 = 12.2 kN M = -23.4 · 7.22 + 49.5 · (0.51 - 0.42) + 1.55 · 7.22² / 2 = 124.1 kN-m [123.4] Shear = -12.2 + 49.5 · 1.25 / 100 = -11.6 kN [11.5]

4.8 STRESS CHECK AT TOP OF COLUMN The design summary report indicates the maximum unity checks for the column are at the

top of the column and the stress check point just below the top of the column. In this section, calculations will be made that check the program output for each of the stress check points. Note the design summary, Section 4.2, indicates a different load condition for each unity check.

A. Program Output: Actions and Stress Reports

=============================================================================== Calc_Manual Actions & Stress Report 9/ 4/00 6:32pm =============================================================================== | ACTIONS(kN,kN-)|CALC. STRESS(MN/m2)|ALLOW STRESS(MN/m2)| UNITY CHECKS Sn Id | Axl Shr Mom | Axl Shr B-o B-i| Axl Shr B-o B-i| Shr O-f I-f | P V M | Fa Fv Fbo Fbi| Fa Fv Fbo Fbi| Ucv Uco Uci -- -- ---- ---- ------ ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- LOAD COMBINATION : 2 DL+WL1 1 6 -40.7 9.8 -111.3 -11 5 -145 145 276 19 218 276 0.28 0.66 0.56 LOAD COMBINATION : 9 DL-LW2 1 6 29.3 23.7 -57.7 8 13 -75 75 182 19 218 276 0.69 0.38 0.21 LOAD COMBINATION :13 DL+CO+LL+WR2/2 1 5 43.8-11.1 72.1 12 7 102 -102 184 22 276 137 0.30 0.27 0.80


This report includes just the three loading conditions that control the design of the column. B. Member Plates

See the Design Summary, Section 4.2, or Section Properties report, Section 4.7, for plate sizes. OUT Flange = 164 x 6 IN Flange = 164 x 6 Web = 600 x 3 (Id = 6), 560 x 3 (Id = 5) C. Shear Check

From Design Summary, the load that controls the shear at the top of column is DL - LW2. = Reactions from dead load and longitudinal wind + longitudinal wind load on

column up to the 7.22 m height. = 23.7 kN Shear Stress = 23.7 / (600 · 3) = 13.1 MN/m² [13]

( ) y

yv

Fth

FF

⋅

⋅⋅= 2

34.54500089.2

(F4-2)

( )23600

34.589.2

45000⋅=vF = 2.09 · 4 / 3 = 2.77 ksi = 2.77 / 0.145 = 19.1 MN/m² [19]

Unity Check = 13.1 / 19 = 0.69 [0.69]


D. Member Unbraced Length See the rigid frame cross section where the outside girt and inside flange brace is at 6000 mm. The vertical distance to stress check point is 7220 mm (Id = 6) and 5780 mm (Id = 5). Therefore: Inside Flange Unbraced Length (Id = 5) = 6000 mm Outside Flange Unbraced Length = 7220 - 6000 = 1220 mm

Major Axis Unbraced Length = 7220 · 1.5 = 10830 mm The 1.5 is the sidewall column unbraced length factor set by the user.

These values are all reported in the unbraced length report as follows. E. Program Output: Unbraced Length Report

=============================================================================== Calc_Manual Stress Check Unbraced Lengths 9/ 4/00 6:32pm =============================================================================== Mem Seg Sec -------------------Cb------------------ Id Id Id Major Loc Minor 1 2 3 4 5 6 7 8 --- --- --- ----- --- ----- ---- ---- ---- ---- ---- ---- ---- ---- 1 1 5 10836 Top 1500 1.13 1.10 1.02 1.04 1.10 1.75 1.70 1.49 Bot 6000 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1 1 6 10836 Top 1224 1.08 1.06 1.09 1.01 1.06 1.33 1.32 1.27 Bot 1224 1.08 1.06 1.09 1.01 1.06 1.33 1.32 1.27

F. Cb For Outside Flange, The Compression Flange Cb = 1.75 + 1.05 · M1 / M2 + 0.3 · (M1 / M2)² For the Outside Flange, on loading 2, M2 = Moment at top of column = 111.3 M1 = Moment at top girt = 97.2 M1 / M2 = 97.2 / 111.3 = - 0.87 Cb = 1.75 - 1.05 · 0.87 + 0.30 · (0.87)² = 1.06 [1.06] See the same value in the unbraced length report. G. Actions For Outside Flange Stress Check


From the Design Summary (4.2), note the DL + WL1 controls. The internal actions for that loading can be calculated from the basic load values given previously. V = -1.8 + 11.6 = 9.8 kN [9.8] N = 8.8 -49.5 = 40.7 kN [40.7] M = 12.0 -124.1 = -112.1 kN-m [-111.3] These values match those in the “Actions and Stress Report” (4.8).

H. Special Program For Stress Check

The member properties and loading can be placed in a special program, W_STRESS, to obtain the controlling equations and unity checks. The values for the outside flange are shown below.

STRESS RATIO FOR WIDE FLANGE MEMBERS INPUT OUTPUT MEMBER Member Size - W-SECT Web Depth (mm) - 600.000 CALC'D ALLOW STRESS Web Thick (mm) - 3.000 ACTION STRESS STRESS RATIO Flange Width (mm) - 164.000 --------- ------ ------ ------ Top Flg Thick (mm) - 6.000 Axial -10.80 275.99 0.04 Bot Flg Thick (mm) - 6.000 D1 Yield Flange(MN/m2) - 345.000 Shear 5.44 19.11 0.28 Yield Web (MN/m2) - 345.000 F4-2 UNBRACED LENGTH Bend-T -145.11 218.29 0.66 Major Axis (mm) - 10860.000 A-B5-3 Minor Axis Top (mm) - 1224.000 Bend-B 145.11 275.99 0.53 Minor Axis Bot (mm) - 1224.000 F1-5 Cb Top - 1.060 Axl+Bnd_T 0.66 Cb Bot - 1.000 H2-1* Wind Adjust - 1.333 Axl+Bnd_B 0.56 ACTION H2-1 Axial (kn) - -40.700 Shear (kN) - 9.800 Axial Qs=1.00 Qa=1.00 Q=1.00 Moment (kN-m) - -111.300 Bend Qs=0.79

The AISC equations controlling the output are listed below each output.

I. Outside Flange Unity Checks

See the Section Properties Report (4.7), at Id point 6 for member section properties. See Actions and Stress Report, (4.8) for stresses for load 2.


a. Calculated Stress fa = Force / Area

=mcm

cmkNMNkN ²100

²381

10007.40

⋅⋅⋅− = -10.7 MN/m² [-11]

fb = M / s

= 3100

1000³76713.111 ⎟

⎠⎞

⎜⎝⎛⋅⋅⋅−−

mcm

kNMN

cmmkN = -145.1 MN/m²[-145]

b. Allowable Axial Stress Tension allowable = 0.60 · Fy (D1)

= 0.60 · 345 · 4 / 3 = 276 MN/m² [276] c. Allowable Bending Stress

1. Check b/t Influence

7.1362

1642

=⋅

=⋅ t

bt

Fy - metric = 345 MN/m² Fy- english = 345 · 0.145 = 50.0 ksi AISC equations are set up for English units. Non compact limit = cy kF95 (TableE.5.1)

( )

( )

elementslender

k

ththk

c

c

∴<=

==

===

1200.8354.05095

354.020005.4

2003600,05.4

46.0

46.0

( ) cys kFtbQ ⋅⋅−= 00309.0293.1 (A-B5-3)

( ) 354.0507.1300309.0293.1 ⋅⋅−=

79.0= (Section H) [0.79]

ysb FQF ⋅= (B5.2.a)


²/0.218345.16334560.079.0 mMN=⋅=⋅⋅= [218]

2. Check Unbraced Length Influence

5.4650

06.110200050

102000,8.35

2.341224

=⋅

=⋅

== b

t

Crl

Since 35.8 < 46.5, unbraced length does not reduce Fb. (F1-6)

d. Unity Check On Outside Flange

0.1≤+bx

bx

t

a

Ff

Ff

(H2-1)

626.0665.0039.0218145

2767.10

=+−=+−

Use bending stress only UC = 0.665 [0.66]

J. Inside Flange Unity Check

a. From the design summary (4.2), the controlling load (13) is DL + CO + LL + WR2/2. From the actions and stress report the actions at Id 5 are:

M = 72.1 kN-m, V = -11.1 kN, N = 43.8 kN b. Calculated Stresses fa = 43.8 kN / 36 cm² = 12.2 MN/m² [12] fb = 72.1 kN-m / 705 cm³ = 102.3 MN/m² [102] c. Check for Slender elements

Flange is the same as outside flange, Qs = 0.79 Qa = 1.0 since web is not uniformly compressed. Q = 1.0 · 0.79 = 0.79

d. Allowable Axial Stress, minor axis unbraced length is the girt spacing.

⎟⎠⎞

rKL major 8.50

21372205.1

=⋅

=

⎟⎠⎞

rKL minor 1.43

8.341500

==


.1205079.0000,2922

14.32

=⋅

⋅=

⋅⋅=

yc FQ

EC π (A-B5-11)

423.01208.50, ==⎟⎠⎞

⎜⎝⎛ RC

rKL

c

4.13682.1

2.248

8423.0423.0

83

35

79.03452

423.01

883

35

21

3

2

3

2

=−

=−⋅+

⋅⋅⎥⎦

⎤⎢⎣

⎡−

=−⋅+

⋅⎥⎦

⎤⎢⎣

⎡−

=RR

FRQF

y

a

²/8.181344.136 mMN=⋅= [184]

e. Allowable Bending Stress Based on b/t of flange, the stress is limited to 218.29, see Section H.

Check Fb based on unbraced length. Cb = 1.75, see Unbraced Length Report, (4.8), for load 13 bottom flange.

2.1415.426000 ==trl

2.1419.10650

12.1000,510<=

∗ Therefore,

( ) yt

bb F

rC

F ⋅≤⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅= 60.0

000,1702

l (F1-6)

²/13734145.09.149.14

2.14175.1170000

2 mMNksi =⋅==⎥⎦⎤

⎢⎣⎡ ⋅

= [137.]

f. Unity Check on Inside Flange

0.11 1

≤

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

⋅+

be

a

bm

a

a

fFf

fCFf

(H1-1)

( )²/396

6.21272205.123

145.0000,2914.312/23

122

2

2

21 mMN

rKEF

bbe =

⎟⎠⎞

⎜⎝⎛ ⋅⋅

⋅⋅=

⋅⋅⋅

=l

π


Cm= 0.85

718.0653.0065.0137

396121

10285.018412

=+=⋅⎟⎠⎞

⎜⎝⎛ −

⋅+

802.0745.0058.0137102

3456.012

60.0=+=+

⋅=+

⋅ bx

bx

y

a

Ff

Ff

[0.80]

4.9 CHECK INTERIOR COLUMN A. Calculations

- Selected member is 3019656, from the DS_WFRM file, the section properties are: Area = 385 cm², Depth = 300 mm, ry = 44.2 mm - Unbraced Length, floor to underside of rafter mm7866144.6602105tan150008000 =−−−°⋅+=

- 1782.44

7866==

rKL

- 9.106345

145.0000,29214.3214.3 =⋅

⋅=⋅

⋅=y

c FEC

( )2

2

2312

rklEFa

⋅⋅Π⋅

= (E2-2)

- ( )

²/5.3217823

145.0000,2914.3122

2

mMNFa =⋅⋅⋅

= [32]

- ²/1.281000

100²5.38

108 2

mMNkN

MNm

cmcmkNareaLoadfa =⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅⎟

⎠⎞

⎜⎝⎛⋅== [28]

- Unity check = 28 / 32.5 = 0.862 [0.86]

B. Program Output: Interior Column Design Report


=============================================================================== Calc_Manual Interior Column Design 9/ 5/00 7:48am =============================================================================== Actions Axial_Stress Bend_Stress Col Col Col Load Axl Mom Calc. Allow Calc. Allow Unity Id Loc. Size Id kN kN-m MN/m2 MN/m2 MN/m2 MN/m2 Check --- ----- -------- ---- ---- ----- ----- ----- ----- ----- ----- 1 15000 3019656 1 108.0 0.0 28 32 0 141 0.86 2 -61.1 0.0 -16 188 0 188 0.08 3 -61.1 0.0 -16 188 0 188 0.08 4 -24.2 0.0 -6 188 0 188 0.03 5 -24.2 0.0 -6 188 0 188 0.03 6 -56.6 0.0 -15 188 0 188 0.08 7 -56.5 0.0 -15 188 0 188 0.08 8 -56.6 0.0 -15 188 0 188 0.08 9 -56.5 0.0 -15 188 0 188 0.08 10 67.2 0.0 17 43 -0 67 0.40 11 67.2 0.0 17 43 -0 67 0.40 12 85.7 0.0 22 43 -0 67 0.51 13 85.7 0.0 22 43 -0 67 0.51 14 -24.7 0.0 -6 188 0 188 0.03 15 -24.7 0.0 -6 188 0 188 0.03 16 14.6 0.0 4 43 -0 67 0.09 17 14.6 0.0 4 43 -0 67 0.09 18 41.2 0.0 11 43 -0 67 0.25 19 41.2 0.0 11 43 -0 67 0.25 20 41.2 0.0 11 43 -0 67 0.25 21 41.2 0.0 11 43 0 188 0.25 22 16.7 0.0 4 43 -0 67 0.10 23 16.7 0.0 4 43 -0 67 0.10 24 16.7 0.0 4 43 0 188 0.10 25 16.7 0.0 4 43 0 188 0.10 26 58.0 0.0 15 32 -0 50 0.46 27 58.0 0.0 15 32 -0 50 0.46

4.10 CHECK NUMBER AND DIAMETER OF ANCHOR BOLTS A. Calculations

- Anchor bolts are selected on the basis of the allowable stresses in Table J3.3. - Maximum reactions are taken from the rigid frame reaction report. - For the left sidewall column the maximum uplift is 86.8. Bolts are compared on the

basis of no stress increase so the load appears as 86.8 * 0.75 = 65.1 kN. - Similarly, the maximum shear is from the diagonal bracing and the frame reaction: 1.3575.0²8.4²3.9 =⋅+ - Allowable shear on 2 3/4" A307 bolts Allowable shear stress = 10 ksi/0.145 = 69 MN/m²


= ( ) 414.3100020692 2 ⋅⋅⋅ = 0.043 MN = 43.0 kN > 35.1 Okay - Allowable tension

Stress = 20 / 0.145 = 138 MN/m² Force = ( ) 1000410002014.31382 2⋅⋅⋅ = 86.6 kN > 65.1 Okay

B. Program Output: Base Plate and Anchor Bolt Design

=============================================================================== Calc_Manual Base Plate and Anchor Bolt Design 9/ 5/00 7:48am =============================================================================== Bolt Type = A307 Weak Column_Base Max_Reactions(kN) Axis ---Plate_Size(mm)--- ---Bolts(mm)--- Loc. Type Comp Tens Shear Tens Width Length Thick Row Diam Gage ----- ---- ----- ----- ----- ----- ----- ------ ----- --------- ---- Left P 47.0 -65.1 -35.1 0.0 164 460.0 12.0 2 20.0 100 Right P 47.0 -43.6 19.5 0.0 164 460.0 12.0 2 20.0 100 IC-1 P 108.0 -61.3 0.0 0.0 196 340.0 12.0 2 20.0 100

4.11 CHECK BASE PLATE THICKNESS

a. The base plate thickness must satisfy these requirements: - Thicknesses available in file: 12, 14, 16, 20, 22 - Thickness required for compression load, Pg. 3-107, AISC. - Thickness required for uplift, Page 15 of AISC publication "Steel Design Guide

Series 1, Column Base Plates". b. Thickness based on compression force. - Maximum downward load = 47 kN - Concrete bearing stress = 47 / 0.164 / 0.46 = 623 kN/m² - Allowable bearing stress = 7241 kN/m², unless set by design parameter BEP32. - Since 623 is < 7241, use minimum base plate size, 164 x 460. - From Pg. 3-107 of AISC,

y

pp F

fnt ⋅⋅⋅= '2 λ

4

' fbdn

⋅=


( ) 0.14

2 ≤⋅+

⋅⋅⋅=

pf

fp

Fbd

bdfq

[ ]

0.1112

≤−−⋅

=q

qλ

where: fp = concrete bearing stress d = column depth bf = column flange width Fp = allowable bearing pressure

70.24.254

460164' =⋅⋅

=n

( )

0666.072414601644601646234

2 =⋅+⋅⋅⋅

=q

[ ] 263.00666.00666.0112 =−−⋅=λ

mmint p 54.14.250608.0345623.070.2263.02 =⋅=⋅⋅⋅=

c. Thickness based on column uplift.

fy

p bFgPt

⋅⋅⋅⋅

=2

2 when fb⋅2 < d 1642 ⋅ = 232 < 460 Okay

P = uplift force = 65.1 kN = 14.6 kip g = bolt gage = 100 mm = 3.94 in d = plate length = 460 mm = 18.1 in bf = flange width = 164 mm = 6.46 in Fy = 345 MN/m² = 50 kip/in²

mmusemmt p 120.9"355.05046.62

94.36.142==

⋅⋅⋅⋅

=

- See Section 4.11 for base plate size.

4.12 BOLTED END PLATE THICKNESS


A. Calculations a. Program Selected Plate

h = 612 mm = 24.1" g = 100 mm = 3.94" bf = 196 mm = 7.72" pf = 59 mm = 2.32" pt = 65 mm = 2.56" tw = 3 mm = 0.118" End plate is 196 mm x 12mm = 7.72" x 0.47" Flange = 164 mm x 6 mm = 6.46" x 0.236" Moment with tension on top = 66 kN-m = 48.6 ft-kip Bolts = A325, plate yield = 345MN/m² = 50 ksi b. Design criteria is from a research report "Unification Of Flush End-Plate Design

Procedures" by D. M. Hendrick and others, March 1985, Report No. FSEL/MBMA 85-01, Civil Engineering Department University of Oklahoma, See the Design Example on page 60.

