Jonathan Goodroad Structural Option Faculty Consultant – Dr. Linda Hanagan Delaware State University Administration and Student Services Building Dover, DE

Structural Technical Report 3

Lateral System Analysis and Confirmation Design November 15, 2004

Executive Summary Delaware State University’s Administration and Student Services Building is a four story building on the east half, and a one story building with a two story atrium on the west half. The main entrance is framed with a full building height rotunda, containing sitting areas and office space on upper stories. The 88,600 square feet of this building serves as space for administrative offices, student service areas, sitting areas, and equipment and storage space. The roof and floor diaphragms are constructed with composite beams and composite slabs. Columns carry the load from the main portion of the building down to a mat foundation. The roof and floor diaphragms are constructed with composite beams and composite slabs. The composite slabs utilize a 2 ½” cover on a 3”, 20 gage steel deck. The lateral system uses the steel framing system with semi-rigid moment connections between the columns and girders. The lateral system was designed to resist wind and seismic forces using BOCA ’96 and ASD. Wind forces were determined to control the design. The system was viewed in the East-West and North-South directions and the East-West direction was the critical direction. The frames in the East-West direction were analyzed. Load distribution was determined and hand calculations checked adequacy of some columns. LRFD and RAMAdvanse aided in the calculation of reactions and member adequacy.The building was determined to have an adequate lateral system. It was deemed capable of resisting the seismic and wind loads.

Introduction:

The Delaware State University Administration and Student Services

Building is a 4 story office building located in Dover, Delaware on the

southeast portion of Delaware State University’s campus. With occupied

floors reaching a height of around 55 feet and housing approximately

72,000 square feet, DESU’s recently constructed Administration building

serves student and administrative offices, as well as student service and

assistance areas. Completed in 2002, the building has a unique

configuration lending to the fact that it is, in a way, two separate buildings.

The east half of the building is the taller side, reaching four stories with a

mechanical penthouse set atop the roof, and a basement underneath.

The western half of the building consists of a single story building and a

two story atrium separating the single story and the east half of the

building. The basement space contains mechanical equipment and room

for archival storage. The

main entrance lies at the

north end of the west half of

the building. The

entranceway is framed by a

full building height rotunda,

View showing South end of the building

View of Rotunda

which also houses offices and a sitting area above the entranceway. The

ground (1st) floor opens into the two-story atrium space. This tall,

expansive room holds information desks for visitors and students, as well

as the entranceway to the bursar and registrar’s offices located on the first

floor of the east half of the structure. Offices are located in the upper

stories and in the single story structure.

Covering a footprint of approximately 24,000 square feet, the

Administration building rests the taller portion of its structure on a 24” thick

mat foundation; the east half of the building rests on the mat, perimeter

grade beams, and a wide grade beam running long ways down the center

of the mat. Supported on the foundation is a 2 ½” composite slab on 3”

steel deck working in conjunction with a wide flange composite steel beam

system. Apart from the areas holding mechanical equipment, the roof is

composed of 1 ½” steel roof deck supported by wide flange steel beams

and girders. The loads of and on the floors are carried down to the

foundation through steel columns; these columns rest on concrete piers,

square footings, and wall footings. The west half of the building uses a

slab-on-grade, with columns resting on wall footings and piers around the

perimeter and by cast-in-place square footings throughout the interior.

In addition to the support of gravity loads, the structural steel system is

designed to withstand lateral loads resulting from wind and seismic action.

The most critical area affected by these loadings is the taller, four-story

west portion of the building. Its height, weight, and size make it more

susceptible to wind and seismic loads than the smaller part of the building.

The four story portion has a mostly rectangular shape aside from

projections extending from the east side of the building. To resist the

horizontal loads, the girders in the building are connected to the columns

using semi-rigid moment connections; also they are oriented in a north-

south and east-west configuration which helps resist the prevailing winds

in these directions. The columns are then fastened to the foundation

elements with bolted connections. This arrangement makes it possible to

resist the forces that wind gusts and earthquakes administer to the

building’s facades. The steel frames are oriented together to optimally

resist the lateral forces to a degree where they will not deflect to an extent

that could cause harm to the building and its occupants. This report is

intended as a groundwork investigation of the lateral systems at work in

the DESU Administration Building.

