Forging new generations of engineers. STRUCTURAL ENGINEERING.

Forging new generations of engineers

STRUCTURAL ENGINEERING

Structure of a Building

The primary function of a building structure is to support and transmit the loads and forces to the ground.

“Tracing the Loads”or

“Chasing the Loads”

Characteristics of a Structure

Stability – needed to maintain shape. The structure is dependent upon balanced forces and equilibriumStrength - ability of the structure to withstand the applied forces, usually includes a “factor of safety”Economic Value – includes choices made about the design, materials, and function of the structure

Structural Elements

Structural elements in the building consist of: Stringers or Beams Girders Columns Footings Connections

Steps in Structural Design1. Planning – what function will the structure

serve2. Preliminary structural configuration and layout3. Establishing the loads to be carried4. Preliminary sizing of members5. Analysis of structural members6. Evaluate and compare the preliminary design7. Redesign or repeat the above steps as this is

an iterative process8. Designing and detailing the structural

components

Forces and Loads

Design Loads

Dead Loads (DL) – fixed loads building materials or components and the weight of

structural components Given load of building, which is either calculated or is known

Live Loads (LL) – transient and moving loads Occupancy loads and furnishing loads, building usage varies Snow loads Construction loads Live Load maybe variable during structures lifetime Building codes specify Live Loads for floor and roof loadings

Design Loads (continued)Wind Load (WL) –

Depends on Height and location of structure (Exposure categories)

Resulting loads yields: Lateral load on walls Downward and upward

pressure on roofs Overturning of the

structure

WIND

WIND

Pressur

Pressur

eeUplift

Uplift

SuctionSuction

Design Loads (continued)

Earthquake Loads (EQ)

Seismic load based on building mass , type and configuration.

Vertical and lateral forces (dynamic)

Building codes can simplify loading

Seismic Forces at Base of Building

Hypocenter

Epicenter

Design Loads and “Factor of Safety”

Structural Design contains a “factor of safety.” In order to accomplish this, Load Factors are applied to the the various calculated loads. Building Code requirements are conservative in the methods of distribution and the weights of loads, which adds to the “factor of safety.”However, to maintain simplicity we will not use any factored loads for the CEA Project.

Loads & Load Paths

Snow and/or roof load

Use and occupancy load such as DL and LL

Self weight of structure DL

Ground reaction

BEAMS AND COLUMNS

LOADS The building dead load is the only

known load. All other forces will vary in magnitude, duration and location.

The building is designed for design load possibilities that may never occur.

The structural efficiency of a building is measured as the ratio of dead to live load.The building designer strives to keep the ratio low.

Beam Design

Beams are used in floors and roofs.Maybe called floor joists, stringers, floor beams or girders.Loads on beams are either concentrated or uniform loadsBeams are designed for Shear, Moment (bending), and Deflection

Beams

Beams are sized appropriately to safely support the loads a structure will carry.Beams are primarily subjected to bending and shear. Deflection and deformation can be calculated.Beams are sized to provide the maximum result with the minimum materials. A factor of safety is included in the design.

Beam DeflectionLimit Deflection to L/240 of total load (whereas L=length in inches) L/300 of total load L/360 of total load (building use throughout life

is unknown) Preferred Limit

WHY?? Ceiling cracks in plaster Roof ponding (flat roofs) Visual or psychological reasons, such as too

much deflection and people think it could be unsafe

Designer’s judgment

Beam Types

Simple

Continuous

Cantilever Moment

(fixed at one end)

Beam TypesFixed

Moments at each end

Propped- Fixed at one end supported at other

Overhang

Forces and SupportsSupports are translated into forces and moments in a free body diagrams. The following are three common supports and the forces and moments used to replace them.

Roller:

Pin Connection:

Fixed Support:

Fy

Fy

Fx

Fx

Fy

Mo

Columns

Columns carry primary Axial Loads and therefore are designed for compression.Additional loads from snow, wind or other horizontal forces can cause bending in the columns.Columns then need to be designed for Axial Load and Bending.