Step 1: Determine Mu and required plate thickness

60.0momentworkingM u =

The 57 ft-k moment is from a loading with wind that has been multiplied

by 0.75 to account for the stress increase permitted with wind.

75.294.372.75.05.0

8160.0/6.48

=⋅⋅=⋅⋅=

−==

gbs

kftM

f

u

( ) ( )

21

2112 ⎪

⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡⋅++⎟

⎟⎠

⎞⎜⎜⎝

⎛+⋅⋅−

=

gsp

spb

ph

FMt

ff

ft

yup

( ) ( )

21

94.3275.232.2

75.21

32.21

272.756.21.24

501281

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎥⎦

⎤⎢⎣

⎡⋅++⎟

⎠⎞

⎜⎝⎛ +⋅⋅−

⋅=


platexTry "47.0"72.7"40.07.1214.19 2

1

=⎭⎬⎫

⎩⎨⎧=

Step 2: Compute the flange force, Ff

( ) ( )k

thMF fuf

7.40

236.01.24120.81

=

−⋅=−=

Step 3: Find the thick plate limit, t1

( )yfff FbFpt ⋅⋅⋅= 21.41

( ) 0:""015.15072.77.4032.221.4 21 =>=⋅⋅⋅= QTherefore

Step 4: Find the thin plate limit, t11 "63.016 == mmdassume b

( )

( ) "17.30625.063.0272.7

0625.021

=+−=

+−= bf dbW

ksiboltofFF yyb 88==

[ ]

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅⋅

⋅⋅Π−⋅⋅=

1

3

11

8.02

85.0

162)(

Wb

F

FdpFapproxt

fy

ybbff

[ ]

9.2902.180

17.38.0272.785.050

168863.032.27.402 3

=⎟⎠⎞

⎜⎝⎛ ⋅+⋅⋅

⋅⋅Π−⋅⋅=

= 0.787"

Check the shear limit of end plate

Okay

FtWF yf

,7.40144350787.017.32

32 111

>=⋅⋅⋅

⋅⋅⋅<

use the exact equation


( )

2

111

21

2

11

2

3

11

233

2

162

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅−⋅+⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅−⋅

⋅⋅Π−⋅⋅=

tWF

FWbt

FF

b

FdpFt

fy

f

fy

f

ybbff

( )

3.1567.1872.180

787.017.327.4035017.3

72.7787.07.40350

272.7

168863.014.332.27.4022

22

2

3

+=

⎟⎠⎞

⎜⎝⎛

⋅⋅⋅−⋅+⎟

⎠⎞

⎜⎝⎛

⋅⋅−⋅

⋅⋅−⋅⋅=

= 0.727 which is near the approximate 0.787 since t11 > 0.5 · tp, Q = Qmax Step 5: Determine prying force

( )f

ybbfypit p

FdWbFtF

⋅

⋅⋅Π+⋅+⋅⋅⋅=

4880.0285.0 312

lim

( )

32.2488863.017.380.0272.785.05047.0 32

⋅

⋅⋅Π+⋅+⋅⋅⋅=

= 7.85 k

kuseofFthus

kFf

85.7,4.20,85.7min

4.2027.402max

1 =

==

( )

( ) 44.1085.063.047.0682.3

085.0682.3

3

3

=−⋅=

−⋅= bp dta

2

1

12

21

34 ⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅−⋅

⋅

⋅==

py

p

tWFF

atW

forcepryingQ


k98.5

47.017.385.7350

44.1447.017.3 2

22

=

⎟⎠⎞

⎜⎝⎛

⋅⋅−⋅

⋅⋅

=

Step 6: Select bolt diameter

mmused

kforceBolt

b 16"63.0"617.044

3.262

3.2698.52

7.40

=∴=⋅Π⋅

=

=+=

B. Program Output: Bolted End Plate Design

=============================================================================== Calc_Manual Bolted-End-Plate Design 9/ 6/00 8:54am =============================================================================== Bolt Type = Gr8.8 Splice Member -SPLICE(mm)-- Tens Load(kN,kN-m) ------Bolt(mm)------- Id Typ Loc. Width Thick Loc. Id Shr Mom Row Diam Space Gage ------ ------ ----- ----- ---- -- --- ---- --- ----- ----- ----- 1 HFF 1- 2 164 12.0 Top: 13 -8 66 1 16.0 80.0 100 Bot: 2 8 83 2 16.0 80.0 100 2 -FF 2- 3 164 10.0 Top: 1 -34 22 1 12.0 80.0 100 Bot: 9 10 22 1 12.0 80.0 100 3 -FF 4- 5 164 10.0 Top: 1 34 22 1 12.0 80.0 100 Bot: 6 -10 22 1 12.0 80.0 100 4 HFF 5- 6 164 12.0 Top: 12 -8 66 1 16.0 80.0 100 Bot: 3 8 83 2 16.0 80.0 100 WELDS: ------ ------Top_Flange----- ----Bottom_Flange---- ---------Web--------- Splice Shear(kN/mm) Shear(kN/mm) Shear(kN/mm) Id Side Size Typ Calc Allow Size Typ Calc Allow Size Typ Calc Allow -- ---- ----- --- ----- ----- ----- --- ----- ----- ----- --- ----- ----- 1 L 6.0 F1 0.515 0.600 8.0 F1 0.653 0.800 3.0 F1 0.014 0.300 1 R 5.0 F1 0.447 0.500 8.0 F1 0.653 0.800 3.0 F1 0.014 0.300 2 L 3.0 F1 0.181 0.300 3.0 F1 0.218 0.300 3.0 F1 0.067 0.300 2 R 3.0 F1 0.189 0.300 3.0 F1 0.194 0.300 3.0 F1 0.067 0.300 3 L 3.0 F1 0.189 0.300 3.0 F1 0.194 0.300 3.0 F1 0.067 0.300 3 R 3.0 F1 0.182 0.300 3.0 F1 0.218 0.300 3.0 F1 0.067 0.300 4 L 6.0 F1 0.515 0.600 8.0 F1 0.653 0.800 3.0 F1 0.014 0.300 4 R 5.0 F1 0.447 0.500 8.0 F1 0.653 0.800 3.0 F1 0.014 0.300


4.13 BOLTED END PLATE: FLANGE TO END PLATE WELD - Weld is to carry the force in the flange - Flange force is calculated from flange stress and flange area. - Consider the outside flange in the column to rafter splice.

- Flange stress = M / S = 3100

1000³76766

⎟⎠⎞

⎜⎝⎛⋅⋅

−m

cmkN

MNcm

mkN = 86.0 MN/m²

- Flange force = 86.0 · 0.164 m · 0.006 m · 1000 = 84.6 kN - Weld strength required = 84.6 / 164 = 0.516 kN/mm [0.515] - From DS_WELD file, weld capacities are: 5 mm = 0.50, 6 mm = 0.60, use 6 mm weld - See Section 4.12 for the bolted end plate design report which includes the welding

report. 4.14 STIFFENER AT COLUMN TO RAFTER SPLICE A. Calculations

a. Layout of Connection A stiffener is required if either

the tension or compression exceeds the capacity of the web.

tendplate = 12 mm = 0.47" tweb = 3 mm = 0.118" Mc = 66 kN-m = 48.6 ft-kip

Mt = 83 kN-m = 61.2 ft-kip Both moments include wind

load. b. Check for Tension Force Use a stiffener if the flange thickness, in this case bolted end plate thickness, is

less than

yc

bf

FP

⋅40.0 (K1-1)

where: 4/3 · flange force when loading includes wind =bfP


column yield stress = 345 MN/m² = 50 ksi =ycF Flange force = (bending stress + axial stress) x area

kN1231000006.0164.01038

4.43767

10008.87=⋅⋅⋅⎟

⎠⎞

⎜⎝⎛ ⋅+

⋅=

kipkNPbf 8.3616412334

==⋅= [165]

mmtep 75.8"342.050

8.364.0 ==⋅=

since end plate thickness is > 8.8 mm, stiffener is not required for tension. c. Check for Compression Force

A pair of stiffeners are required opposite the compression flange when the column web depth is greater than:

bf

ycwcc P

Ftd

⋅⋅<

34100 (K1-8)

kNkipPbf 5.11245.43.2583

668.31=⋅=

⋅= [123.6]

mmdc 222"75.83.25

50197.04100 3

==⋅⋅

<

Column web depth is 600, > 48, use stiffener.

d. Size the Stiffeners - Available stiffeners come from the DS_RFPLT file. - Plate width is one half flange width, 164/2 = 82 - The first available stiffener is 6 mm x 70 mm. - Criteria for sizing the stiffener is in K1.8. - .7062 stiffenersmmbyTry − - 22 14657062525 mmArea =⋅⋅+⋅=


- ( ) 43 312,524,11265270 mmI =⋅+⋅= - mmAIr 2.321465312,524,1 ===

- 9.132.3260075.0 =⋅=r

KL

- ²./3.1999.28 mMNksiFa ==

- kNMN

kNmm

mmmm

MNPallow 29210001000

²1465²

3.1992

=⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅= [292]

- Unity check on stiffeners = 123 / 213 = 0.58 [0.56]

B. Program Output: Stiffener Report

=============================================================================== Calc_Manual Stiffener Report 9/ 6/00 1:24pm =============================================================================== Stiff -Plate_Size- Web Load -----Force(kN)---- Location No. Width Thick Length Id Calc Allow UC ---------- --- ----- ----- ------ ---- ----- ----- ---- Left Col 1 70.0 6.0 600.0 13 165.3 292.3 0.57 Right Col 1 70.0 6.0 600.0 12 165.3 292.3 0.57 Int Col 1 2 70.0 6.0 655.2 1 52.9 291.0 0.18

4.15 STIFFENER ABOVE INTERIOR COLUMN - Rafter web: 5 x 660 mm - Rafter flange : 164 x 8 mm - Column compression force = 106 kN - Check web yielding:

( ) yw

FkNt

R⋅≤

⋅+⋅66.0

5 (K1-2)

where: R = reaction = 106 kN tw = web thickness = 5 mm = 0.197" N = length of bearing, 300 mm = cap plate length k = tflg + 5 mm = 8 + 5 = 13 mm


( ) ( )

OkaymMNmMNm

mmkN

MNmm

kN

kNtR

w

∴=⋅<=

⎟⎠⎞

⎜⎝⎛⋅⋅=

⋅+⋅=

⋅+⋅

²/22834566.0²/56

10001000²

056.0

1353125106

52

- Check web crippling, use web stiffeners when R exceeds:

fw

yw

f

ww t

tF

tt

dNt ⋅⋅

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎠⎞

⎜⎝⎛⋅+⋅⋅

5.1

2 315.67 (K1-4)

where: d = member depth tf = flange thickness

5

85085

66031231197.05.67

5.12 ⋅

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛⋅⋅+⋅⋅

= 39.8 k = 177.2 kN > 106 kN (column reaction) - Stiffeners are not required, however, they are always used to provide stability for the

connection. - Allowable load on the stiffener is calculated the same as that in Section 4.14. - See the stiffener report in Section 4.14.

4.16 INTERIOR COLUMN CONNECTION TO RAFTER UPLIFT (not in program) A. Flange Bending From Tension in Bolts


- Layout Elevation Plan

Enlargement Around Bolt

- Check bending in flange due to bolt force.

mm

weldwebgagea

5.425252100

2 21

=−−=

−−=

mmb 42=

since a = b, one half of bolt force goes to the web and one half to the stiffener. Head flat distance = 1.0625" = 27 mm for 16 mm bolts Distance from head flat to weld = 42 - 27 / 2 = 28.5 mm Bending in plate; M (see enlargement around bolt)

mmkNM

kNforceboltF

FM

−=⋅=

=⋅==

⋅=⋅

8025.2865.5

65.521

42.45

"5.282

21

Plate width for bending = 27 + 2 · 42 = 111, maximum is ½ flange width, 164 / 2 = 82 mm.


Calculate bending stress ²/5.911000

1000³6882

80 2

2 mMNkN

MNm

mmmmmmkN

=⋅⎟⎠⎞

⎜⎝⎛⋅

⋅−

=

B. Total Tension Stress In Flange

- As the rafter lifts up, it also has tension in the lower flange from bending in the rafter. - The 45.2 k uplift force is from loading 3. From the Actions and Stress Report for load 3, stress check point 20, the tension stress in the flange is 84 kN/m². - On a transverse section cut through the flange at the stiffeners, the tension stress caused by the bolts during uplift is added to the tension stress in the flange due to rafter bending. 4/3 · 91.5 + 84.0 = 206 kN/m² - Allow bending stress 3

475.0 ⋅⋅= yF (F2-1) OkaymkN ∴=⋅⋅= ²/34534575.0 3

4

4.17 DESIGN OF INTERIOR COLUMN CAP PLATE A. Calculations a. Plate Thickness For wide flange columns, the cap plate is designed the same as a base plate for uplift.

See Section 4.11. Column size : depth = 300 mm, flange width = 196 Uplift = 45.1 kN = 10.1 k (reduced by 0.75 for permitted stress increase)

fyp bF

gPt⋅⋅⋅⋅

=2

2 when fb⋅2 < d 1962 ⋅ = 277 < 300 Okay

mmt p 8.6"27.0196502

1001.102==

⋅⋅⋅⋅

=

use t = 10 mm, smallest available plate

b. Bolt Diameter Bolt = GR8.8 = A325, try 16 mm diameter Allowable tension stress = 44 ksi = 303 MN/m² Allowable load on 4 16 mm diameter bolts

( )

boltsdiausekN

kNMN

kNmm

MN

.1641.45

5.243100016.0²

3034

4 22

−∴>

=⋅⋅⋅Π⋅=

B. Program Output: Interior Column Cap Plate


=============================================================================== Calc_Manual Interior Column Cap Plate 9/ 5/00 8:46pm =============================================================================== Bolt Type = Gr8.8 Col Cap -Plate(mm)-- ------Load(kN,kN-m)---- ------Bolt(mm)------- Id Type Width Thick Id Axial Shear Moment Row Diam Space Gage --- ---- ----- ----- -- ----- ----- ------ --- ----- ----- ----- 1 P- 196.0 10.0 3 -45.0 0.0 0.0 2 24.0 0.0 120.0

4.18 CHECK SIZE OF FLANGE BRACE A. Calculate Force in Flange Brace

- From flange brace report, the maximum flange brace force is near the peak of the building.

- Layout of flange brace is shown on the erection details. The slope of the flange brace is

633 mm horizontal to about 661 mm vertical. - Maximum compressive force in lower flange at building peak is from the DL + LL +

CL loading

kN

MNkNmm

mMN

areastressforce

1681000164.0008.0²

128=⋅⋅⋅=

⋅=

- The percent of the flange force required for stability to be provided by the flange brace

is set by the user as 2 percent. See rigid frame design parameter 44. - Diagonal force in brace

( ) kN84.4633

66163302.016822

=+

⋅⋅= [4.67]

B. Member Stress Check

a. Member section properties - Select the flange brace from the smallest available in the DS_FLGBR.SIZ file.

Try 50x50x4. - Flange braces are on one side only, hence the full force is carried by one angle in

compression. - Use the angle design procedure on page 3-55 of the AISC Manual. - Angle drawing


Load Applied

- For a 50x50x4 angle ksimMNFy 0.34²/235 ==

mmcmAIr

cmIII

cmrAI

mmYcmImmrcmArea

w

zxw

zz

x

z

4.1994.1897.37.14

7.1482.326.922

82.399.0897.3

8.1326.990.9897.3

4

422

4

2

====

=−⋅=−⋅=

=⋅=⋅=

==

==

b. Check for local buckling

15.120.13

00447.034.1

0.133476,5.12450

=∴>

⋅⋅−=

===

s

ys

Q

FtbQ

tb

(A-B5-1)

Limiting flange bending yy FF ⋅=⋅⋅= 60.06.00.1 c. Calculate allowable axial stress - Allowable axial stress to follow code section (A-B5-11)

- Flange brace length between bolts mm915661633 22 =+=


- zr

KL⎟⎠⎞

⎜⎝⎛ for minor principal axis 4.92

90.9915

==

- wr

KL⎟⎠⎞

⎜⎝⎛ for major principal axis 2.47

4.19915

==

- 7.129340.12900022 22

' =⋅⋅Π⋅

=⋅⋅Π⋅

=y

c FQEC

- a = 71.07.1294.92' ==⎟⎠⎞

⎜⎝⎛

cCr

KL

- 3

2

81

83

35

21

aa

FaQF

y

a

⋅−⋅+

⋅⎥⎦

⎤⎢⎣

⎡−⋅

= (A-B5-11)

- ( ) ²/1.9683.1

8.175

71.08171.0

83

35

235271.010.13

2

mMNFa ==⋅−⋅+

⋅−⋅=

d. Calculate moments in angle

- Mz = ez · P = 3.96 · 4.67 = 18.5 kN-mm ez (to mid thickness) = 3.96 mm - Mw = ew · P = 12.73 · 4.67 = 59.4 kN-mm ew (to mid thickness) = 12.73 mm

e. Calculate stress in angle

- mmBCI

CMf w

w

wwbw 4.35414.1502, ===

⋅=

= ²/3.147.14

4.354.59 mMN=⋅

- mmYBCI

CMf zz

zzbz 8.158.132

25022, =⋅−=⋅−=

⋅=


= ²/65.782.3

8.155.18 mMN=⋅

f. Check combined axial + bending

- ,15.0040.096

897.367.4<==

a

a

Ff

Therefore,

,0.1≤−+b

bz

b

bw

a

a

Ff

Ff

Ff

,0.1195.023560.0

65.73.14040.0 <=⋅+

+ Okay [0.20]

C. Program Output: Flange Brace Report

=============================================================================== Calc_Manual Flange Brace Report 9/ 6/00 6:16am =============================================================================== Flange Brace Yield= 235 MN/m2 Flange Brace Bolt = 12.0 (Gr4.6) Surf No. Id Brace Flange_Braces ---- ----- ------------- 1 1 Loc : 4 Sides: 1 Part : L50X50X4 Force: 2.75 BrcUC: 0.11 ConUC: 0.35 2 6 Loc : 1 3 5 7 9 10 Sides: 1 1 1 1 1 1 Part : L50X50X4 L50X50X4 L50X50X4 L50X50X4 L50X50X4 L50X50X4 Force: 2.00 1.45 2.19 1.14 2.62 4.67 BrcUC: 0.08 0.06 0.09 0.05 0.11 0.20 ConUC: 0.26 0.19 0.28 0.15 0.34 0.60

4.19 CHECK FLANGE BRACE TO PURLIN CONNECTION - 12 mm GR4.6 bolts are used. - Allowable shear load : allowable shear stress = 10 ksi = 69 MN/m²

kN80.741269 2 =⋅Π⋅= (E3.4) - Allowable bearing 22.21 tDCFu ⋅⋅⋅= (E3.3)


mmDwashersforC

FF yu

1200.31

3.1

==

⋅=

, purlinZmmt 1620060.1=

Allowable bearing 22.2161222.22353.1 ⋅⋅⋅⋅= = 7.93 kN - Both 7.80 and 7.93 are > 4.67 Okay - Unity check on connection = 4.67 / 7.80 = 0.60 [0.60]

4.20 WELD OF WEB TO FLANGE A. Calculations

- For each segment the maximum shear between web and flange is calculated from

V Q / I

where: V = shear force on member Q = flange area · distance from C.G. of flange to C.G. of member I = moment of inertia - At column base, load 4, V = 25.7 kN

( )

4

3

9711

8.1991646262400

cmI

cmQ

=

=⋅⋅+=

mmkNcmkNcm

cmkNV /053.0/529.09711

³8.1997.254 ==

⋅= [0.053]

B. Program Output: Web to Flange Weld

=============================================================================== Calc_Manual Weld Report: Web To Flange 9/ 6/00 6:16am =============================================================================== -Weld_Provided- ----Max_Weld_Shear----- One_Side_Of_Web Member Segment Section Load Shear Size Shear Id Id Id Id (kN/mm) (mm) (kN/mm) ------ ------- ------- ------ ------- ----- ------- 1 1 1 4 0.053 3.0 0.400 2 2 7 1 0.043 3.0 0.300


4.21 CHECK WEB AT TOP OF SIDEWALL COLUMN A. Calculations

- The column web plate at the column to rafter connection is subject to the shear due to the rafter connection.