The lateral system arranged in the east-west direction utilizes a

combination of three very similar frame arrangements to make up the ten

frames that support the building. The two outer frames, denoted Type A,

on column lines 4 and 13 are nearly identical and are treated as so in the

following analysis. The eight interior frames on column lines 5, 6, 7, 8, 9,

10, 11, and 12 are arranged in two groups of similar frames of Type B on

column lines 5 to 9, and Type C on lines 10 to 12. The only variances

between the different types are minor dimensional and sizing differences.

The frames are spaced at 21’-4” and 22’-8” widths. The different frames

can be viewed graphically in the Appendix. The East-West direction was

determined to be the most critical and therefore was the focus of this

analysis. The greater width of the building in this direction was the main

cause for the greater load felt by the structure in the east-west direction.

In the North-South direction there are three major paths of lateral

resistance. The quantity of area susceptible to wind in this direction is

considerably less than in the North-South direction as there is in the East-

West (66’ in width vs. 197’). This offered an initial consideration in

determining the critical load resistance direction.

This report will cover the determination of loads and analyses of different

load cases. Also, the distribution of the forces and the method with which

they were procured will be shown along with a likely path for load transfer

to the foundation. The lateral system was analyzed with RAMAdvanse™;

results of this analysis will be discussed along with strength and

overturning checks. Along with the discussion of checks, interior and

exterior columns were checked using portal analysis.

Loads and Load Cases:

Seismic loads and Wind loads were calculated in Technical Report 1 using

the BOCA ’96 building code. The seismic loads from Technical Report 1

were used for this analysis with the addition of some loads from smaller

elements that were previously overlooked. The Wind calculations

underwent a greater change as it was determined that the story force

values calculated

earlier were

insufficient and under

designed. These

changes will allow for

a more accurate and

conservative design.

It was determined

after reviewing the

loads and testing combinations that seismic forces were not the controlling

factor in the design of the lateral system. Load distribution analyses made

it evident that the East-West direction controlled the lateral design. The

wider building face produced a greater force from the wind pressures. In

addition, the relatively substantial length of the building combined with its

narrow width in the North-South direction seemed to be much more

effective in resisting the wind pressures. Therefore this report analyzes

the effects of the lateral forces on the long face of the east side of the

building. In the future, further investigation should be performed

concerning the North-South direction.

Wind Loads: V=80mph Exposure C Importance Factor I=1.0

Wind Story Forces (S-N)

Floor Elevation Height

(ft.) Width (ft.)

Windward P (psf)

Leeward P (psf)

Windward Force (kips)

Leeward Force (kips)

Total Force (kips)

Overturning Moment

(ft-k) 2nd 15.33 21.995 55.4 13.785 10.511 16.80 12.81 29.61 453.848253rd 28.66 13.33 55.4 16.715 10.511 12.34 7.76 20.11 576.235414th 42 13.33 55.4 18.438 10.511 13.62 7.76 21.38 897.88925Roof 55.33 6.665 55.4 19.988 10.511 7.38 3.88 11.26 623.09776Penthouse 66 10.66 27.7 21.023 10.511 6.21 3.10 9.31 614.55389

Base Shear = 56.35 35.32 91.66 3165.6246

Wind Story Forces (E-W)

Floor Elevation Height

(ft.) Width (ft.)

Windward P (psf)

Leeward P (psf)

Windward Force (kips)

Leeward Force (kips)

Total Force (kips)

Overturning Moment

(ft-k) 2nd 15.33 21.995 197 13.785 13.139 59.73 56.93 116.6 1788.42993rd 28.66 13.33 197 16.715 13.139 43.89 34.50 78.40 2246.85524th 42 13.33 197 18.438 13.139 48.42 34.50 82.92 3482.7037Roof 55.33 6.665 98.5 19.988 13.139 13.12 8.63 21.75 1203.3145Penthouse 66 10.66 98.5 21.023 13.139 22.07 13.80 35.87 2367.4491 Base Shear = 187.24 148.36 335.6 11088.753