Column Forces FExternal

WCOL (External

R1 (Internal)

R2 (Internal)

RSoil (External)

WFTG (External)

Horizontal loads caused by wind, snow, seismic or internal building load

Building Dead Loads

Weight of the structure (steel, concrete, timber)

Partitions/ WallsDuctworkPipingElectrical fixturesFloor coveringsRoof coveringsCeiling

Typical Building Dead Loads

Concrete (density 150 lb/ft3)per 1 inch thickness 12.5 lb/ft2

Steel and Timber based on structural element weight sPartitions/ Walls— Wood stud 2x4 12” to 16” on center

with ½” gypsum board both sides 6 lb/ft2

— Brick (4” thick) 40 lb/ft2

— Concrete Block (8” Wall) 38 lb/ft2


Floor Covering Tile 12 lb/ft2

Hardwood 4 lb/ft2

Linoleum 1 lb/ft2

Sub floor ¾” plywood 3 lb/ft2

Ceiling Suspended 2 lb/ft2

Drywall 5 lb/ft2


Roofing Sheathing (3/4”) 3 lb/ft2

Asphalt Shingles 3 lb/ft2

Insulation Loose ½ lb/ft2

3 ply ready roofing 1 lb/ft2

5ply felt and gravel 6 lb/ft2

Mechanical Electrical, Ductwork and Plumbing these loads can vary - Estimated 10 lb/ft2

Estimate depends on the type of building Some may use a percentage of Dead Load

Typical Building Uniform Live Loads

Retail First Floor 100 lb/ft2

Upper Floors 80 lb/ft2

Stadiums and Arenas Bleachers 100 lb/ft2

Fixed Seats 60 lb/ft2

Library Stacks 150 lb/ft2

Reading rooms 60 lb/ft2

Offices 50 lb/ft2

Typical Building Uniform Live Loads

Schools Classrooms 40 lb/ft2

First floor corridors 100 lb/ft2

Corridors above first floor 80 lb/ft2

Stadiums and Arenas Bleachers 100 lb/ft2

Fixed Seats 60 lb/ft2

Residential (one and two family) 40 lb/ft2

Hotels and Multifamily Private rooms and corridors 40 lb/ft2

Private rooms and corridors 100 lb/ft2

Snow Load

Snow Load depends on your location. Almost all building codes have Snow Load requirements.Ground Snow Load ( in New York State) Rochester, NY 50 lb/ft2

Albany, NY 55 lb/ft2

Watertown, NY 65 lb/ft2

White Plains, NY 45 lb/ft2

Design for Wind Loads

Dead Loads figure in the evaluation of a building when designing for Wind Load.The building Dead Load can help resist the Overturning and Uplift conditions caused by wind. Typically, a building framed with steel beams and columns will have some type of bracing, such as steel cross bracing or masonry block walls on exterior or in elevator shaft to handle the wind load conditions.The floor slab also helps resist wind loads and shear loads

Building Design

Steel Frame with Concrete Floors and Flat Roof

RETAIL BUILDING

Design notes:

Revit File is for illustrative purposes only. It is a preliminary framing plan and therefore not all steel framing members are accurately noted and resized for final design. Visibility of Wall, Roof, and Slab can be changed to see total framing planNot all walls, slabs, or the roof are shownBuilding left in “Under Construction” stageSteel framed building designed for retail space

FootingColumn

Girder

Beam

Partial View of 2nd floor FramingFor Clarity the Ground Floor Slab, 2nd Floor Slab and Roof Framing and Roof Deck are not shown

3D View of Retail Building

Steel Framing and 1st Floor Slab Shown

Steps in Calculation

1. Analysis of structural members, designing for Moment and checking for Deflection

2. Evaluate and compare to preliminary design3. Redesign or Recalculate as necessary, such

as repeat the above steps as this is an iterative process

4. Calculate Beams loading, transfer loads to Girder, and carry the load to the column and then down to the footing

“Load Chasing” for Structural Design

The structural design is done by “chasing the loads” of the Dead and Live Load though the slabs, to beams, to girders then onto the columns or walls. The loads are then carried down to the footing or foundation walls and then to the earth below.

Chasing Loads for this project

Calculate Beam loading and obtain reactions Transfer reaction loads to GirderCarry the girder reactions to the column and then down to the footing

FOUNDATION PLAN

Partial 2nd FLOOR FRAMING PLAN

Design Area

Beam B.3

Girder 3BC

Tributary or Contributing Area for Beam B.3 is shownPartial 2nd FLOOR FRAMING PLAN