- AISC does not have a clear requirement for this. To activate the following requirement

from "Steel Structures" by Salmon and Johnson, set rigid frame design parameter 36 to a value greater than zero.

bmcolyweb ddF

Mt⋅⋅⋅

=63.2

,0.575.160.060.0²/345

8363.2<=

⋅⋅−⋅

= mmmmmMN

mkN Okay with 5 mm web

B. Program Output: Special Segment Report

=============================================================================== Calc_Manual Special Segment Report 9/ 6/00 6:16am =============================================================================== SEGMENT SIZE AT LEFT COLUMN: ----------------------------- Web Thick= 5.0 ( 5.0) Flange Width= 164.0 ( 164.0) Flange Thick= 6.0 ( 6.0)

4.22 CHECK FLANGE AT TOP OF SIDEWALL COLUMN - Set rigid frame design parameter 37 to have the program check the adequacy of the

flange at the top of the column to carry the force in the adjacent flange on the rafter. - In this case the two flanges are the same size and therefore Okay. - See Special Segment report in Section 4.20.

4.23 CHECK AREA REDUCTION IN TENSION FLANGE (Not in program) A. Calculations

- Where the interior column attaches to the rafter, bolt holes are placed in the rafter bottom flange.

- There are loading conditions where that rafter flange is in tension, hence the flange area reduction caused by the bolt holes needs to be investigated.

- AISC Section B10 provides criteria for determining the effective flange area when holes are placed in tension flanges.


If: 0.5 · Fu · Afn < 0.6 · Fy · Afg where: Afn = net flange area, Afg = gross area, Fu = tensile strength, and Fy = yield strength. Then, the effective flange area, Afe is: Afe = 5 · Fu · Afn / (6 · Fy) - For a 164 x 8 flange with 2 16 mm bolts, Afg = 8 · 164 = 1312 mm² Afn = (164 - 2 · 18) · 8 = 1024 mm² Fu = 1.3 · 345 = 450 MN/m²

Fy = 345 MN/m²

0.50 · Fu · Afn = 0.5 · 450 · 1024 = 230400 0.60 · Fy · Afg = 0.6 · 345 · 1312 = 271584

Since 230 < 271, Afe = (5 · 450 · 1024) / (6 · 345) = 1113 mm² - Ratio of available flange area to total flange area is 1113 / 1312 = 0.848 - From the Actions and Stress Report, the maximum tension stress ratio is 0.28 for design

load 2. - Since the flange is loaded to 0.28 and 0.85 is available, the flange is adequate with the

two bolt holes.

B. Program Output: Influence of Holes in Tension Flange

4.24 CALCULATING THE LIVE LOAD DEFLECTION A. Calculations

- For load cases, DL + LL + CL, the mid span vertical deflection is 22.6 mm. - Rafter frame dead load is (439 + 112) · 9.81 / (7.5 · 15) = 0.049 kN/m² - Ratio of live load to total load


= 0.60 / (0.60 + 0.12 + 0.10 + 0.049) = 0.69 - Live load deflection = 0.69 · 22.6 = 15.6 mm [16.5]

- Vertical deflection ratio 9095.16

15000== [908]

B. Program Output: Deflection Report

=============================================================================== Calc_Manual Design Summary Report 9/ 6/00 6:16am =============================================================================== DEFLECTIONS : (mm) Lateral Defl Vertical Defl Load @ Top Of Col @ Midspan Of Col Id Left Right LT-1 1-RT ---- ---- ----- ----- ----- 1 -0.2 0.1 -22.6 -22.6 2 71.0 71.0 5.4 20.3 Max Live Vertical = -16.5, Span/Deflection = 908 Max Horizontal Drift= 71.0, Eave Height/Drift= 109.

4.25 CALCULATING THE DRIFT RATIO

- The maximum horizontal deflection for the frame is 71.0 mm. - The horizontal deflection is reported at the top of the sidewall column along the rafter

surface. - For this building with 210 mm purlins and 210 mm sidewall offset, the height of the

corner of the column is:

780075015000

2102108000 =⋅+−

- Drift ratio = 9.10971

7800= [109]

The program reports the drift ratio as an integer. See Section 4.24.


5. SIDEWALL DESIGN 5.1 Introduction.......................................................................................................... 5-1 5.2 Analysis Model .................................................................................................... 5-1 5.3 Moment of Inertia at Girt Laps ............................................................................ 5-1 5.4 Detailed Check on Girt 3, Span 2 ........................................................................ 5-2 A. Load, Shear, and Moment Diagrams ....................................................... 5-2 B. Program Output: Girt Design Report....................................................... 5-2 C. Check Reactions....................................................................................... 5-4 D. Check Moments from Area in Shear Diagram ........................................ 5-4 E. Member Stress Checks............................................................................. 5-4 F. Check Girt Deflection .............................................................................. 5-5 5.5 Check Right Door Jamb....................................................................................... 5-6 A. Program Output: Door Jamb/Header Report ........................................... 5-6 B. Load on Door Jamb.................................................................................. 5-7 C. Check Bending in Jamb ........................................................................... 5-7 D. Check Jamb Deflection ............................................................................ 5-7 5.6 Check Left Door Jamb ......................................................................................... 5-7 5.7 Check Door Header.............................................................................................. 5-7 5.8 Check Wall Panels ............................................................................................... 5-8

5. SIDEWALL DESIGN

5.1 INTRODUCTION

The front sidewall will be illustrated with the design calculations. See the drawing on Page 2-10 to view the framing. For ease of reference, portions of the input and output files are included with the calculations. Program output is enclosed in boxes to separate it from the calculations. The sidewall framing consists of wall girts, door jambs, and door headers. The wall girts are supported by the sidewall and endwall columns. The girts are also attached to the door jambs. The door jambs could either support the girt or place a load on the girt depending on the member deflection at the attachment point. Therefore, the girt/jamb analysis needs to consider the member deflection.

5.2 ANALYSIS MODEL

The jambs and girts are considered to be a grid with pin connected members supported by the floor, corner column, rigid frame sidewall column, and eave strut.

5.3 MOMENT OF INERTIA AT GIRT LAPS

- Member connections


- Both members are attached to this support. At the lap point the members are bolted

together. - In the analysis of the members it is necessary to know the moment of inertia over the

full length of the member. - Over the lap, the moment of inertia is calculated from the wall design parameter (wall1)

times the sum of the moment of inertia of the girts on each side of the lap. - See Section 5.5.1 of the Design Manual.

5.4 DETAILED CHECK ON GIRT 3, SPAN 2

A. Load, shear, and moment diagrams This is the third girt up on the above drawing. The program output shear and moment diagrams are shown below.

B. Program Output: Girt Design Report


============================================================================== SAMPLE Girt Design Report 4/06/00 8:15am ============================================================================== ------------------- GIRT # 3 ; SPAN # 2 ------------------- GIRT LAYOUT: Bay Girt Bay Lap Dist(ft) Girt Girt Id Size Width Left Right Location Weight --- -------- ----- ---- ----- -------- ------ 2 8.5Z16 11.13 2.17 12.0000 39.3 3 8.5Z16 25.00 2.17 12.0000 80.4 ------ 119.8 WIND PRESSURE : ---------------- GIRT ANALYSIS: ---------SHEAR(k )-------- --------------MOMENT(f-k )-------------- Bay Left Left Right Right Left Left Mid-Span Right Right Id Sup Lap Lap Sup Sup Lap Mom Loc Lap Sup --- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 2 -0.11 -0.94 -1.15 0.00 2.06 5.56 4.73 6.99 3 1.44 1.24 -0.88 6.99 4.09 -4.18 15.51 0.00 STRESS/DEFLECTION: Span ------SHEAR(k )------ -----MOMENT(f-k )---- Mom+Shr DEFLECTION(in) Id Loc Calc Allow UC Loc Calc Allow UC Loc UC Calc Allow ---- --- ------ ----- ---- --- ------ ----- ---- --- ---- ------ ----- 2 RL -0.94 3.12 0.30 RL 4.73 5.39 0.88 RL 0.61 -0.37 3 LL 1.24 3.12 0.40 MS -4.18 6.59 0.64 LL 0.54 -0.97 2.50 UNBRACE LENGTHS --------------- Bay ------------Minor------------ Id Major LS LL MS RL RS --- ----- ----- ----- ----- ----- ----- 2 11.1 9.0 9.0 9.0 9.0 2.2 3 25.0 2.2 3.9 0.0 0.0 0.0 WIND SUCTION : ---------------- GIRT ANALYSIS: ---------SHEAR(k )-------- --------------MOMENT(f-k )-------------- Bay Left Left Right Right Left Left Mid-Span Right Right Id Sup Lap Lap Sup Sup Lap Mom Loc Lap Sup --- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 2 0.12 1.03 1.26 0.00 -2.26 5.56 -5.18 -7.66 3 -1.58 -1.36 0.97 -7.66 -4.48 4.59 15.51 0.00 STRESS/DEFLECTION: Span ------SHEAR(k )------ -----MOMENT(f-k )---- Mom+Shr DEFLECTION(in) Id Loc Calc Allow UC Loc Calc Allow UC Loc UC Calc Allow ---- --- ------ ----- ---- --- ------ ----- ---- --- ---- ------ ----- 2 RL 1.03 3.12 0.33 RL -5.18 6.59 0.79 RL 0.73 0.40 3 LL -1.36 3.12 0.44 MS 4.59 4.61 1.00 LL 0.65 1.07 2.50 UNBRACE LENGTHS --------------- Bay ------------Minor------------ Id Major LS LL MS RL RS --- ----- ----- ----- ----- ----- ----- 2 11.1 0.0 0.0 0.0 0.0 0.0 3 25.0 0.0 0.0 19.0 19.0 19.0


C. Check Reactions

Wind pressure loading, w = ( ) plf0.932

0.65.47.17 =+

⋅

Load sum = ( ) k36.3'0.25'1.110.93 =+⋅

Reactions = ,36.388.044.115.111.0 k=+++− okay

D. Check Moments from Area in Shear Diagram

( ) 99.62

1.1115.111.0=

⋅+

Positive moment = ( ) ,18.499.6246.92544.1 =−−⋅ okay

E. Member Stress Checks - The program checks each girt at 5 locations along each span: 2 supports, 2 lap points,

and at mid span (point of maximum moment). - At each point checks are made on shear, moment, and moment plus shear. - The results for that location with the highest unity check are reported. - In this example, 3 stress checks will be made, one at a lap, one at the support, and one at

mid span. a. Unity Check at Support with Lap - Moment in one member = 6.99 / 2 = 3.50 ft-k (since both are the same size) - Shear in one member = 1.44 / 2 = 0.72 k - Moment allow is based on an unbraced length of the bottom flange which is equal to

the lap. - Use the C_STRESS program to calculate the allowable values. kShearkftM allowallow 12.3,71.6 =−= - Unity checks Shear = 0.72 / 3.12 = 0.23 Moment = 3.50 / 6.71 = 0.52

Moment + Shear = 0.122

≤⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

aa VV

MM (C3.3.1-1)

= 0.23² + 0.52² = 0.32 [0.33]


b. Unity Check at Lap on 25’ Span - M = -4.09 ft-k, V = 1.24 k - Unbraced length = lap to inflection point = 6.1 - 2.2 = 3.9’ - Cb = 1.75 (moment = 0 at one end) - From C_STRESS program: Mallow = 6.63 ft-k, UC = 4.09 / 6.63 = 0.62 [6.59] Vallow = 3.12 k UC = 1.24 / 3.12 = 0.40 [3.12] M + V = 0.62² + 0.40² = 0.54 [0.54] c. Unity Check at Mid Span - Use wind suction: M = 4.59 ft-k - Unbraced length = span - distance to inflection point = 25. - 6.1 = 18.9’ (see report unbraced length = 19’) - Minimum allowable moment = 0.70 · Mo (C3.1.3) Mo = Mallow with unbraced length = 0 - From C_STRESS program, Mallow = 1.02 Unbraced length = 18.9’ Mallow = 6.71 Unbraced length = 0 Use Mallow = 0.70 · 6.63 = 4.64 ft-k [4.61] UC = 4.59 / 4.61 = 0.996 [1.00]

F. Check Girt Deflection - Girt deflection can be divided into that due to simple span uniform load and that due to

a simple span with a moment at one end. - The simple span deflection is: (Pg. 2-296 in AISC Manual)

Defl = inIE

LW 98.21000295.929500384

172825.9353845 44

=⋅⋅⋅

⋅⋅⋅=

⋅⋅⋅⋅

- Mid span beam deflection due to a moment at one end of a simple span beam is given

as:


in

ftin

ininkftkft

IELMDefl

72.11728/295.92950016

2599.616

3

3

42

22

2

=⋅⋅⋅−

⋅⋅⋅

⋅=

⋅⋅⋅

=

- Combining the deflections = ( ) [1.07] in945.075.072.198.2 =⋅− - The calculated values do not consider the deflection reduction due to the added stiffness

at the support from the girt lap. Calculated values are at mid span, which may not be the location for maximum deflection.

- Allowable deflection = in50.2120

1225=

⋅

5.5 CHECK RIGHT DOOR JAMB A. Program Output: Door Jamb/Header Report

============================================================================== SAMPLE Sidewall Jamb/Header Summary 4/06/00 8:15am ============================================================================== JAMB/HEADER LAYOUT: Bay Member Member Member Member Id Id Size Length Weight --- ------ -------- ------ ------ 2 Jamb-L 8.5c16 23.33 69.1 2 Jamb-R 8.5c16 23.33 69.1 2 Header 8.5c16 12.00 35.5 3 Jamb-L 8.5c16 7.50 22.2 3 Jamb-R 8.5c16 7.50 22.2 STRESS/DEFLECTION: Bay Member Ld ----Shear(k )---- ---Moment(f-k )-- ---Deflect(in)-- Id Id Id Calc Allow UC Calc Allow UC Calc Allow UC --- ------ -- ----- ------ ---- ----- ------ ---- ----- ------ ---- 2 Jamb-L WP 0.66 3.12 0.21 3.53 6.51 0.54 0.58 2.33 0.25 WS -0.72 3.12 0.23 -3.87 7.02 0.55 -0.64 2.33 0.27 Jamb-R WP -1.08 3.12 0.35 -5.69 7.02 0.81 -1.61 2.33 0.69 WS 1.19 3.12 0.38 6.24 6.51 0.96 1.76 2.33 0.76 Header WP -0.07 3.12 0.02 -0.21 7.02 0.03 -0.02 1.20 0.01 WS 0.08 3.12 0.02 0.23 2.81 0.08 0.02 1.20 0.01 3 Jamb-L WP -0.07 3.12 0.02 -0.04 7.02 0.01 0.00 0.75 0.00 WS 0.08 3.12 0.02 0.05 7.02 0.01 0.00 0.75 0.00 Jamb-R WP -0.32 3.12 0.10 -0.93 7.02 0.13 -0.02 0.75 0.03 WS 0.35 3.12 0.11 1.02 7.02 0.15 0.02 0.75 0.03


B. Load on Door Jamb - Jamb load = wjamb · Opening Width / 2 = -19.4 · 12 / 2 = -116.4 plf - If the jamb were not partially supported by the girts, the jamb moment would be: M = 116.4 · (23.3)² / 8 = 7.9 ft-k - The reported moment is 6.24, this means the girts partially support the jamb. C. Check Bending in Jamb - See Design Manual, Section 6.4 - For wind suction, unbraced length = maximum girt spacing - From C_STRESS: 8.5C16, unbraced length = 6.8’ Mallow = 6.52 ft-k [6.51] UC = 6.24 / 6.51 = 0.96 [0.96] D. Check Jamb Deflection - Considering no supports from girts

Defl = inIE

LW 18.275.090.210001.92950038417283.234.1165

3845 44

=⋅=⋅⋅⋅⋅⋅⋅

=⋅⋅

⋅⋅ [1.26]

- Hence, girts do provide some support 5.6 CHECK LEFT DOOR JAMB

- This jamb is 1.5’ from the column. The girts play a major role in its support. The calculated moment is 62 percent of the moment in the other jamb.