Seismic Loads: Av=0.05 Exposure Group B Performance Categ. C

Aa=0.05 R=4.5 Ca=4

Vertical Distribution of Seismic Forces

Floor W hi (ft.) Wihi1.155 Cvx Fx (kips) Moment (ft-k)

2nd 1350.85 15.33 31616.10141 0.094773 12.63612 193.71167613rd 1397.1 28.66 67356.80638 0.201911 26.92073 771.54809234th 1139.7 42 85436.5059 0.256107 34.14671 1434.161624Roof 831.3 55.33 85679.58507 0.256835 34.24386 1894.712642Penthouse 130.33 66 16467.11964 0.049362 6.581471 434.3770829Walls 311.08 42 23319.8107 0.069904 9.32031 391.4530122 311.08 28.66 14997.74914 0.044958 5.994203 171.7938448 311.08 15.33 7280.702393 0.021825 2.909904 44.60882275Parapet 14 55.33 1442.937797 0.004325 0.576704 31.90903043 Σ = 333597.3184 1 133.33 5368.275828

The seismic loads are notably less than the wind loads. The design of the structure considered wind the controlling load. In the analysis, different load combinations were utilized using both wind and seismic in the combinations. None of the loads that included seismic controlled the design. Below are the load combinations considered.

Load Combinations:

1. 1.2DL+1.6LL DL-Dead Load 2. .9DL+E LL-Live Load 3. .9DL+1.6W E-Seismic Load 4. 1.2DL+E+.5LL W-Wind Load 5. 1.2DL+1.6WL+.5LL

For gravity loads only, 1.2DL+1.6LL controlled the design as it gives the

highest performance loads for gravity. With lateral loads included, Case 5

produced the largest magnitude of load and controlled for all three types of

frames.

Load Distribution: To determine the correct distribution of lateral loads, the stiffness of each

different type of frame was calculated. The path of the loads is defined by

the stiffness of each framing element. The stiffer the element, the larger

the fraction of the load that element resists. This calculation is resolved by

applying a 1 kip force to the frame to determine the deflection caused by

this. As the stiffness is actually a force per unit distance, the reciprocal of

the deflection caused by a 1 kip force will produce the value of the

stiffness.

Once each stiffness value was determined, the center of rigidity was

calculated to determine whether there would be any effect caused by

eccentricity in the rigidity. The center of rigidity in the x-direction is at 99’,

while the centroid of the building is at 98’-6”. The eccentricity is only 6”,

which would create a negligible torsion about the centroid of the building.

Additionally, with the stiffness of each frame calculated, the magnitude of

load on each frame can be calculated. The fraction of the total load on

each frame is directly related to the fraction of the combined stiffness of all

of the frames. After finding this proportion, multiply that value with the

total load to find the load on the frame. Stiffness calculations can be

found in the Appendix.

Pressure Height Bldg. Wdth.

Percentage of Force for Frame

Floor (psf) (ft) (ft) 4 5 6 7 8 9 10 11 12 131 13.785 15.33 197 10.3 9.8 9.8 9.8 9.8 9.8 10.2 10.2 10.2 10.3

2 16.735 13.33 197 10.3 9.8 9.8 9.8 9.8 9.8 10.2 10.2 10.2 10.33 18.438 13.33 197 10.3 9.8 9.8 9.8 9.8 9.8 10.2 10.2 10.2 10.34 19.988 13.33 197 10.3 9.8 9.8 9.8 9.8 9.8 10.2 10.2 10.2 10.3

Penthouse 21.023 10.66 197 10.3 9.8 9.8 9.8 9.8 9.8 10.2 10.2 10.2 10.3

Force on Frame (kips)

Floor Frame 4

Frame 5

Frame 6

Frame 7

Frame 8

Frame 9

Frame 10

Frame 11

Frame 12

Frame 13

1 4.29 4.08 4.08 4.08 4.08 4.08 4.25 4.25 4.25 4.292 4.53 4.31 4.31 4.31 4.31 4.31 4.48 4.48 4.48 4.533 4.99 4.75 4.75 4.75 4.75 4.75 4.94 4.94 4.94 4.994 5.41 5.14 5.14 5.14 5.14 5.14 5.35 5.35 5.35 5.41

Penthouse 4.55 4.33 4.33 4.33 4.33 4.33 4.50 4.50 4.50 4.55

After calculating these loads, RAMAdvanse was used to determine the drift for

the total structure. The design used a very conservative allowable drift of H/600.