6’-8” Width

Column B-3

Partial Roof FLOOR FRAMING PLAN

Column B-3

Steps for Calculating Beam Loading

1. Find weights of building elements2. Compute weight carried per linear foot of beam

and multiple by Tributary Width3. Assume weight of beam per lineal foot4. Add beam weight to superimposed dead load to

get Total Dead Load (DL) 5. Select Design Live Load (LL) use applicable

building codes 6. Combine DL + LL, this will be the Uniform Load

on Beam, w7. Calculate any Concentrated Loads on Beam

Steps for Calculating Beam Loading continued

8. Use MD Solids to set up Beam Loading and generate the Moment, Shear and End Reactions for the beam

9. Select Member Shape using the Standard Steel Shapes

10. Define Stress Limits (set Steel Yield Stress Fy=36ksi or 50 ksi)

11. Compare Beam Design to Allowable Deflection Limits ( L/360)

12. Select most economical beam ( typically the lightest beam weight)

13. Deflection may control beam size

Beam and Girder Calculations

Second Floor

2nd Floor Loading for Beam B.3 - Dead Load

Span Length 18’-0”Dead Load

4” thick concrete slab 50 lb/ft2

Flooring- Ceramic Tile 10 lb/ft2

Partitions (Drywall with metal stud) 8 lb/ft2

Suspended Ceiling 2 lb/ft2

Mechanical/ Electrical Items 10 lb/ft2

Total DL 80 lb/ft2

Assumed Dead Load Weight of Beam 20 lb/ft

2nd Floor Loading for Beam B.3 - Live Load

Live Load

Retail Space 80 lb/ft2

Total Load DL + LL (per lineal foot of beam) [80lb/ft2 + 80 lb/ft2 ] x 6.67 ft = 1067.2 lb/ft

Add the Beam Weight of 20 lb/ft

Total DL + LL + Beam Weight = 1087.2 lb/ft

Use 1090 lb/ft

Assume: Simple Beam Loading Condition

Span Length is 18 feet.

Uniform Load w = 1090 lb/ft

Uniform Load w= 1090 lb/ft

2nd Floor Loading for Beam B.3

Moment

Shear

Max. Moment = 44,145lb-ft Max. Shear = 9,810 lb

2nd Floor Beam B.3 - Shear and Moment

Design Results for Beam B.3

Note: Beams were sized using MD Solids

By Limiting the Deflection to L /360Where L = 18ft x 12 in/ft = 216 inches

Limit Deflection = L/360 = 216/360 = 0.60 inches


Typically you design for Moment and then check Deflection

Before finishing using MD Solids, use this method that looks at the Moment and Allowable Bending Stress to find out the Required Section Modulus.

Where: SRequired = M/Fb

S is the Section Modulus Required

M is the maximum Moment

Fb is the Allowable Bending Stress

Fb= o.66Fy

For Fy=36,000psi Fb= 24,000 psi

For Fy=50,000psi Fb=33,000 psi


SRequired = M/Fb

M=44,145 ft-lbs

SRequired = (44,145 ft-lb)(12 in/ft) / 24,000 lb/in2

SRequired = 22.07 in3

This is the Required Section Modulus for Beam B.3

Using this value and a reference for Steel Beams, you can select a beam section that fits this requirement.

MD Solids calculates the following :

Standard steel shapes that will be acceptable for the specified bending moment and shear force.

You must select Standard Steel Shapes for the U.S. and use Fy=36,000 psi for Yield Strength of Steel


Selecting Beam Sizes

In selecting wide-flanged structural sections , keep in mind the following:Section Modulus of beam should be large enough so that the Allowable Bending Stress is not exceeded NOTE: MD Solids considered thisLimit Deflection to L/360 where L is in inchesMoment of Inertia of beam should be large enough so that deflection limits are not exceeded, MD Solids calculates the deflection based on the selected structural shape.

Comparisons of the results for Beam B.3

Beam Sz (in4) Deflection (inches)

W10x22 23.2 0.7523

W12x22 25.4 0.5691

W14x22 29.0 0.4461

W10x26 27.9 0.6165

W12x26 33.4 0.4352

W14x26 33.5 0.3624

Limiting Deflection to L/360

This most likely will control the beam design.

SELECT

2nd Floor Loading for Girder 3-BC

Uniform Load w= 50 lb/ft (Estimated weight of Girder)

P1 = P2 =19,620 lb. These are the reactions from each beam similar to Beam B.3 that rest on the Girder

2nd Floor Shear and Moment Girder 3BC

Max. Moment = 133,365 lb-ft Max. Shear = 20,120.0 lb

Design Results for Girder 3BC

The following standard steel shapes will be acceptable for the specified bending moment and shear force.