5.7 CHECK DOOR HEADER - Load on header = ( ) plf9.1222267.0244.19 =−−⋅− - Moment = kft −=⋅ 23.08129.12 2 [0.23] - Allowable moment for suction is based on an unbraced length equal to the door width - From C_STRESS: Mallow = 2.79 ft-k [2.81] -UC = 0.23 / 2.81 = 0.082 [0.08]


5.8 CHECK WALL PANELS A. Program Output: Wall Panel Report

============================================================================== SAMPLE Wall Panel Report 4/06/00 10:45am ============================================================================== PANEL REACTIONS: (Back Sidwall, Bay= 1) Panel: Type = DR ; Gage = 26.00 ; Yield = 50 MOMENTS & DEFLECTION: ---------Moment(ft-lb/ft)--------- Span Span LD Support Midspan ---Deflect(in)-- Id (ft) Id Calc Allow UC Calc Allow UC Calc Allow UC ---- ----- -- ----- ----- ---- ----- ----- ---- ----- ----- ---- 1 4.00 WP 30.5 174.4 0.17 -26.0 154.8 0.17 -0.04 0.53 0.08 WS -32.8 154.8 0.21 28.0 174.4 0.16 0.05 0.53 0.09 2 3.50 WP 30.5 174.4 0.17 -4.8 154.8 0.03 0.00 0.47 0.00 WS -32.8 154.8 0.21 5.1 174.4 0.03 0.00 0.47 0.00 3 4.50 WP 48.8 174.4 0.28 -16.3 154.8 0.11 -0.02 0.60 0.03 WS -52.5 154.8 0.34 17.5 174.4 0.10 0.02 0.60 0.04 4 6.00 WP 67.8 174.4 0.39 -31.5 154.8 0.20 -0.09 0.80 0.11 WS -72.9 154.8 0.47 33.9 174.4 0.19 0.09 0.80 0.12 5 5.33 WP 67.8 174.4 0.39 -40.9 154.8 0.26 -0.11 0.71 0.15 WS -72.9 154.8 0.47 44.0 174.4 0.25 0.11 0.71 0.16

- The panel spans are the girt spacing for the wall - The panels are checked as a continuous beam over the girt supports - An approximate check on the support moments is W · L² / 10, ftlbftM −=⋅= 0.771064.21 2 [72.9]


6. ROOF DESIGN

I. The first three sections are for the design of a standing seam roof and uses the 1986 - 89 AISI Code.

6.1 Introduction.......................................................................................................... 6-1 6.2 Purlin Design ....................................................................................................... 6-1 A. Program Output: Roof Design Report ..................................................... 6-1 B. Program Output: Selected Purlins............................................................ 6-2 C. Layout of Loads on Purlin ....................................................................... 6-2 D. Calculate Purlin Loads and Reactions ..................................................... 6-2 E. Program Output: Purlin Analysis............................................................. 6-4 F. Purlin Analysis......................................................................................... 6-4 G. Program Output: Purlin Strength and Deflection..................................... 6-5 H. Allowable Shear in Purlin........................................................................ 6-5 I. Allowable Moment in Purlins.................................................................. 6-6 J. Web Crippling at End Support................................................................. 6-6 K. Program Output: Web Crippling, Lap Bolt Shear ................................... 6-7 L. Lap Bolt Shear ......................................................................................... 6-8 M. Purlin Deflection...................................................................................... 6-8 6.3 Check Roof Panels............................................................................................... 6-8 A. Program Output: Roof Panel Data ........................................................... 6-8 B. Loads on Roof Panels .............................................................................. 6-9 C. Moments in Panels................................................................................... 6-9 D. Panel Unity Check ................................................................................... 6-9 E. Panel Deflection....................................................................................... 6-9

II. The next three sections are for the design of a screw down roof and uses the 1996 AISI Code.

6.4 Introduction........................................................................................................ 6-11 6.5 Purlin Design ..................................................................................................... 6-11 A. Program Output: Roof Design Loads .................................................... 6-11 B. Program Output: Selected Purlins.......................................................... 6-12 C. Layout of Loads on Purlin ..................................................................... 6-12 D. Calculate Purlin Loads and Reactions ................................................... 6-12 E. Program Output: Purlin Analysis........................................................... 6-14 F. Purlin Analysis....................................................................................... 6-14 G. Program Output: Purlin Strength and Deflection................................... 6-15 H. Allowable Shear in Purlin...................................................................... 6-15 I. Allowable Moment in Purlins................................................................ 6-16 J. Web Crippling Strength at Interior Support........................................... 6-16 K. Combined Bending and Web Crippling, Interior Support ..................... 6-17

6.5 Continued L. Program Output: Web Crippling, Lap Bolt Shear ................................. 6-18 M. Web Crippling at End Support............................................................... 6-18 N. Lap Bolt Shear ....................................................................................... 6-19 O. Purlin Deflection.................................................................................... 6-20 6.6 Check Roof Panels............................................................................................. 6-20 A. Program Output: Roof Panel Data ......................................................... 6-20 B. Loads on Roof Panels ............................................................................ 6-20 C. Moments in Panels................................................................................. 6-20 D. Panel Unity Check ................................................................................. 6-21 E. Panel Deflection..................................................................................... 6-21

6. ROOF DESIGN

6.1 INTRODUCTION

Based on the entered building data and options set by the designer the program prepares a roof design input file. Then, designs the roof by making the roof design output file. For ease of reference, portions of the input and output files are included with the hand calculations. Program output is separated from the calculations with a box drawn around the program output.

6.2 PURLIN DESIGN

A. Program Output: Roof Design Loads

*(33)BASIC LOADS: * Dead Collat Live Snow Basic Wind_Load_Ratio Friction Edge Seismic * Load Load Load Load Wind Defl Factor Coef Strip Coef 2.0 3.0 20.0 10.0 20.3 .75 1.00 .00 7.500 .0480 *(34)WIND PRESSURE/SUCTION: (psf ) * * Wind Wind Wind * Press Suct Suct_R 7.7 -21.9 .. Purlins 0.0 -33.9 .. Gable Extension 8.1 -30.2 .. Panels 8.7 -6.3 -14.0 .. Bracing *(36)PURLIN DESIGN LOADS: * * Surf No_Des Load Live/ Wind Wind Aux_Load * Id Loads Id Dead Collat Snow Press Suct Id Coef 2 3 1 1.00 1.00 1.00 .00 .00 0 .00 2 1.00 1.00 .00 1.00 .00 0 .00 3 1.00 .00 .00 .00 1.00 0 .00


B. Program Output: Selected Purlins

============================================================================== SAMPLE Purlin Design Report 4/ 4/00 9:48pm ==============================================================================

----------------------------- ROOF PURLIN

DESIGN RUN # 1, SURFACE # 2 (Edge Strip Zone= 7.50)

----------------------------- PURLIN LAYOUT: Bay Span Purlin Span Lap_Dist(ft) No. No. Unit Total Id Id Size (ft) Left Right Space Rows Brace Weight Weight --- ---- -------- ----- ----- ----- ----- ---- ----- ------ ------ 1 8.5 Z13 1.08 5.00 2 0 4.6 9.3 1 2 8.5 Z13 23.92 2.17 5.00 2 2 111.9 223.8 2 3 8.5 Z15 25.00 2.17 2.17 5.00 2 1 97.1 194.2 3 4 8.5 Z12 24.58 2.17 5.00 2 2 134.6 269.1 5 8.5 Z12 0.42 5.00 2 0 2.1 4.2 ------ Total(lb)= 700.6 Purlin DL= 0.93 (psf )

C. Layout of loads on purlin

D. Calculate purlin loads and reactions - Use the edge strip loading where the purlin spacing is 5.00’ - Applied loads are: - Roof dead load, DL = 2.0 psf


- Roof live load, LL = 20.psf - Wind uplift, WL = 1.19 · 21.9 = 26.06 psf - loads in the plane of the purlin web RS = 1, RS1 = 12.042 - Dead load, collateral load

plfSpacingCLRS

plfSpacingDLRS

94.140.53042.12

121

12

96.90.52042.12

121.12

=⋅⋅=⋅⋅=

=⋅⋅=⋅⋅=

- Live load

plf

RSSpacingLL

RS

3.990.520042.12

12

112

112

2

=⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⋅=

- wind load = WL · Spacing = 26.06 · 5.0 = 130.3 plf - DL + CL + LL = 9.96 + 14.94 + 99.3 = 124.2 plf - DL + WS = 9.96 - 130.3 = -120.3 plf - Calculate sum of reactions on purlin DL + CL + LL = 75.0 · 124.2 = 9.31 k DL + WS = 75.0 · 120.3 = -9.02 k - Sum of reactions (sum the shear values from the purlin analysis report) DL + CL + LL = 0.13 + 1.16 + 1.81 + 1.54 + 1.56 + 1.85 + 1.20 + 0.05 = 9.30, Okay

DL + WS = 0.13 + 1.12 + 1.75 + 1.50 + 1.51 + 1.80 + 1.16 + 0.05 = 9.02, Okay


E. Program Output: Purlin Analysis

LOAD COMBINATION # 1 : DL+CO+LL -------------------------------------------------- PURLIN ANALYSIS: --------SHEAR(k )-------- -------MOMENT(f-k )------- Span Left Left Right Right Left Left Mid-Span Right Right Id Sup Lap Lap Sup Sup Lap Mom Loc Lap Sup ---- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 1 0.00 -0.13 0.00 0.00 0.00 0.07 2 1.16 -1.54 -1.81 0.07 -5.35 9.34 4.21 7.84 3 1.54 1.28 -1.29 -1.56 7.84 4.79 -1.75 12.43 4.97 8.06 4 1.85 1.59 -1.20 8.06 4.33 -5.78 14.93 0.01 5 0.05 0.00 0.01 0.00 0.41 0.00

F. Purlin Analysis a. For DL + CL + LL the purlin loading, members, shear diagram and moment

diagram are shown below. The shears and moments are taken from the “Purlin Analysis Report”

b. The purlin analysis depends on the relative moment of inertia (I) of the members. Over the purlin lap the program uses I = C · (I1 + I2) where I1 and I2 are values for the purlins in the adjacent spans. For this example C = 1.0. The value is set as roof design parameter 1.


Other programs for statically indeterminate structures have been used to check the purlin analysis.

c. The designer can use other values for the lap stiffness and it will have some

influence on the internal actions G. Program Output: Purlin Strength and Deflection

LOAD COMBINATION # 1 : DL+CO+LL -------------------------------------------------- STRENGTH/DEFLECTION: Span ------SHEAR(k )------ -----MOMENT(f-k )---- Mom+Shr DEFLECTION(in) Id Loc Calc Allow UC Loc Calc Allow UC Loc UC Calc Allow ---- --- ------ ----- ---- --- ------ ----- ---- --- ---- ------ ----- 1 RS -0.13 7.26 0.02 RS 0.07 8.01 0.01 RS 0.00 0.17 2 RL -1.54 7.26 0.21 MS 5.35 5.54 0.97 RS 0.32 -1.02 1.59 3 RL -1.29 3.19 0.41 RL 4.97 5.68 0.87 RL 0.93 -0.10 1.67 4 LL 1.59 11.35 0.14 MS 5.78 6.27 0.92 LS 0.26 -1.01 1.64 5 LS 0.05 11.35 0.00 LS 0.01 9.77 0.00 LS 0.00 0.06 UNBRACE LENGTHS --------------- Span ------------Minor------------ Id Major LS LL MS RL RS ---- ----- ----- ----- ----- ----- ----- 2 23.9 8.0 8.0 8.0 3.1 2.2 3 25.0 2.2 4.9 5.4 5.1 2.2 4 24.6 2.2 3.1 8.2 8.2 8.2

H. Allowable Shear in Purlin - check shear stress on 8.5Z13 purlin - h = D - 2 · Radius - 2 · t = 8.5 - 2 · 0.312 - 2 · 0.088 = 7.70” - h / t = 7.70 / 0.088 = 87.5 - 3.731.5338.15534.5000,2938.138.1 =⋅=⋅⋅=⋅⋅ yv FKE - For h / t > 1.38 · yv FKE ⋅ (C3.2-3)

htKEV va353.0 ⋅⋅⋅=

26.770.7088.034.52900053.0 3 =⋅⋅⋅= [7.26] I. Allowable Moment in Purlins a. Section 5.5.3 in the Design Manual describes the process used by the program to

determine the load capacity of the purlins.


b. The unbraced length of the compression flange depends on loading and location

of stress checkpoint, as shown below. In the following table, assume the inflection point (IP) is outside of the laps.

Unbraced Length By Location For End Bay

Loading Midspan (2) Lap (1) Support Downward Bridg Ang

Span [8.0] Lap to [3.1’] Lap [2.2’]

Upward Bridg Ang Span [8.0]

Lap to [3.1’] Lap [2.2’]

(1) = the closer of IP and bridging angles (2) = distance between IP’s or from IP to bridging angle. Maximum value is that

given in Section C3.1.3 which for continuous Z purlins is 70% of the fully braced moment capacity.

- the “unbraced length” report is available by entering ‘2’ for the “Purlin

Summary” report on input file line 5. - two rows of bridging angles are used in the first bay - the resulting unbraced lengths are shown in [ ] in the above table. c. Allowable moment from C_STRESS program - using the 8.5Z13 purlin in the first span, the allowable moments are:

Allowable Moment Loading Midspan Lap Support

DL + CL + LL 5.51 8.01 8.01 *DL + WS 7.35 10.9 10.9

* Includes 1/3 increase with wind loading - The 8.01 and 5.51 value matches the program output. J. Web Crippling at End Support - the edge of the purlin bearing is 13 - 6/2 = 10” from the end of the purlin which is <

1.5 · purlin depth, therefore, use equation C3.4-1 for end reaction. - equation [ ] [ ]tNthCCCKtP tha ⋅+⋅⋅−⋅⋅⋅⋅⋅= 01.0133.017943

2 when N/t > 60 replace [1+0.01 · N/t] with [0.70 + 0.015 · N/t] where:


67.1335533

2.68088.06

7.7088.02312.025.8

===

==

=⋅−⋅−=

yFK

tN

h

( ) ( )

62.0088.0312.015.015.150.0,0.115.015.1

0.1909030.070.09030.070.0

779.067.133.033.133.033.1

4

22

3

=⋅−=≥≤−=

=⋅+=⋅+=

=⋅−=⋅−=

tRC

thC

KC

th

[ ]

[ ] [ ] 72.1088.06015.070.0015.070.0

1.150088.070.733.0179

=⋅+=⋅+

=⋅−

tN

61.1

72.11.15062.0779.067.1088.0 2

=⋅⋅⋅⋅⋅=nP

- Reaction, from program, P = 0.13 + 1.16 = 1.29 k - ratio = 1.29 / 1.61 = 0.80 [0.80] K. Program Output: Web Crippling, Lap Bolt Shear

LAP BOLT SHEAR: LAP BOLT SHEAR RATIO Span SHEAR(k ) ( 0.5in A307 ) Id Left Right Left Right ---- ---- ----- ---- ----- 2 0.79 0.40 3 1.02 1.12 0.52 0.57 4 0.74 0.38 WEB CRIPPLING: WEB CRIPPLING RATIO Bearing Width (in) Reqd_Flg_Width End 3 4 5 6 For UC= 1.03 ----- ---- ---- ---- ---- -------------- Left 1.03 0.95 0.88 0.80 3.1 Right 0.67 0.62 0.58 0.55 2.0


L. Lap Bolt Shear - lap bolt shear = moment in lap purlin at support / lap length - moment in lap purlin = support moment · t - purlin / (t - both purlins) ( ) kft −=+⋅= 41.3067.0088.0067.084.7 - shear / bolt : 3.41 / 2.17 / 2 = 0.79 k [0.79] - allowable shear in ½” A307 bolt (E3.3) ksiFv 0.10= kallowShear 96.145.0.10 2 =⋅Π⋅= - shear ratio = calculated / allowable = 0.79 / 1.96 = 0.40 [0.40] 22.222.2 tdFF ubrn ⋅⋅⋅= (E3.3) k15.3088.050.0553.1 =⋅⋅⋅= > 1.96 k, Okay M. Purlin Deflection - purlin deflections are based on the same I that was used for the analysis. - checks with other analysis programs give the same deflection. - mid span deflections will be less when a larger I is used at the lap areas.

6.3 CHECK ROOF PANELS A. Program Output: Roof Panel Data

============================================================================== CALC_MAN Roof Panel Report 4/27/00 4:00pm ============================================================================== ROOF PANEL DATA: Panel: Type = S2 ; Gage = 24.00 ; Yield = 50.0 MOMENTS & DEFLECTIONS: -------- Moment (ft-lb/ft)---------- Surf Purlin Load Support Midspan -- Deflect(in) -- Id Space Id Calc Allow Ratio Calc Allow Ratio Calc Allow Ratio ---- ------ ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 2 5.000 D+L 58.5 64.2 0.91 -42.1 64.2 0.66 -0.01 0.667 0.02 D+WP 27.0 85.6 0.32 -19.4 85.6 0.23 0.00 0.667 0.01 D+WS -75.5 85.6 0.88 54.3 85.6 0.63 0.02 0.667 0.02


B. Loads on Roof Panels - see Section 6.2 A for load on panels. Loads normal to roof panels are: - dead: wn = 2 · 12 / 12.042 = 1.99 psf - collateral: wn = 3 · 12 / 12.042 = 2.99 - live: wn = 20 · (12 / 12.042)2 = 19.86 - wind: wn = -31.7 psf C. Moments in Panels - moments are based on 3 or more equal spans. See Design Manual Section 5.8. - maximum midspan moment coefficient = 0.077 - maximum support moment coefficient = 0.107 - mid span moments - DL + LL : (1.99 + 19.86) · 0.077 · 52 = 42.06 ft-lb/ft [42.1] - DL + WP : (1.99 + 8.1) · 0.077 · 52 = 19.4 ft-lb/ft [19.1] - DL + WS : (-1.99 + 30.2) · 0.077 · 52 = 54.3 ft-lb/ft [54.3] - support moments - DL + LL : 42.06 · 0.107 / 0.077 = 58.4 [58.5] - DL + WP : 19.4 · 0.107 / 0.077 = 27.0 [27.0] - DL + WS : 54.3 · 0.107 / 0.077 = 75.5 [75.5] D. Panel Unity Check U.C. = M-calculated / M-allowable M-allowable is in the DS_PANEL file. U. C. = 58.5 / 64.2 = 0.91 [0.91] E. Panel Deflection - for 3 or more equal spans. The maximum deflection is:

IE

LW⋅

⋅⋅ 40065.0

- for the DL + LL case W = 1.99 + 19.86 = 21.85 plf L = 5’


E = 29,500 ksi I = 0.3559 in4, from DS_PANEL file

Defl = 3

3

2

17281000356.029500

585.210065.04

44

ftin

Klb

inK

ftlb

inft

⋅⋅⋅

⋅⋅

= 0.014 in [0.01]


6.4 INTRODUCTION

Based on the entered building data and options set by the designer the program prepares a roof design input file. Then, designs the roof by making the roof design output file. For ease of reference, portions of the input and output files are included with the hand calculations. Program output is separated from the calculations with a box drawn around the program output.