The typical design drift is around H/400. The structure did, however, make the

criteria of H/600. The drift values can be viewed below.

Drift due to Wind only (E-W) (in.)

Frame (Col. Lines) 4 & 13 5 thru 9

10 thru 12 H (ft) H/600

Story 2 0.164 0.175 0.174 15.33 0.3066 3 0.358 0.367 0.367 28.66 0.5732 4 0.532 0.534 0.542 42 0.84 Roof 0.635 0.632 0.649 55.33 1.1066 Penthouse 0.7 0.693 0.714 66 1.32 Values obtained from RAMAdvanse analysis

Overturning Moment resulting from lateral forces causes uplift forces at

the foundation where the columns are connected. To determine whether

or not this uplift force was an issue, the reaction forces were determined

and then compared to an unfactored dead load on that reaction point. The

largest uplift force was a 16 kip load at an exterior column in a Type B

frame. The dead load on this column at the base was near 100 kips. This

makes the uplift force a negligible one.

Spot Checks: To determine the adequacy of the members, one interior and one exterior

column were hand-checked through portal analysis. This analysis used

the aid of LRFD values and calculation information. The rest of the

building was analyzed using RAM and RAMAdvanse. See the Appendix

for hand calculations.

All of the members were determined to be more than adequate, providing

a capacity much larger than required by this analysis. Further

investigation into this is required, as the degree of over design does not

appear to be sensible. There is possible error in my analysis or my

computer modeling.

Conclusions: After the calculations and analysis for DESU’s Administration building, it is

evident that the lateral system is adequately designed to resist the design loads.

Wind loads controlled and were calculated with the load combination

1.2DL+1.6WL+.5LL. Some uniformity of frame layout was assumed in the

interest of time. All of the calculations proved design well beyond industry

standard. Further investigation will determine the degree of this overdesign in

more detail.

Appendix Contents:

Lateral Frame Drawings

Determination of Stiffness Table

Spot Check Hand Calculations

Type A East-West Lateral Resisting Frame (Col. Lines 4 & 13)

Type B East-West Lateral Resisting Frame (Col. Lines 5-9)

W16x26 W16x26

W18x40 W18x40

W18x40 W18x40

W18x40 W18x40

W12x87

W12x50

W12x72

W12x136

W12x87

W12x65

TS10x6x.5

TS10x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

W21x44 W21x50

W24x55 W24x55

W24x55 W24x55

W24x55 W24x55

W24x55 W24x55

W12x87

W12x50W12x72

W12x136W12x87

W12x65

TS10x6x.5

TS10x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

Type C East-West Lateral Resisting Frame (Col. Lines 10-12)

W24x76 W24x55

W24x62 W24x55

W24x62 W24x55

W24x55 W24x62

W24x62W24x55

W12x87

W12x50W12x72

W12x136W12x87

W12x65

TS10x6x.5

TS10x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

TS14x6x.5

Load Distribution

Frame Unit Load ∆ (in.) k (1/∆) %w

Dist. From x (ft.) (K)x(Dist.)

4 1 kip 0.0398 25 10.31779 0 0.00 5 1 kip 0.0422 23.7 9.781263 21.166 501.63 6 1 kip 0.0422 23.7 9.781263 43.833 1038.84 7 1 kip 0.0422 23.7 9.781263 65.166 1544.43 8 1 kip 0.0422 23.7 9.781263 87.833 2081.64 9 1 kip 0.0422 23.7 9.781263 109.166 2587.23

10 1 kip 0.0407 24.6 10.1527 131.833 3243.09 11 1 kip 0.0407 24.6 10.1527 153.166 3767.88 12 1 kip 0.0407 24.6 10.1527 175.833 4325.49 13 1 kip 0.0398 25 10.31779 197 4925.00

Σ k = 242.3 100Center of Rigidity 99.11

Centroid of Bldg. 98.50

5% offset 88.5 or 108.5