W16x45 Sz= 72.7 in3 Deflection=0.5773”

W18x46 Sz= 78.8in3 Deflection=0.4761”

Deflection Limit = L/360 = (20 ft x 12 in/ft)/360

Deflection Limit = 0.666”

In MD Solids you should have selected Standard Steel Shapes for the U.S. and used Fy=36,000 psi for Yield Strength of Steel

Roof Calculations for Column Loading

Column B-3

Tributary Roof Area Carried by Column

Column B-3 Loads

We will not size the columns for this project as that is more involved than what we need to do for this CEA project. In addition to the Axial Loads, other loads from snow, wind, or other horizontal forces can cause Bending in columns.Columns are therefore designed for Axial Load and Bending.

Footing Loads for Column B-3

We will size the footing for Column B-3Use Allowable Soil Bearing Capacity = 3000 psfLoads transferred to footing are generated from: Dead and Live Loads from structural

elements above ( 2nd Floor and Roof ) Columns Dead Load ( Self Weight) Loads from 1st Floor slab Dead load of Footing itself

Roof Loads

Dead Load

Roof Type:Corrugated Steel Deck with Insulation and 5 ply Membrane Roof and gravel

Ceiling Suspended 2 lb/ft2

Mechanical Equipment 10 lb/ft2

Steel Deck 5 lb/ft2

Insulation 2 lb/ft2

Roof Membrane and Gravel 6 lb/ft2

Roof Framing 10 lb/ft2

Total 35 lb/ft2

Roof Loads continued

Snow LoadRochester, NY 55 lb/ft2

Total Load on RoofDL + SL = 35 lb/ft2 + 55 lb/ft2 = 90 lb/ft2

This load may seem high, but consider that no additional load was added for Mechanical Roof top equipment

Roof Loads continued

Axial Load On Column B-3 from Roof

Tributary Area of Roof = 18 ft x 20 ft= 360 ft2

DL + SL = 90 lb/ft2

(DL+SL)( Trib. Area)=(90 lb/ft2)(360 ft2)=32,400 lb

Size Footings Under Columns

Loads on Column and Footing

•Loads on Column B-3 have been generated from the Beam and Girder reactions at the Roof , the 2nd Floor

•Additionally, the self weight of the column and footing will also be added to the total load used to Size the Footing

Roof Loads

2nd Floor Loads

1st Floor/ Slab Loads

Soil Bearing Reaction

COLUMN

Column B-3 2nd Floor Partial Plan

Loads on Column and Footing

Loads on the Column

2nd Floor

Girder x 2 = (20,120 lb) 2 = 40,240lb

Beams x 2 = (9,810 lb) 2 = 19,620lb

Roof

Concentrated Load = 32,400 lb

Column Self Weight

21 ft height x 50 lb.ft estimated = 1,050 lb

TOTAL 93,310 lb

USE 94,000 lbs

Loads on Footing

Total Load on Footing = 94,000lb

The Soil is capable of resisting a total bearing pressure of force of 3000 lb/ft2

Using the following formula:

Pressure = Load /Area q= P/A

q = 3000 lb/ft2 is the allowable bearing capacity of the soil

Soil Bearing Capacity Available


We will need to deduct the weight of the footing, which the footing thickness is 12 inches. This is an estimate, typically standard thickness, but the footing load is high.

(1 ft thick) x 150 lb/ft2 = footing weight in lb/ft2

Weight of Footing = 150 lb/ft2

Soil Capacity Available = 3000 lb/ft2 - 150lb/ft2

Soil Capacity Available = 2850 lb/ft2 = qnet

Sizing the Footing for Column B-3

Soil Capacity Available = 2850 lb/ft2 = qnet

Total Load of Footing = 94,000 lb


Rearranging the formula so that we can get the required Area of the footing

P/ q net = Area

94,000 lb / 2850 lb/ft2 = 32.98 ft2 = Area Req’d

Footing Size = 5.75 ft X 5.75 ft

USE 6’-0” x 6’-0” Square Footing

Reference Sources

– Jefferis, A., & Madsen, D. A. (2001). Architectural Drafting and Design. Albany, NY: Delmar, a division of Thomson Learning.

– Kane, K., & Onouye, B., (2002). Statics and Strength of Materials for Architecture and Building Construction.(2nd ed.). Saddle River, NJ: Pearson Education, Inc

– Shaeffer, R. E., (2002). Elementary Structures for Architects and Builders (4th ed.). Columbus, OH: Prentice Hall.

– Manual of Steel Construction, (8th ed), American Institute of Steel Construction

– http://www.emporis.com/en/ – http://www.pbs.org/wgbh/buildingbig/lab/forces.html– ASCE Minimum Design Loads for buildings and Other

Structures,ASCE 7-98

http://www.pbs.org/wgbh/buildingbig/lab/forces.html

Forging new generations of engineers. STRUCTURAL ENGINEERING.

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