6.5 PURLIN DESIGN

A. Program Output: Roof Design Loads

*(33)BASIC LOADS: * Dead Collat Live Snow Basic Wind_Load_Ratio Friction Edge Seismic * Load Load Load Load Wind Defl Factor Coef Strip Coef 2.0 3.0 20.0 10.0 20.3 .75 1.00 .00 7.500 .0480 *(34)WIND PRESSURE/SUCTION: (psf ) * * Wind Wind Wind * Press Suct Suct_R 7.7 -21.9 .. Purlins 0.0 -33.9 .. Gable Extension 8.1 -31.7 .. Panels 8.7 -6.3 -14.0 .. Bracing *(36)PURLIN DESIGN LOADS: * * Surf No_Des Load Live/ Wind Wind Aux_Load * Id Loads Id Dead Collat Snow Press Suct Id Coef 2 3 1 1.00 1.00 1.00 .00 .00 0 .00 2 1.00 1.00 .00 1.00 .00 0 .00 3 1.00 .00 .00 .00 1.00 0 .00


B. Program Output: Selected Purlins

============================================================================== SAMPLE Purlin Design Report 4/ 4/00 9:48pm ==============================================================================

----------------------------- ROOF PURLIN

DESIGN RUN # 1, SURFACE # 2 (Edge Strip Zone= 7.50)

----------------------------- PURLIN LAYOUT: Bay Span Purlin Span Lap_Dist(ft) No. No. Unit Total Id Id Size (ft) Left Right Space Rows Brace Weight Weight --- ---- -------- ----- ----- ----- ----- ---- ----- ------ ------ 1 8.5 Z15 1.08 4.90 2 0 3.6 7.2 1 2 8.5 Z15 23.92 3.25 4.90 2 0 89.9 179.8 2 3 8.5 Z16 25.00 3.25 3.25 4.90 2 0 93.2 186.5 3 4 8.5 Z15 24.58 3.25 4.90 2 0 92.1 184.3 5 8.5 Z15 0.42 4.90 2 0 1.4 2.8 ------ Total(lb)= 560.5 Purlin DL= 0.76 (psf )

C. Layout of loads on purlin

D. Calculate purlin loads and reactions - Use the edge strip loading where the purlin spacing is 4.90’


- Applied loads are: - Roof dead load, DL = 2.0 psf - Roof live load, LL = 20.psf - Wind uplift, WL = 1.19 · 21.9 = 26.06 psf - loads in the plane of the purlin web RS = 1, RS1 = 12.042 - Dead load, collateral load

plfSpacingCLRS

plfSpacingDLRS

66.149.43042.12

121

12

77.99.42042.12

121.12

=⋅⋅=⋅⋅=

=⋅⋅=⋅⋅=

- Live load

plf

RSSpacingLL

RS

3.979.420042.12

12

112

112

2

=⋅⋅⎟⎠⎞

⎜⎝⎛=

⋅⋅⋅=

- wind load = WL · Spacing = 26.06 · 4.9 = 127.7 plf - DL + CL + LL = 9.77 + 14.66 + 97.3 = 121.7 plf - DL + WS = 9.77 - 127.7 = -117.9 plf - Calculate sum of reactions on purlin DL + CL + LL = 75.0 · 127.7 = 9.13 k DL + WS = 75.0 · 117.9 = -8.8 k - Sum of reactions (sum the shear values from the purlin analysis report) DL + CL + LL = 0.13 + 1.13 + 1.78 + 1.50 + 1.54 + 1.84 + 1.16 + 0.05 = 9.13, Okay

DL + WS = 0.13 + 1.09 + 1.73 + 1.46 + 1.49 + 1.78 + 1.12 + 0.05 = 8.85, Okay


E. Program Output: Purlin Analysis

LOAD COMBINATION # 1 : DL+CO+LL -------------------------------------------------- PURLIN ANALYSIS: --------SHEAR(k )-------- -------MOMENT(f-k )------- Span Left Left Right Right Left Left Mid-Span Right Right Id Sup Lap Lap Sup Sup Lap Mom Loc Lap Sup ---- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 1 0.00 -0.13 0.00 0.00 0.00 0.07 2 1.13 -1.39 -1.78 0.07 -5.14 9.25 2.78 7.94 3 1.50 1.11 -1.14 -1.54 7.94 3.70 -1.35 12.36 4.02 8.37 4 1.84 1.44 -1.16 8.37 3.05 -5.47 15.09 0.01 5 0.05 0.00 0.01 0.00 0.42 0.00

F. Purlin Analysis a. For DL + CL + LL the purlin loading, members, shear diagram and moment

diagram are shown below. The shears and moments are taken from the “Purlin Analysis Report”

b. The purlin analysis depends on the relative moment of inertia (I) of the members. Over the purlin lap the program uses I = C · (I1 + I2) where I1 and I2 are values for the purlins in the adjacent spans. For this example C = 1.0. The value is set as roof design parameter 1.


Other programs for statically indeterminate structures have been used to check the purlin analysis.

c. The designer can use other values for the lap stiffness and it will have some

influence on the internal actions. For example, in this case if C = 0.50 the moments are shown below:

Moments

Location C = 1 C = 0.5 Percent Change

Mid Span 5.14 5.45 +6.0 Lap 2.78 2.10 -24.5

Support 7.94 7.13 -10.0 G. Program Output: Purlin Strength and Deflection

STRENGTH/DEFLECTION: Span ------SHEAR(k )------ -----MOMENT(f-k )---- Mom+Shr DEFLECTION(in) Id Loc Calc Allow UC Loc Calc Allow UC Loc UC Calc Allow ---- --- ------ ----- ---- --- ------ ----- ---- --- ---- ------ ----- 1 RS -0.13 3.26 0.04 RS 0.07 5.68 0.01 RS 0.00 0.22 2 RL -1.39 3.26 0.43 MS 5.14 5.68 0.90 RS 0.63 -1.26 1.59 3 RL -1.14 2.34 0.49 RL 4.02 4.94 0.81 RL 0.90 0.02 1.67 4 LL 1.44 3.26 0.44 MS 5.47 5.68 0.96 LS 0.69 -1.42 1.64 5 LS 0.05 3.26 0.02 LS 0.01 5.68 0.00 LS 0.00 0.09 UNBRACE LENGTHS --------------- Span ------------Minor------------ Id Major LS LL MS RL RS ---- ----- ----- ----- ----- ----- ----- 2 23.9 18.4 0.0 0.0 2.2 3.3 3 25.0 3.3 4.4 0.0 4.7 3.3 4 24.6 3.3 2.4 0.0 0.0 19.0

H. Allowable Shear in Purlin - check shear stress on 8.5Z15 purlin - h = D - 2 · Radius = 8.5 - 2 · 0.312 = 7.876” - h / t = 7.876 / 0.067 = 117.5 - 4.515.5396.05534.5500,2796.0 96.0 =⋅=⋅=⋅⋅ yv FKE - 1.415 · 53.5 = 75.7 - For h / t > 1.415 · yv FKE ⋅ (C3.2-3)


44.5876.7067.034.529500905.0

905.0

3

3

=⋅⋅⋅=

⋅⋅⋅= htKEV vh

kfactorsafetyVV nallow 26.367.144.5

=== [3.26]

I. Allowable Moment in Purlins a. Section 5.5.3 in the Design Manual describes the process used by the program to

determine the load capacity of the purlins. b. The unbraced length of the compression flange depends on loading and location

of stress checkpoint, as shown below. In the following table, assume the inflection point (IP) is outside of the laps.

Unbraced Length By Location

Loading Midspan Lap Support Downward 0 Lap to (1) [2.2’] Lap [3.25’]

Upward (2) [7.97’] 0 0 (1) = the closer of IP and bridging angles

(2) = distance between IP’s or from IP to bridging angle. Maximum value is that given in Section C3.1.3 which for continuous Z purlins is 70% of the fully braced moment capacity.

- the “unbraced length” report is available by entering ‘2’ for the “Purlin

Summary” report on input file line 5. - two rows of bridging angles are used in the first bay - the resulting unbraced lengths are shown in [ ] in the above table. c. Allowable moment from C_STRESS program - using the 8.5Z15 purlin in the first span, the allowable moments are:

Allowable Moment Loading Midspan Lap Support

DL + CL + LL 5.68 5.68 5.68 *DL + WS 5.50 7.58 7.58

* Includes 1/3 increase with wind loading - The 5.68 value matches the program output. J. Web Crippling Strength at Interior Support - use the 8.5Z15 purlin which has a 6” wide support


- controlling equation: ( )[ ] [ ]tNthCCCCKtP thqn ⋅+⋅⋅−⋅⋅⋅⋅⋅⋅= 007.0174.053821

2 (C3.4-4) when N/t > 60, replace [f(N)] with [0.75+0.011 · N/t] where: N = bearing width = 6.0 in t = thickness = 0.067 in K = 894 · Fy / E = 894 · 55 / 29500 = 1.67 C1 = 1.22 - 0.22 · K = 1.22 - 0.22 · 1.67 = 0.853 C2 =1.06 - 0.06 · R / t = 1.06 - 0.06 · 0.312 / 0.067 = 0.780 Cq = 1.0, U.S. units Cth = 0.70 + 0.30 · (th / 90)² = 0.70 + 0.30 · (90 / 90)² = 1.0 h = 8.5 - 2 · 0.312 = 7.88 [538 - 0.74 · 7.88 / 0.067] = 451. [0.75 + 0.011 · 6. / 0.067] = 1.74

k

Pn

94.374.1.4510.10.178.0853.067.1067.0 2

=⋅⋅⋅⋅⋅⋅⋅=

kfactorsafety

PP n

allow 13.285.194.3 === [2.19]

K. Combined Bending and Web Crippling, Interior Support - check for the first interior support - equation:

67.1,67.1=Ω

Ω≤+

nno PP

MM (C3.5.1-3)

P = that part of the reaction carried by the 15 gage purlin = total reaction · (t-15g) / (t-15g + t-16g) = (1.78 + 1.50) · 0.067 / (0.067 + 0.060) = 1.73 k M = support moment carried by 15g purlin = 7.94 · (0.067 / (0.067 + 0.060)) = 4.18 ft-k


Mno = Mallow · 1.67 = 5.68 · 1.67

175.1439.0736.094.373.1

67.168.518.4

=+=+⋅

Since this is greater than 1.0, web reinforcement is required or, support the purlin

by the web. L. Program Output: Web Crippling, Lap Bolt Shear

LAP BOLT SHEAR: LAP BOLT SHEAR RATIO Span SHEAR(k ) ( 0.5in A307 ) Id Left Right Left Right ---- ---- ----- ---- ----- 2 0.58 0.30 3 0.65 0.68 0.33 0.35 4 0.61 0.31 WEB CRIPPLING: WEB CRIPPLING RATIO Bearing Width (in) Reqd_Flg_Width End 3 4 5 6 For UC= 1.03 ----- ---- ---- ---- ---- -------------- Left 2.12 1.93 1.76 1.62 10.0 Right 2.02 1.83 1.67 1.54 10.0

M. Web Crippling at End Support - the edge of the purlin bearing is 13 - 6/2 = 10” from the end of the purlin which is <

1.5 · purlin depth, therefore, use equation C3.4-1 for end reaction. - equation [ ] [ ]tNthCCCCKtP thqn ⋅+⋅⋅−⋅⋅⋅⋅⋅⋅= 01.0161.033143

2 where:

50.0,45.0067.0312.015.015.150.0,0.115.015.1

779.067.133.033.133.033.1

4

3

usetRC

KC

=⋅−=≥≤−=

=⋅−=⋅−=

[ ]

[ ] [ ] 90.1067.0601.0101.01

3.259067.088.761.0331

=⋅+=⋅+

=⋅−

tN


44.1

90.13.25950.0779.067.1067.0 2

=⋅⋅⋅⋅⋅=nP

778.085.144.1 ==allowP k [0.78] - Reaction, from program, P = 0.13 + 1.13 = 1.26 k - ratio = 1.26 / 0.78 = 1.62 [1.62] Note the Web crippling report (above) has a web crippling ratio of 1.62 for a 6 inch

wide flange on the left endwall. These calculations consider if the bearing edge is greater than 1.5 · member depth from the end of the member.

- From the Code Section C3.4, increase Pn by 1.3 if the following conditions are

present: h / t < 150, h / t = 7.88 / 0.067 = 117.6, okay R / t < 4, 0.312 / 0.067 = 4.65, do not use 1.3 t > 0.060, t = 0.067, okay support member thickness > 3/16”, okay - if the R is < 0.25 then the 1.3 factor applies. However, the load ratio is greater than

1.3. - Therefore, the purlin needs web reinforcement or to be supported by the web. N. Lap Bolt Shear - lap bolt shear = moment in lap purlin at support / lap length - moment in lap purlin = support moment · t - purlin / (t - both purlins) ( ) kft −=+⋅= 75.3067.0060.0060.094.7 - shear / bolt : 3.75 / 3.25 / 2 = 0.58 k [0.58] - allowable shear in ½” A307 bolt

ksiFv 0.104.20.24== (E3.3)

kallowShear 96.145.0.10 2 =⋅Π⋅= - shear ratio = calculated / allowable = 0.58 / 1.96 = 0.296 [0.30] 22.222.2 tdFF ubrn ⋅⋅⋅= (E3.3) k14.2060.050.0553.1 =⋅⋅⋅= > 1.96 k, Okay


O. Purlin Deflection - purlin deflections are based on the same I that was used for the analysis. - checks with other analysis programs give the same deflection. - mid span deflections will be less when a larger I is used at the lap areas.

6.6 CHECK ROOF PANELS A. Program Output: Roof Panel Data

============================================================================== SAMPLE Roof Panel Report 4/ 4/00 9:48pm ============================================================================== ROOF PANEL DATA: Panel: Type = S2 ; Gage = 24.00 ; Yield = 50.0 MOMENTS & DEFLECTIONS: -------- Moment (ft-lb/ft)---------- Surf Purlin Load Support Midspan -- Deflect(in) -- Id Space Id Calc Allow Ratio Calc Allow Ratio Calc Allow Ratio ---- ------ ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- 2 5.000 D+L 58.5 240.2 0.24 -42.1 372.5 0.11 -0.01 0.667 0.02 D+WP 27.0 320.2 0.08 -19.4 496.5 0.04 0.00 0.667 0.01 D+WS -79.5 496.5 0.16 57.2 320.2 0.18 0.02 0.667 0.02

B. Loads on Roof Panels - see Section 6.2 A for load on panels. Loads normal to roof panels are: - dead: wn = 2 · 12 / 12.042 = 1.99 psf - collateral: wn = 3 · 12 / 12.042 = 2.99 - live: wn = 20 · (12 / 12.042)2 = 19.86 - wind: wn = -31.7 psf C. Moments in Panels - moments are based on 3 or more equal spans. See Design Manual Section 5.8. - maximum midspan moment coefficient = 0.077 - maximum support moment coefficient = 0.107 - mid span moments - DL + LL : (1.99 + 19.86) · 0.077 · 52 = 42.06 ft-lb/ft [42.1] - DL + WP : (1.99 + 8.1) · 0.077 · 52 = 19.4 ft-lb/ft [19.1]


- DL + WS : (-1.99 + 31.7) · 0.077 · 52 = 57.2 ft-lb/ft [57.2] - support moments - DL + LL : 42.06 · 0.107 / 0.077 = 58.4 [58.5] - DL + WP : 19.4 · 0.107 / 0.077 = 27.0 [27.0] - DL + WS : 57.2 · 0.107 / 0.077 = 79.5 [79.5] D. Panel Unity Check U.C. = M-calculated / M-allowable M-allowable is in the DS_PANEL file. [0.11] U. C. = 42.06 / 373.5 = 0.11 E. Panel Deflection - for 3 or more equal spans. The maximum deflection is:

IE

LW⋅

⋅⋅ 40065.0

- for the DL + LL case W = 1.99 + 19.86 = 21.85 plf L = 5’ E = 29,500 ksi I = 0.3559 in4, from DS_PANEL file

Defl = 3

3

2

17281000356.029500

585.210065.04

44

ftin

Klb

inK

ftlb

inft

⋅⋅⋅

⋅⋅

= 0.014 in [0.01]


7. ENDWALL DESIGN 7.1 Introduction.......................................................................................................... 7-1 7.2 Loads on Endwalls............................................................................................... 7-1 A. Program Output: Endwall Design Loads ................................................. 7-1 7.3 Column Design .................................................................................................... 7-2 A. Design Loads for Columns and Bracing.................................................. 7-2 B. Program Output: Program Selected Columns and Rafters ...................... 7-3 C. Program Output: Column 3 Stress Report ............................................... 7-4 D. Calculating Column Internal Actions ...................................................... 7-4 E. Stress Check on Columns ........................................................................ 7-5 F. Column Deflection................................................................................... 7-7 G. Program Output: Column Deflections and Reactions.............................. 7-7 H. Column Reactions.................................................................................... 7-7 7.4 Rafter Design ....................................................................................................... 7-7 A. Program Output: Rafter Design Loads .................................................... 7-8 B. Sketch of Design Loads ........................................................................... 7-8 C. Program Output: Rafter 1 Stress Report .................................................. 7-9 D. Calculating Rafter Internal Actions ......................................................... 7-9 E. Stress Check on Rafter........................................................................... 7-10 F. Rafter Deflection.................................................................................... 7-11 7.5 Check Rafter Splice ........................................................................................... 7-11 A. Program Output: Rafter Splice Report................................................... 7-11 B. Check Rafter Splice ............................................................................... 7-11 7.6 Endwall Panel Check ......................................................................................... 7-12

7. ENDWALL DESIGN 7.1 INTRODUCTION

The right endwall will be illustrated with the design calculations. See the drawing on page 2-8 to view the framing. The endwall design program includes: columns, rafters, rafter splices, girts, jambs, headers, bracing, and wall panels. This chapter includes calculations on endwall columns, rafters, rafter splices, and wall panels. Example calculations for girts, jambs and headers are in Chapter 5. Endwall bracing is reported in Chapter 8. For ease of reference, portions of the input and output files are included with the hand calculations. Program output is enclosed in boxes to separate it from the calculations.

7.2 LOADS ON ENDWALLS The endwall design loads are given in the endwall design input file.

A. Program Output: Endwall Design Loads

*(29)BASIC LOADS: * Dead Collat Live Snow Basic Wind_Load_Ratio Seismic * Load Load Load Load Wind Deflect Factor Load 2.0 3.0 16.0 10.0 20.3 .75 1.00 0.00 *(30)WIND PRESSURE/SUCTION: * * Wind Wind * Press Suct 17.7 -19.3 .. Column 17.7 -19.3 .. Girt/Header 17.7 -19.3 .. Jamb 19.9 -24.6 .. Panel *(31)WIND COEFFICIENTS: * Surf Rafter_Wind_1 Rafter_Wind_2 Bracing_Wind Long Surface * Id Left Right Left Right Left Right Press Friction 1 .00 .00 .00 .00 .40 -.59 .00 .00 2 -1.19 -.68 -.83 -.32 -1.19 -.68 -1.19 .00 3 -.68 -1.19 -.32 -.83 -.68 -1.19 -1.19 .00 4 .00 .00 .00 .00 -.59 .40 .00 .00 *(32)COLUMN & BRACING DESIGN LOADS: * * No. Load Rafter_Wind Brace_Wind Column_Wind | Aux_Load *Load Id Dead Collat Live Left Right Left Right Press Suct Seis| Id Coef 6 1 1.00 1.00 1.00 .00 .00 .00 .00 .00 .00 .00 0 .00 2 1.00 .00 .50 .00 .00 1.00 .00 .00 1.00 .00 0 .00 3 1.00 .00 .50 .00 .00 .00 1.00 .00 1.00 .00 0 .00 4 1.00 .00 .00 .00 .00 .00 .00 1.00 .00 .00 0 .00 5 1.00 .00 .00 1.00 .00 .00 .00 .00 1.00 .00 0 .00 6 1.00 .00 .00 .00 1.00 .00 .00 .00 1.00 .00 0 .00


Most of the data on the first three lines came from calculations with the wind code. See Chapter 3.

7.3 COLUMN DESIGN A. Design Loads for Columns and Bracing

The design load combinations are given in line 32 above. The following sketches illustrate each of the design loads.

DESIGN LOAD SKETCH

1

2, 3

4

5, 6 Same as 2,3 only rafter wind-1 replaces bracing wind and the only roof l load is from dead load. No diagonal bracing is considered.


Column design loads were selected to meet the expected loading for the column and to calculate the maximum reactions for the column. The maximum upward reaction comes from loading 1. The maximum uplift reaction for the columns comes from loading 5 and 6, where the loading is just dead load plus wind load on the rafter. The column Live/Snow is the larger of the live load and the snow load. It is common to use full wind and one half live this is used in design loads 2 and 3. Loadings 2 and 3 call for diagonal bracing in the plane of endwall. The diagonal bracing creates axial loads in the columns, which are considered in the design. Design load 4 has wind pressure on the column along with longitudinal wind uplift on the roof.

B. Program Output: Program Selected Columns and Rafters

============================================================================== SAMPLE Column & Rafter Design 4/ 5/00 6:48am ============================================================================== MEMBER SIZES: Mem Mem Mem --- Wide Flange Section -- C-Section Mem Id Loc Type W-Dep W-Thk F-Wid F-Thk Depth Gage Weight ----- ----- ------- ----- ----- ----- ----- ----- ---- ------ Col-1 0.7 W10542 9.5 0.135 5.0 0.250 308.89 Col-2 20.0 W10542 9.5 0.135 5.0 0.250 330.79 Col-3 40.0 W10542 9.5 0.135 5.0 0.250 353.49 Col-4 60.0 W10542 9.5 0.135 5.0 0.250 353.49 Col-5 80.0 W10542 9.5 0.135 5.0 0.250 330.79 Col-6 99.3 W10542 9.5 0.135 5.0 0.250 308.89 Raf-1 W8x10 7.5 0.170 3.9 0.205 221.28 Raf-2 W8x10 7.5 0.170 3.9 0.205 280.45 Raf-3 W8x10 7.5 0.170 3.9 0.205 280.45 Raf-4 W8x10 7.5 0.170 3.9 0.205 221.28 -------- Total = 2989.80

Column 3 is selected for the detailed calculations. The design actions and stress ratio for that column are shown below.


C. Program Output: Column 3 Stress Report

DESIGN ACTIONS/STRESSES: (W/R/U-Section) --- Axial (k ,ksi )----- Shear (k ,ksi )---Moment (f-k ,ksi )- Mem Load Design Calc Allow Design Calc Allow Design Calc Allow Id Id Load Stress Stress Load Stress Stress Load Stress Stress ----- ---- ------ ------ ------ ------ ------ ------ ------ ------ ------ Col-3 1 5.82 1.53 21.54 0.00 0.00 16.01 0.00 0.00 30.87 Col-3 2 -2.75 -0.72 43.99 -5.01 3.91 21.34 32.50 -28.26 41.15 Col-3 3 2.62 0.69 28.71 -5.01 3.91 21.34 32.50 -28.26 41.15 Col-3 4 -4.92 -1.29 43.99 4.59 3.58 21.34 -29.81 -25.92 41.15 Col-3 5 -4.76 -1.25 43.99 -5.01 3.91 21.34 32.50 -28.26 41.15 Col-3 6 -2.53 -0.66 43.99 -5.01 3.91 21.34 32.50 -28.26 41.15 STRESS RATIO: Mem Load Id Id Axial Shear Moment Axl+Mom Shr+Mom ----- ---- ----- ----- ------ ------- ------- Col-3 1 0.07 0.00 0.00 0.07 Col-3 2 0.02 0.18 0.69 0.69 Col-3 3 0.02 0.18 0.69 0.70 Col-3 4 0.03 0.17 0.63 0.63 Col-3 5 0.03 0.18 0.69 0.69 Col-3 6 0.02 0.18 0.69 0.69

D. Calculating Column Internal Actions a. Column length

- The column attaches to the underside of the endwall rafter - Column length is roof height minus deduction for purlin and rafter. - Length of column 3. = 24 + 40 / 12 - (8.5 + 8) / 12 · 12.042 / 12 = 25.96’

b. Shear and moment from wind pressure and suction - Wind pressure = 17.7, Wind suction = 19.3 psf - Column spacing = 20’ - For wind suction :

Shear = 20 · 19.3 · 25.96/2 = 5.01k [5.01] Moment = 20 · 19.3 · (25.96)²/8 = 32.5 ft-k [32.5]

- For wind pressure : Shear = 20 · 17.7 · 25.96/2 = 4.59 k [4.59] Moment = 20 · 17.7 · (25.96)²/8 = 29.8 ft-k [29.8]

c. Axial load - The axial load is the reaction to the rafter plus forces from the diagonal bracing.


- Rafter reaction is based on the continuity of the rafter. - If we assume simple span rafters, then approximate reactions from the roof load are:

Load 1 = DL + CL + LL = (2 + 3 + 16) · 20 · 25/2 = 5.25 k [5.82] Load 2 = DL + LL/2 +BWL = (2 + 16/2 - 20.3 · 1.19 · 0.9) · 20 · 25/2 = -2.94 k [-2.75] Load 3 = DL + LL/2 +BWR = (2 + 16/2 - 20.3 · 0.68) · 20 · 25/2 = -0.95 k Load 4 = DL+ LW = (2 - 20.3 · 1.19) · 20 · 25/2 = -5.54 k [4.92] Load 5 = DL + BWL = (2 - 20.3 · 1.19 · 0.9) · 20 · 25/2 = 4.94 k [-4.76] Load 6 = DL + BWR = (2 - 20.3 · 0.68) · 20 · 25/2 = -2.95 k [-2.53]

- Load 3 also has the vertical load from the “Endwall Diagonal Bracing Report,” the vertical reaction is 3.13 k. When combined with the load from the uplift, Load 3 = (-0.95) + 3.13 = 2.18 k. [2.62]

E. Stress Checks on Columns

a. Column: W10542, A = 3.8 in², Sx = 13.8 in3, rx = 4.27 in, Fy = 55 ksi, ry = 1.17 in, Ix = 69.1 in, rt = 1.33 in. tw = 0.135 in, D = 10.0 in, dw = 9.5 in

b. Load 1, DL + CL + LL M = 0, V = 0, P= 5.82 k KL/r) major = 25.96 · 12 / 4.27 = 73.0 KL/r) minor = 6.0 · 12 / 1.17 = 61.5 From formula (E2-1), fa = 21.54 ksi [21.54] fa = 5.82 / 3.8 = 1.53 ksi [1.53] fa / Fa = 1.53 / 21.54 = 0.071 [0.07]

c. Load 2, DL + LL/2 + BWL M = 32.5 ft-k, V = 5.01 k, P = -2.75 k fa = -2.75 / 3.8 = -0.72 ksi, [-0.72] fv = 5.01 / (0.135 · 9.5) = 3.91 ksi [3.91]


fb = 32.5 · 12 / 13.8 = 28.3 ksi [28.26] fa(tension) = 0.60 · fy (D1) = 0.60 · 55 · 4 / 3 = 44 ksi [43.99] h / t = 9.5 / 0.135 = 70.4

( ) y

yv Fth

FF 34.5

/190

89.2⋅⋅= (F4-2)

ksi33.2134

5534.5

4.70190

89.255

=⋅⋅⋅= [21.34]

( )

yyb

tyb FF

CrF

F ⋅≤⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

⋅⋅

⋅−= 60.0

1000153032

2l

(F1-6)

11.5433.1126 ==⋅= bt Crl

( ) ksiFb 17.413455

115300001.5455

32 2

=⋅⋅⎥⎦

⎤⎢⎣

⎡

⋅⋅

−= [41.15]

Stress ratio, axial = 0.72 / 44. = 0.016 [0.02] Stress ratio, shear = 3.91 / 21.34 = 0.183 [0.18] Stress ratio, bending = 28.3 / 41.17 = 0.687 [0.69] Axial + bending

0.1≤+b

b

a

a

Ff

Ff

(H2-1)

On the tension flange

0.02 + 28.26 / 44. = 0.66

On compression flange, the axial tension would reduce the ratio so only the bending ratio on the compression flange is used. UC = 0.69 [0.69]

d. Load 3, DL + LL/2 + BWR

M = 32.5, V = 5.01, P = 2.62 The actions are the same as load 2 only for the compressive axial load. The allowable axial stress is the same as for load 1. The axial + bending check is:


0.160.0

≤+⋅ bx

b

y

a

Ff

Ff

(H1-2)

708.0687.0208.017.413.28

5560.08.362.2

=+=+⋅

[0.70]

F. Column Deflection - Formula:

Defl = windstrength

winddeflectionofratioIE

LW⋅

⋅⋅⋅⋅

3845 4

- Column 3, load 2 w = 20 · 19.3 = 386.0 lb/ft

Defl = 3

3

4

244 172810001.6929000384

96.25.3865ft

inlb

kinin

kft

ftlb

⋅⋅⋅⋅⋅⋅⋅

⋅⋅

in [1.47] 48.175.097.1 =⋅= Allowable deflection in46.3901296.25 =⋅= [3.46]

G. Program Output: Column Deflection and Reactions

MEMBER DEFLECTIONS/COLUMN REACTIONS: Mem Load Deflection (in) Reaction (k ) Id Id Calc Allow Horz(OP) Vert Horz(IP) ----- ---- ------ ------ ------- ----- ------- Col-3 1 0.00 3.46 0.00 5.82 0.00 Col-3 2 1.47 3.46 5.01 -5.88 2.52 Col-3 3 1.47 3.46 5.01 2.62 0.00 Col-3 4 -1.35 3.46 -4.59 -4.92 0.00 Col-3 5 1.47 3.46 5.01 -4.76 0.00 Col-3 6 1.47 3.46 5.01 -2.53 0.00

H. Column Reactions

- Note the vertical reactions reported match the column axial load reported above. - Note the horizontal reaction out of plane match the shear values calculated earlier. - The horizontal in-plane reaction is from the cable bracing in bay 3. See the bracing

report.

7.4 RAFTER DESIGN


A. Program Output: Rafter Design Loads

*(34)RAFTER DESIGN LOADS: * * No. Load Rafter_Wind_1 Rafter_Wind_2 | Aux_Load *Load Id Dead Collat Live Left Right Left Right Seis | Id Coef 5 1 1.00 1.00 1.00 .00 .00 .00 .00 .00 0 .00 2 1.00 .00 .00 1.00 .00 .00 .00 .00 0 .00 3 1.00 .00 .00 .00 1.00 .00 .00 .00 0 .00 4 1.00 .00 .00 .00 .00 1.00 .00 .00 0 .00 5 1.00 .00 .00 .00 .00 .00 1.00 .00 0 .00

B. Sketch of Design Loads

The above loads are on the end bay of the building. The load on the endwall rafter depends on the inset of the endwall rafter as shown below:

R = Reaction on endwall rafter

R aL

LWaLLLW

−⋅=

−⋅⋅

=2

22

R ( ) WW⋅=

−⋅= 71.12

42.02525

2

2


C. Program Output: Rafter 1 Stress Report

DESIGN ACTIONS/STRESSES: (W/R/U-Section) --- Axial (k ,ksi )----- Shear (k ,ksi )---Moment (f-k ,ksi )- Mem Load Design Calc Allow Design Calc Allow Design Calc Allow Id Id Load Stress Stress Load Stress Stress Load Stress Stress ----- ---- ------ ------ ------ ------ ------ ------ ------ ------ ------ Raf-1 1 0.24 0.08 15.92 -3.23 2.54 14.40 11.09 -17.03 23.76 Raf-1 2 0.35 0.12 21.60 3.20 2.51 19.20 -11.12 -17.09 31.67 Raf-1 3 -0.99 -0.33 28.79 1.64 1.29 19.20 -5.56 -8.55 31.67 Raf-1 4 0.42 0.14 21.60 2.10 1.65 19.20 -7.36 -11.31 31.67 Raf-1 5 -0.75 -0.25 28.79 0.55 0.43 19.20 -1.80 -2.77 31.67 STRESS RATIO: Mem Load Id Id Axial Shear Moment Axl+Mom Shr+Mom ----- ---- ----- ----- ------ ------- ------- Raf-1 1 0.01 0.18 0.72 0.72 Raf-1 2 0.01 0.13 0.54 0.54 Raf-1 3 0.01 0.07 0.27 0.27 Raf-1 4 0.01 0.09 0.36 0.36 Raf-1 5 0.01 0.02 0.09 0.09

The endwall rafter is divided into 4 pieces. Rafter 1 starts at the left eave and extends 2 feet beyond the first column.

D. Calculating Rafter Internal Actions a. Calculate loads on rafter R = 12.71 · 2 = 25.4 plf (dead) 3 = 38.1 (collateral) 16 = 203.4 (live) b. Load 1, DL + CL + LL Resolve the load into a vertical load on a horizontal span then you can use the

horizontal span values. - Dead = 25.4 · 12.042 / 12 = 25.5 - Collateral = 38.1 · 12.042 / 12 = 38.2 - Live = 203.4 - Sum = 267.1 plf add rafter dead load of 13.6 plf, sum = 280.7 plf - Moments and shears are from a 5 span continuous beam. Approximate moments

from a 4 span beam are on page 2-309 of the AISI Manual. - Rafter 1: Moments = [11.09] kft −=⋅⋅ 02.12281.020107.0 2

Shear = kft −=⋅⋅ 41.3281.020607.0 [3.23]


c. Load 2, DL + Wind_1L - Wind load = 20.3 · 1.19 = 24.1 - Vertical component on horizontal projection

1.24042.12

1212042.121.24 =⋅⋅

- Load on rafter = 24.1 · 12.71 = 307 plf - DL + WL = 25.2 + 13.6 - 307. = -268.2 plf - Hence, moment and shear are about the same magnitude as for load 1. Checks

okay. d. Axial Load in Rafter - For analysis the endwall rafter is modeled as a beam with a pinned support at the

left end with all other supports being on rollers. - The axial load in the rafter is the sum of the in-plane load components from both the

applied loads and the column reactions. - The axial load reported for each rafter is that load which produces the highest stress

ratio. - The reported axial load on the rafter 1 is just to the right of the interior column.

( ) ( )

k255.0458.051.0203.0

042.12276'20

042.1231.046.6

042.1231.076.2

=−+=

=⋅−−

+−

[0.24]

E. Stress Check on Rafter

a. Load 1: DL + CL + LL - The maximum moment is at the support. The designer considers the lower flange to

be braced by the roof purlins. Hence the unbraced length is equal to a maximum of the purlin spacing of 5. In this case, the purlin is 1.3’ on one side of the column and the inflection point is 2’ from the other side of the column.

- Using the W_STRESS program for:

W8x10, Fy = 36, Major unbraced length = 20’, Minor unbraced length = 2’, and the above actions, then, the stress levels match

the program output.


- The mid span moment is about 70 percent of the support moment and has the same unbraced length, therefore the stress ratio will not be critical.

b. Load 2: DL + Wind_1L - Member unbraced lengths are the same. - Allowable stresses are increased by one-third due to wind. - Since actions are about the same as load case 1, the stress ratios are about 1/3 less

than for case 1.

F. Rafter Deflection - The mid span deflection of the first bay is approximately that of a 4 span beam.

This is given in the AISI Manual, pg. 2-309 as:

Defl = IE

LW⋅

⋅⋅ 40065.0

W = 267.1 · 12 / 12.042 = 266.2 L = 20 · 12.042 / 12 = 20.07

Defl = ( )8.3029000

172807.202.2660065.0 4

⋅⋅⋅⋅

= 0.54 in [0.47]

- Allowable deflection

= 180

120.20 ⋅ = 1.33 in, Okay

7.5 CHECK RAFTER SPLICE A. Program Output: Rafter Splice Report

============================================================================== SAMPLE Rafter Splice Report 4/ 5/00 11:46am ============================================================================== Surf Surf Splice ---Plate--- ---Design_Load--- ----------Bolts----------- Id Loc Id Width Thick Axl Shr Mom Type Diam Rows Space Gage ---- ----- ------ ----- ----- ----- ----- ----- ---- ----- ---- ----- ---- 2 22.1 Mom- 1 6.0 0.375 1.0 2.3 5.8 A325 0.750 1 0.00 3.50 1.0 2.3 -5.8 A325 0.750 1 0.00 3.50

B. Check Rafter Splice a. Check moment at 2.1’ from support


.521.2267.01.287.21.11

21.21.2

2

2supsup

=⋅+⋅−=

⋅+⋅−= WVMM [5.8]

b. Available plates and bolts From DS_RFPLT file, the minimum plate size is 6” x 3/8”, and minimum bolt is ¾”

diameter. c. Connection design process is the same as is used for bolted end plates in the rigid

frame. See Section 4.13. d. Approximate check on bolt capacity - The bolts are set in 2.25” from the outside flange - Calculate the force in the bolts, considering a couple between the bolts and the mid

thickness of the outside flange.

( ) kForce 6.12220.025.2875.7

128.5=

−−⋅

=

- From 4-3 of AISC Manual, the allowable tension in 2 - ¾” A325 bolts is: 2 · 19.4 = 38.8 k > 12.6, Okay - This approximate check does not consider the prying action of the bolts. See

Section 4.13.

7.6 ENDWALL PANEL CHECK - Panels are checked as a continuous beam based on the purlin spacing. - Panels are checked in each bay, that bay with the maximum unity check is reported. - The panel check can be at mid bay or at the location with the longest panel span. This

is set with endwall design parameter 16. - An approximate check on the support moment is 1/10 · W · L². W = 24.6 psf, L = 6.5’ ft

lbftMom −=⋅= 9.103105.66.24 2 [107.2]


8. BRACING DESIGN 8.1 Introduction.......................................................................................................... 8-1 8.2 Panel Shear in Right Endwall .............................................................................. 8-1 8.3 Cable Bracing in Right Endwall .......................................................................... 8-2 A. Program Output: Endwall Diagonal Report............................................. 8-2 B. Calculations on Bracing........................................................................... 8-2 8.4 Forces at Tops of Columns from Longitudinal Wind.......................................... 8-3 8.5 Bracing Forces in Roof Members ........................................................................ 8-4 A. Framing Layout and Forces ..................................................................... 8-4 B. Program Output: Roof Design Report ..................................................... 8-4 C. Program Output: Eave Strut Report......................................................... 8-5 D. Program Output: Roof Diagonal Bracing Report .................................... 8-6 8.6 Allowable Axial Loads in Purlins........................................................................ 8-7 8.7 Calculated Bending in Purlins ............................................................................. 8-7 8.8 Allowable Bending in Purlins.............................................................................. 8-8 8.9 Combined Axial Plus Bending in Purlins ............................................................ 8-9 8.10 Sidewall Diagonal Bracing .................................................................................. 8-9 A. Program Output: Sidewall Diagonal Bracing Report .............................. 8-9 B. Calculations............................................................................................ 8-10 8.11 Design of Wind Bent ......................................................................................... 8-10 A. Program Output: Wind Bent Design Report.......................................... 8-11 B. Calculations............................................................................................ 8-11 8.12 Select Eave Strut Bolts....................................................................................... 8-13 A. Program Output: Strut Bolt Report ........................................................ 8-13 B. Calculations............................................................................................ 8-14 8.13 Select Bolts for Purlins ...................................................................................... 8-15 A. Program Output: Bolt for Purlins........................................................... 8-15 B. Calculations............................................................................................ 8-16 8.14 Seismic Analysis................................................................................................ 8-17 A. Seismic Force......................................................................................... 8-17 B. Check Sidewall Bracing......................................................................... 8-17 C. Seismic Force in Roof Truss.................................................................. 8-17

D. Seismic Force in Roof Cables................................................................ 8-18 E. Seismic Force in Roof Purlins ............................................................... 8-18 F. Seismic Force in Eave Struts ................................................................. 8-19 8.15 Added Wind Load to Illustrate Program Addition of Purlin Struts ................... 8-20 A. General................................................................................................... 8-20 B. Program Output: Braced Purlin Report.................................................. 8-20 C. Program Output: Eave Strut Report....................................................... 8-21 D. Bolts for Eave Struts and Purlin Struts Near The Eave Struts............... 8-21 E. Bolts for Purlins and Purlin Struts ......................................................... 8-22

8. BRACING DESIGN

8.1 INTRODUCTION

Roof and sidewall bracing is used to resist the longitudinal loading on the building. Endwall bracing is used to resist the transverse wind on the endwall. Roof and sidewall bracing are designed in the roof design program while the endwall bracing is designed in the endwall program. Options available to provide bracing include: panel shear, diagonal bracing (rod, cable, angle), wind bents, wind columns, and weak axis bending in the sidewall column. In this example cable bracing is used in one endwall, cable bracing is used in the roof and one sidewall, and a wind bent is used in the other sidewall.

8.2 PANEL SHEAR IN RIGHT ENDWALL

- Prior to designing the diagonal bracing, a check will be made on the endwall panel shear.

- The wind loading is from Section 3.2.C.e and shown below:

3.1520.1259.03.2045.1758.1368.03.2032.3072.2419.13.2022.10371.121.840.03.201

==⋅===⋅===⋅==⋅=⋅=

WWW

plfpsfW

- The load on the endwall depends on the inset of the endwall rafter as shown below.


=R Reaction on endwall rafter

( ) WWR

aLLW

aL

LLWR

⋅=−

⋅=

−⋅=

−

⋅⋅=

71.1242.025

252

22

2

2

- Resulting wind force at eave height

k52.273.028.183.124.1

12505.175

12502.307

2243.152

2242.103

=+−+=

⋅+

⋅−

⋅+

⋅=

- Panel shear along the endwall ft

lbft

lb 2.251002520 == [25.2]

8.3 CABLE BRACING IN RIGHT ENDWALL A. Program Output: Endwall Diagonal Bracing Report

============================================================================== SAMPLE Endwall Diagonal Bracing Summary 4/ 5/00 11:46am ============================================================================== PANEL SHEAR WITH NO BRACING: Panel Shear (Allow) = 100.0 Panel Shear (Calc ) = 25.2 CABLE BRACING REQUIRED: Bay Level ------Diag_Brace----- Diag_Force(k ) Brace_Tension(k ) Id Height Type Size Part Wind Seismic Calc Allow --- ------ ---- ------ -------- ------ ------- ------ ------ 3 25.54 C 0.312 10-105 4.02 0.00 4.02 7.46 COLUMN BASE REACTIONS: Bay Col Max Max Id Id Horz Vert(+/-) --- ---- ---- --------- 3 3 -2.52 3.13 3 4 2.52 3.13

B. Calculations on bracing a. Wind force at eave height (see Section 8.2) = 2.52 k b. Slope of cable - See drawing PS18 for location of cable slots. They are set at 5.0” down from

the top of the column and 7.6” up from the bottom of the column.


- Top slot is at:

( ) '4.2512

5.85.81240'24 =

++−+

- Cable slope is: Rise = 25.4 - 7.6 / 24.8’, Horizontal = 20’ Diagonal = ( ) 86.3120. 24.8 2

122 =+ c. Cable tension = 2.52 · 31.86 / 20 = 4.01 k [4.02] d. Cable selection - From the DS_CABLE file, the smallest available cable is 5/16” diameter with an

allowable tension of 7.46 k. e. Cable reactions Horizontal = 2.52 k [2.52] Vertical = 4.01 · 24.8 / 31.86 = 3.12 k [3.13]

8.4 FORCE AT TOP OF COLUMN FROM LONGITUDINAL WIND

- Framing layout - Force at top of column = wind pressure · column load area. - Column load area = spacing · average height

.273233.27203

.257267.25202

.122242.24

2201

⋅=⋅⋅=

⋅=⋅⋅=

⋅=⋅⋅=−

wwF

wwF

wwF

- At the windward end, w = 8.9 psf

43.2328.22

08.11

===

FF

kF


- At the leeward end, w = -6.4

75.1364.1278.01

===

FFF

8.5 BRACING FORCES IN ROOF MEMBERS A. Framing layout and forces.

Notes on Calculations 1. The forces in span 2 and 4 are equal to the calculated top of column forces shown

above. 2. The shear in a bay is the accumulation of the column forces from the center line

of the building to the eave. 3. Shear in bay times the length ratio is the force in the diagonal member.

B. Program Output: Braced Purlin Report


============================================================================== SAMPLE Braced Purlin Report 4/10/00 4:59pm ============================================================================== Surf Span Brace Purlin Load ----Axial(k )---- --Moment(f-k )-- Axl+Mom Id Id Loc. Size Id Calc Allow UC Calc Allow UC UC ---- ---- ----- -------- ---- ----- ----- ---- ----- ----- ---- ------- 2 2 20.0 8.5 Z15 1 1.83 10.30 0.18 2.54 5.54 0.46 0.61 2 1.83 10.30 0.18 0.44 7.61 0.06 0.23 3 0.91 10.30 0.09 3.77 7.61 0.50 0.41 4 0.15 10.30 0.01 1.05 7.61 0.14 0.11 2 3 20.0 8.5 Z16 1 5.17 9.16 0.57 1.98 6.63 0.30 0.70 2 5.17 9.16 0.57 0.34 6.63 0.05 0.60 3 2.59 9.16 0.28 2.95 6.63 0.44 0.74 4 0.74 9.16 0.08 0.82 6.63 0.12 0.19 2 4 20.0 8.5 Z15 1 1.83 10.30 0.18 2.70 5.34 0.51 0.66 2 1.83 10.30 0.18 0.47 7.61 0.06 0.24 3 0.91 10.30 0.09 4.01 7.61 0.53 0.43 4 0.15 10.30 0.01 1.12 7.61 0.15 0.11 2 2 40.0 8.5 Z15 1 1.95 10.30 0.19 2.54 5.54 0.46 0.62 2 1.95 10.30 0.19 0.44 7.61 0.06 0.24 3 0.97 10.30 0.09 3.77 7.61 0.50 0.42 4 0.15 10.30 0.01 1.05 7.61 0.14 0.11 2 3 40.0 8.5 Z16 1 1.95 9.16 0.21 1.98 6.63 0.30 0.31 2 1.95 9.16 0.21 0.34 6.63 0.05 0.24 3 0.97 9.16 0.11 2.95 6.63 0.44 0.51 4 0.30 9.16 0.03 0.82 6.63 0.12 0.14 2 4 40.0 8.5 Z15 1 1.95 10.30 0.19 2.70 5.34 0.51 0.67 2 1.95 10.30 0.19 0.47 7.61 0.06 0.25 3 0.97 10.30 0.09 4.01 7.61 0.53 0.44 4 0.15 10.30 0.01 1.12 7.61 0.15 0.11

Note for surface 2, span 3, load 1 that the reported axial load is 5.17 while the calculated load is 6.46. Also, note 5.17 / 6.46 = 0.80, that is, the reported purlin axial loads are 80% of the calculated axial loads. If the designer believes the purlin axial loads are shared with the adjacent purlins then they can reduce the load in the calculated purlin by setting roof design parameter 39 for the building. For this example, roof39 equals 0.80.

C. Program Output: Eave Strut Report


============================================================================== SAMPLE Eave Strut Report 4/ 4/00 9:48pm ============================================================================== Wall Bay Eave Axial_Calc Axial Axial Id Id Size Wind Seis Allow Ratio ---- --- -------- ------ ------ ----- ----- 2 1 8.5C16 9.20 1.47 18.47 0.49 2 2 8.5C16 9.20 1.35 18.47 0.49 2 3 8.5C16 1.09 0.12 18.47 0.06 4 3 8.5C16 1.09 0.12 18.47 0.06 4 2 8.5C16 0.00 0.00 18.47 0.00 4 1 8.5C16 1.09 0.12 18.47 0.06

- Hand calculations on the eave struts are for the wind direction shown. However, the eave strut report contains the maximum eave strut forces for wind from either direction. On the back sidewall (wall4) there is a wind bent in the second bay so the eave strut forces are carried by the wind bent and not by the eave strut.

- The allowable axial load in the eave strut is based on the 96 AISI Code. Since the eave

strut is braced in one plane by the roof panels and the other plane by the wall panels, the unbraced length is zero.

- Using the C_STRESS program, 8.5C16 member, unbraced length = 0, Fy = 55, 1/3

stress increase for wind, the allowable axial load is 18.47 k which matches the program output.

D. Program Output: Roof Diagonal Bracing Report

============================================================================== SAMPLE Roof Diagonal Bracing Report 4/ 4/00 9:48pm ============================================================================== Panel Shear (Allow) = 0.0 Panel Shear (Calc ) =106.0 Bay Brace_Loc. ------Diag_Brace----- Diag_Force(k ) Brace_Tension(k ) Id Start End Type Size Part Wind Seismic Calc Allow --- ------- ------- ---- ------ -------- ----- ------- ------ ------ 2 0.00 20.00 C 0.375 10-106 10.40 1.42 10.40 10.46 20.00 40.00 C 0.312 10-105 5.36 0.71 5.36 7.46 40.00 50.00 C 0.312 10-105 0.00 0.00 0.00 7.46 50.00 60.00 C 0.312 10-105 0.00 0.00 0.00 7.46 60.00 80.00 C 0.312 10-105 5.26 0.71 5.26 7.46 80.00 100.00 C 0.375 10-106 10.19 1.42 10.19 10.26

a. Roof Panel Shear One option in roof bracing is to use panel shear. The panel shear will carry the loads

from the tops of the interior column to the eave line along the sidewall. Wind forces to one eave line are P2 + P3 at both ends of the building. See section 8.4.


panel shear = plf0.108'75

75.164.143.228.2=

+++ [108.1]

b. Roof Diagonal Bracing Cable tension = shear in bay · cable length / frame spacing (2nd bay), tension = (1.75 + 2.43) · 32 / 25 = 5.35 k [5.36] (edge bay), tension = (1.75 + 2.43 + 2.28 + 1.64) · 32 / 25 = 10.37 k [10.40] From the DS_CABLE file, the allowable tension for 3/8” cable is 10.46 k and for

5/16” cable is 7.46 k use 3/8” and 5/16” cables.

8.6 ALLOWABLE AXIAL LOAD IN PURLINS

- Use Section C4.4 of the 96 AISI Code since the purlins are through fastened to the panels:

ACCCPn ⋅⋅⋅= 321 where:

=X (screw offset from web) / flange width = 0.50

935.054.050.079.054.079.01 =+⋅=+⋅= XC t of 15 gage = 0.067

0084.193.0067.017.193.017.12 =+⋅=+⋅= tC b = 2.5”, d = 8.5”

2.158.225.863.15.25.28.2263.15.23

=+⋅−⋅=+⋅−⋅= dbC

A = full area of member = 0.971 in²

kPn 91.13971.02.150084.1935.0 =⋅⋅⋅= Adjust for wind load (1.333) and for factor of safety (1.80)

kPn 31.1080.1333.191.13 =⋅= [10.30]

8.7 CALCULATED BENDING MOMENTS IN PURLINS

- From the bracing loads “Wind Pressure/Suction” line note the roof uplift is 14.0 psf.


- On the same input line, see below, note the purlins were designed for an uplift of 21.9 psf.

*(34)WIND PRESSURE/SUCTION: (psf ) * * Wind Wind Wind * Press Suct Suct_R 7.7 -21.9 .. Purlins 0.0 -33.9 .. Gable Extension 8.1 -31.7 .. Panels 8.7 -6.3 -14.0 .. Bracing

- The purlin moments for bracing can be calculated from the purlin moments from purlin

design with DL + WS by using a ratio of the loads. - For bracing, the roof load is uniform hence the edge strip loading should be used. - Recall the edge strip loading to be the interior loading times roof design parameter 19,

which is 1.19. - There are 5 stress checkpoints on each member. The critical point for bending plus

axial will be the same as the critical point for bending. - From the purlin design for edge strip loading, see below, the DL + WS design moments

are: Span 2(Bay 1) = 5.01, Span 3 = 3.92, Span 4 = 5.34 - The load ratio is:

50.0.219.19.21

.2.14)()(

=−⋅

−=

−−

DLWSPurlinsDLWSBracing

- The design moments with bracing are: Span 1: 5.01 · 0.50 = 2.51 [2.54] Span 2: 3.92 · 0.50 = 1.96 [1.98] Span 3: 5.34 · 0.50 = 2.67 [2.70] - These values about match those in the braced purlin report for load 1. See 8.5.B.


LOAD COMBINATION # 3 : DL+WS -------------------------------------------------- STRENGTH/DEFLECTION: Span ------SHEAR(k )------ -----MOMENT(f-k )---- Mom+Shr DEFLECTION(in) Id Loc Calc Allow UC Loc Calc Allow UC Loc UC Calc Allow ---- --- ------ ----- ---- --- ------ ----- ---- --- ---- ------ ----- 1 RS 0.13 4.42 0.03 RS 0.07 7.61 0.01 RS 0.00 -0.20 2 RL 1.35 4.42 0.31 MS 5.01 5.54 0.91 RS 0.33 1.14 1.59 3 RL 1.12 3.17 0.35 RL 3.92 6.63 0.59 RL 0.47 -0.02 1.67 4 LL -1.41 4.42 0.32 MS 5.34 5.34 1.00 LS 0.37 1.29 1.64 5 LS -0.05 4.42 0.01 LS 0.01 7.61 0.00 LS 0.00 -0.08

8.8 ALLOWABLE BENDING IN PURLINS - The special program can be used to calculate the allowable bending stress and the

interaction of bending plus axial. The special program run for the first purlin in the braced purlin report is shown below. The notes below the report describe some of the values.

8

CM

LOAD RATIOS FOR C & Z MEMBERS INPUT OUTPUT MEMBER Member Size - 8.5Z15 Web Depth (in) - 8.500 CALC'D ALLOW LOAD Thickness (in) - 0.067 ACTION LOAD LOAD RATIO Top Flg Width (in) - 2.500 --------- ------ ------ ------ Bot Flg Width (in) - 2.688 Axial 1.79 10.13(3) 0.18 Lip Length (in) - 0.680 C4.4-1 Inside Radius (in) - 0.312 Shear 0.00 4.35 0.00 Angle (deg) - 55.000 C3.2-3 Steel Yield (ksi) - 55.000 Bending 2.54 5.58(3) 0.45 UNBRACED LENGTH C3.1.2-1 Major Axis (ft) - 23.920(1) Axl+Bnd 0.60(3) Minor Axis (ft) - 7.970(2) C5.2.1-1 Cb - 1.000 Shr+Bnd 0.11 Wind Adjust - 1.333 ACTION Axial (k) - 1.790 Shear (k) - 0.000 Moment (f-k) - 2.540

Notes: (1) Purlin Span (2) Purlin Span/3, since 2 rows of bridging angles are used. (3) Matches hand calculations

.9 COMBINED AXIAL PLUS BENDING IN PURLINS

- See 96 AISI Code Section C.5.2.1

alculations Manual 06/06 BS, Inc. Page 8-9

0.1≤⋅⋅⋅Ω

+⋅Ω

αn

mb

n

c

MMC

PP

where:

67.18.1

=Ω=Ω

b

c

applied axial load and axial strength =nPP, applied moment and flexural strength =nMM , 85.0=mC

( )4

22

36.10,'9.23,1

/

1

inILK

LKIEP

PP

e

ec

===

⋅⋅⋅Π=

⎟⎠⎞⎜

⎝⎛ ⋅Ω−=α

( )

( ) 91.06.36/83.18.11

6.36129.231

36.10500,292

2

=⋅−=

=⋅⋅⋅⋅Π

=

α

kPe

601.0423.0178.054.551.2

91.085.0

30.1083.1

=+=⋅+ [0.61]

8.10 SIDEWALL DIAGONAL BRACING A. Program Output: Sidewall Diagonal Bracing Report


============================================================================== SAMPLE Sidewall Diagonal Bracing Report 4/10/00 5:12pm ============================================================================== PANEL SHEAR: Wall Id Calc Allow ---- ----- ----- 2 167.2 100.0 4 158.4 100.0 DIAGONAL BRACING: Wall Bay Level ------Diag_Brace----- Diag_Force(k ) Brace_Tension(k ) Id Id Height Type Size Part Wind Seismic Calc Allow ---- --- ------ ---- ------ -------- ------ ------- ------ ------ 2 1 24.00 C 0.500 10-108 13.05 1.92 13.05 17.93 BASE REACTIONS: Wall Bay Col Wind_Max Seismic_Max Id Id Id Horz Vert(+/-) Horz Vert(+/-) ---- --- --- ----- --------- ----- --------- 2 1 1 -9.98 8.41 -1.47 1.24 2 1 2 9.98 8.41 1.47 1.24

B. Calculations Wind force at top of sidewall (Section 8.4) a. k96.975.164.178.043.228.208.1 =+++++

b. Slope of diagonal bracing: horizontal = 25’ (bay width) vertical = eave height - purlin depth - sf - sg = 24’ - 8” - 6.6” - 19” = 21.2’ length = '8.322.2125 22 =+

c. Cable force

= 9.96 · 32.8 / 25. = 13.06 k [13.05]

d. Use a ½” diameter cable with allowable tension of 17.9 k e. Vertical reaction = 9.96 · 21.2 / 25 = 8.45 k [8.41]

8.11 DESIGN OF WIND BENT


A. Program Output: Wind Bent Design Report

============================================================================== SAMPLE Wind Bent Design Report 4/ 8/00 6:22am ============================================================================== DESIGN FOR WIND BENT #: 1 ------------------------- Wall : 4 Bay: 2 Bent Width : 25.00 Bent Height : 22.79 Deflect. Limit: 90.0 Yield Stress : 55.0 Design Load : Wind = 9.78, Seismic= 1.47 MEMBER SELECTED: Column : W121283 Weight= 2261.3 Rafter : W1212103 Weight= 1402.5 End Plate Size : 0.750 x12.00 Bolts : 8 - 1.000 Space: 3.50 Stiffener Plate Size : 0.313 x 5.91 STRESS, DEFLECTION, REACTIONS: ---Bending_Stress--- Axl+Mom -----Deflection----- ---Reactions-- Member Calc Allow UC UC Calc Allow UC Horiz Vert ------ ------ ------ ---- ------- ------ ------ ---- ------ ------ Column 18.40 44.87 0.41 0.42 2.83 2.97 0.95 4.89 8.72 Rafter 14.33 43.99 0.33 0.33

B. Calculations a. Layout Bay = 25’ Eave height = 24’ lhh = 14.5” lw = 3.4” b. Program selected members, welded plates Member Flange Web ( )4inS x ( )2inAx Column ½ · 12 0.179 · 11 69.5 14.0 Rafter 5/8 · 12 0.179 · 10.75 84.0 16.9 c. Actions in wind bent - Column moment at bottom of splice


= ( )( ) kft −=+−⋅ 4.10612125.1424277.9

- Vertical reaction = ( )( ) k71.8251265.1424277.9

=+−⋅ [8.72]

- Rafter moment on inside face of column:

= ( )( ) kft −=⋅−+−⋅ 2.100171.81265.1424277.9

d. Bending stress Column, Fb = 106.4 · 12 / 69.5 = 18.4 ksi [18.40] Rafter, Fb = 100.2 · 12 / 84.0 = 14.3 ksi [14.33] e. Allowable bending stress See Section 5.10.3 of the Design Manual on the design of wind bents. - Column - From the W_STRESS program, unbraced length = 0, Fy = 55 1/3 stress increase for wind, Fb = 44.88 ksi [44.87] - Rafter - The compression flange extends from the column rafter splice to the mid point

in the rafter where the moment is zero. - Unbraced length = 25 / 2 - 12 / 12 = 11.5’ - Cb = 1.75, due to zero moment at one end - W_STRESS program: Fb = 44.0 ksi [44.0] f. Calculated and allowable axial stress Member Axial Area Stress rKL aF aa FF Column 8.71 14.0 0.62 0 33 0.02 Rafter 4.88 16.9 0.29 25 · 12 / 3.26 = 92 16.5 0.02 g. Check axial + bending stress

0.1≤+b

b

a

a

FF

FF

(H1-3)

Column: 428.088.444.18

3362.0

=+ [0.42]

Rafter: 356.00.44

95.145.16

27.0=+ [0.35]


h. Check wind bent deflection - Layout - Formula,

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

+⋅⋅⋅

=bc I

LIh

EhFD

26

2

- Calculations h = 24 - (14.5 + 6) / 12 = 22.29’, L = 25.’ Ic = 416.8 in4, Ib = 504.2 in4

Wind load for deflection = wind load for stress · 0.75. The 0.75 is set by roof

design parameter 8.

3

3

4

222 17282.5042

0.258.416

29.22000,296

29.2275.077.9ft

ininK

ftinftKD ⋅⋅

⋅⋅⋅⋅⎟⎠⎞

⎜⎝⎛

⋅+⋅

⋅⋅⋅

=

= 2.83 in [2.83]

- Allowable deflection = 97.290

1229.22=

⋅ [2.97]

- Deflection ratio = 95.097.283.2

= [0.95]

8.12 SELECT EAVE STRUT BOLTS A. Program Output: Strut Bolt Report


============================================================================== SAMPLE Strut Bolt Report 4/ 8/00 6:22am ============================================================================== EAVE STRUTS: Wall Frm_Line ----Bolt_Selected----- ---Bolt_Capacity--- Id Id Type No Type Diam Wshr Calc Allow Ratio ---- -- ---- -- ----- ----- ---- ----- ----- ----- 2 1 RF 4 A307 0.500 0 ** 9.20 10.47 0.88 2 2 RF 4 A307 0.500 0 ** 9.20 10.47 0.88 2 3 RF 4 A307 0.500 0 ** 9.20 10.47 0.88 2 4 EW 2 A307 0.500 0 1.09 5.23 0.21 **NOTE: NOT STANDARD BOLT CONNECTIONS

B. Calculations a. Capacity of ½” A307 bolt in 16 gage eave struts - For bolt shear, see 96 AISI Section E3.4

."25.114.227

."104.224

21

21

diaksifactorsafetyF

diaksifactorsafetyFF

nv

nvr

>===

≤===

allowable, ½” A307 bolt = vP kFA allowvb 96.110196.0 =⋅=⋅ - For bearing, see 96 AISI Section E3.3, no washers 22.222.2 tdFfactorsafetyPF unr ⋅⋅⋅== use , yu FF ⋅= 3.1 ( ) ingt 0601.016 =

kallowablePb 15.2060.050.0553.122.222.2

=⋅⋅⋅⋅=

- Use allowable load per bolt of 1.96 k. For wind loading the allowable load is 1.96 · 4 / 3 = 2.61 k b. Typical eave strut to rigid frame connection. - With sidewall design parameter 27 and 28 the minimum and maximum number of

bolts from eave strut to rigid frame is set to 2 and 4. - If the A307 bolt is not adequate the program will use the bolts listed in order on lines

77 to 82 of the DT_BOLT file.


c. Typical eave strut to endwall rafter connection. - Similar to above only design parameters 33 and 34 are used for a hot rolled endwall

rafter. They also are set to 2 and 4. d. Sidewall design parameter 26 is set to ‘2’. This instructs the program to advance the

number of bolts prior to changing the bolt selection. e. Selected bolts. - Required number of bolts = 9.20 / 2.61 = 3.52, use 4. - Use 4 bolts at each end of the eave struts in bays 1 and 2. - You can use 2 bolts at each end of the eave strut in the last bay. - However, if 4 bolts are needed on one side of the rigid frame, since they have a

common lap plate, 4 bolts are also used for the eave strut on the other side. - See the roof drawing on page 2-6 where the special bolts are called out.

8.13 SELECT BOLTS FOR PURLINS A. Program Output: Bolts for Purlins

============================================================================== SAMPLE Strut Bolt Report 4/10/00 5:12pm ============================================================================== PURLINS: Surf Frm_Line Brace ----Bolt_Selected----- Load ---Bolt_Capacity--- Id Id Type Loc No Type Diam Wshr Id Calc Allow Ratio ---- -- ---- ----- -- ----- ----- ---- ---- ----- ----- ----- 2 1 RF 20.00 2 A307 0.500 0 1 1.83 5.23 0.35 2 2 RF 20.00 2 A325 0.500 2 ** 1 6.49 8.63 0.75 2 3 RF 20.00 2 A325 0.500 2 ** 1 6.49 7.73 0.84 2 4 EW 20.00 2 A307 0.500 0 1 1.83 5.23 0.35 2 1 RF 40.00 2 A307 0.500 0 1 1.95 5.23 0.37 2 2 RF 40.00 2 A307 0.500 0 1 3.35 5.23 0.64 2 3 RF 40.00 2 A307 0.500 0 1 3.35 5.23 0.64 2 4 EW 40.00 2 A307 0.500 0 1 1.95 5.23 0.37 **NOTE : Not standard bolt connection

All purlins that carry strut forces are reported, however, only those on surface 2 are in this table.

- In the end bay, the load transfer is equal to the axial load in the purlin. - That is: Loc 20, 2.28 · 0.80 = 1.82 k [1.83] Loc 40, 2.43 · 0.80 = 1.94 k [1.95]


- For the interior bays, one must consider the load transfer between the two lapped purlins and the rigid frame.

- The load transferred will be the transverse component of the cable force, that is

equivalent to the “shear in bay” as reported in Section 8.5. Loc 20, 8.10 · 0.80 = 6.48 k [6.49] Loc 40, 4.18 · 0.80 = 3.28 k [3.35] - Note the 0.80 factor comes from the user set criteria that only 80 percent of the purlin

load is carried by the purlin under study. B. Calculations

a. Typical purlin to rigid frame connection - Roof design parameters 50 and 51, the minimum and maximum number of bolts

from purlin to rigid frame, are set to 2 and 2. - Bolts are selected from lines 71 to 76 in the DT_BOLT file. The bolt choices start

with ½” A307 (no washers), then ½” A325 (no washers), and last ½” A325 (2 washers).

b. Typical purlin to endwall rafter connection - The minimum and maximum number of bolts are set with roof design parameters 42

and 43 to 2 and 2. c. Bolt selection - Note the capacity of 2 ½” A307 bolts: 2 · 2.61 = 5.22 k is larger than all but two of the calculated bolt forces. - Therefore, the standard 2 ½” A307 bolts are adequate for all but two of the purlin

connections. - From Section 8.12 the bearing capacity of 2 ½” bolts without washers is:

k73.53415.22 =⋅⋅ < 6.49, Not okay

- Bearing capacity with washers: k74.722.2373.5 =⋅ > 6.49, Okay - Allowable shear on 2 ½” A325 bolts is: (Table E3.4-1)

k1.1434245.0

254 2 =⋅⋅⋅Π⋅ > 6.49, Okay

8.14 SEISMIC ANALYSIS


The bracing needs to resist the seismic loads in the longitudinal direction. Each bracing report contains reactions to the seismic loads along with the wind loads. In this section of the hand calculations the seismic forces will be checked.

A. Seismic Force - Formula for total base shear This is calculated in Section 3.4c as V = 0.048 · W, where W is the building weight

used for seismic calculations. - W = W(roof) + W(endwall) + W(sidewall) W(roof) = W · L · (DL + CL + DL(frame)) + 0.20 · SL(when SL > 30) = 75 · 100 (2.0 + 3 + 2) = 52.5 k W(endwall) = 2 · 100 · (24 + 25/12)/2 · 2 psf = 5.2 k W(sidewall) = 24/2 · 75 · 2 · 2 psf = 3.6 k W = 52.5 + 5.2 + 3.6 = 61.3 k (Frame dead load and wall dead loads are set at 2 psf unless set differently with roof

design parameters 32(rigid frame), 33(sidewall), and 34(endwall)). - The total seismic force is:

V = 0.048 · 61.3 = 2.94 k

B. Check Sidewall Bracing - One half of the total seismic force will be carried by each sidewall. - Cable force for seismic

= k93.1258.32294.2

=⋅ [1.92]

- Horizontal reaction = 2.94 / 2 = 1.47 k [1.47] - Vertical reaction = 2.94 / 2 · 21.2 / 25 = 1.25 k [1.24] - See sidewall bracing report in Section 8.10.

C. Seismic Loads in Roof Truss - The method of calculating roof bracing forces from seismic loads is described in

program enhancement 8-99-1. - Roof and endwall seismic loads will be carried by the roof bracing to the building eave.

On each side of the roof this force is:


0.048 · (52.5 + 5.2)/2 = 1.38 k - The 1.38 k force is divided into a force at mid length of each strut purlin. The strut

purlins line up with the diagonal bracing. - The magnitude of the force is dependent on the contributory area for each strut purlin.

- Purlin: kF 184.038.175502520

=⋅⋅⋅

=

- Eave strut: kF 092.038.1755025102 =⋅⋅⋅

=

- The following drawing shows the location of the roof seismic loads.

D. Seismic Force in Roof Cables - In the roof bay between the 20’ and 40’ location the bay shear is 3 · F, cable tension = shear force · cable length / frame spacing = 3 · 0.184 · 32 / 25 = 0.706 k [0.71] - Similarly for the cable tension in the first bay, = 6 · 0.184 · 32 / 25 = 1.413 k [1.42] - See Section 8.5D to view the program output.

E. Seismic Force in Roof Purlins - In span 2 the purlins will have the force generated in that bay, F = 0.184 · 0.80 = 0.147 k [0.15] - In span 4 the seismic force creates a tension force in the strut, however, for the seismic

force in the other direction, the strut will be in compression. - For span 3 at the 40’ location the strut carries a 2 · F load, = 2 · 0.184 · 0.80 = 0.294 k [0.30]


- For span 3 at the 20’ location, the strut carries the 3 · F from the 40’ location plus the 2 · F from the 20’ location,

= 5 · 0.184 · 0.80 = 0.736 k [0.74] - The 0.80 factor comes from the designer option to consider 80% of the calculated load

to be carried by the purlin under study. - See loading 4 of the braced purlin report in Section 8.5 to view the program output.

F. Seismic Force in Eave Struts - In the back sidewall there is a wind bent in bay 2, hence the eave strut force in that bay

is zero. - The back sidewall eave strut forces in spans 2 and 4 are those generated in that bay from

the roof, F / 2, plus that generated from the weight of the sidewall. - sidewall seismic weight = 3.6 k - seismic force = 0.048 · 3.6 = 0.173 = S - seismic force per bay = 0.173 / 6 = 0.0288 = S / 6 - force in eave strut = 0.092 + 0.0288 = 0.121 k [0.12] - The eave strut forces on the front sidewall can be seen from the sketch shown below

which has the seismic force in the opposite direction. The seismic force generated in each sidewall bay is labeled as S / 6.

- In span 4 the eave strut force is: F / 2 + S / 6 = 0.092 + 0.0288 = 0.121 k [0.12] - In span 3 the eave strut force is: = 2 · F / 2 + 2 · S / 6 + 6 · F = 2 · 0.092 + 2 · 0.0288 + 6 · 0.184 = 1.346 k [1.35] - In span 2 the eave strut force is the same as span 3 only F / 2 + S / 6 is added. = 1.346 + 0.092 + 0.0288 = 1.467 k [1.47]


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