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 equilibrium Strength - 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: n n n Stringers or Beams Girders Columns Footings Connections

Steps in Structural Design 1. 2. 3. 4. 5. 6. 7. 8. Planning – what function will the structure serve Preliminary structural configuration and layout Establishing the loads to be carried Preliminary sizing of members Analysis of structural members Evaluate and compare the preliminary design Redesign or repeat the above steps as this is an iterative process Designing and detailing the structural components

Forces and Loads

Design Loads Dead Loads (DL) – fixed loads n n 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 n n n 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) – n ure s res P t iifft pll p U U Depends on Height and location of structure (Exposure categories) ND WI Resulting loads yields: § § § Lateral load on walls Downward and upward pressure on roofs Overturning of the structure Suc tion

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 Epicenter Hypocenter Seismic Forces at Base of Building

Design Loads and “Factor of Safety” Structural Design contains a “factor of safety. ” In order to accomplish this, Load Factors are applied to 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 loads Beams are designed for Shear, Moment (bending), and Deflection

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 Deflection Limit Deflection to n n n 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? ? n n 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 Types Fixed Moments at each end Propped- Fixed at one end supported at other Overhang

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.

F (External) Column Forces Horizontal loads caused by wind, snow, seismic or internal building load WCOL (External) R 1 (Internal) R 2 (Internal) WFTG (External) RSoil (External)

LOADS

Building Dead Loads Weight of the structure n (steel, concrete, timber) Partitions/ Walls Ductwork Piping Electrical fixtures Floor coverings Roof coverings Ceiling

Typical Building Dead Loads Concrete (density 150 lb/ft 3) per 1 inch thickness 12. 5 lb/ft 2 Steel and Timber based on structural element weight s Partitions/ Walls — Wood stud 2 x 4 12” to 16” on center with ½” gypsum board both sides 6 lb/ft 2 — Brick (4” thick) — Concrete Block (8” Wall) 40 lb/ft 2 38 lb/ft 2

Typical Building Dead Loads Floor Covering n Tile n Hardwood n Linoleum n Sub floor ¾” plywood Ceiling n Suspended n Drywall 12 lb/ft 2 4 lb/ft 2 1 lb/ft 2 3 lb/ft 2 2 lb/ft 2 5 lb/ft 2

Typical Building Dead Loads Roofing n Sheathing (3/4”) n Asphalt Shingles n Insulation Loose n 3 ply ready roofing n 5 ply felt and gravel 3 lb/ft 2 ½ lb/ft 2 1 lb/ft 2 6 lb/ft 2 Mechanical Electrical, Ductwork and Plumbing these loads can vary - Estimated 10 lb/ft 2 Estimate depends on the type of building Some may use a percentage of Dead Load

Typical Building Uniform Live Loads Retail n n First Floor Upper Floors 100 lb/ft 2 80 lb/ft 2 Stadiums and Arenas n n Bleachers Fixed Seats 100 lb/ft 2 60 lb/ft 2 Library n n Stacks Reading rooms Offices 150 lb/ft 2 60 lb/ft 2 50 lb/ft 2

Typical Building Uniform Live Loads Schools n n n Classrooms First floor corridors Corridors above first floor 40 lb/ft 2 100 lb/ft 2 80 lb/ft 2 Stadiums and Arenas n n Bleachers Fixed Seats Residential (one and two family) Hotels and Multifamily n n Private rooms and corridors 100 lb/ft 2 60 lb/ft 2 40 lb/ft 2 100 lb/ft 2

Snow Load depends on your location. Almost all building codes have Snow Load requirements. Ground Snow Load ( in New York State) n Rochester, NY 50 lb/ft 2 n Albany, NY 55 lb/ft 2 n Watertown, NY 65 lb/ft 2 n White Plains, NY 45 lb/ft 2

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 plan Not all walls, slabs, or the roof are shown Building left in “Under Construction” stage Steel framed building designed for retail space

Girder Beam Footing Column Partial View of 2 nd floor Framing For Clarity the Ground Floor Slab, 2 nd Floor Slab and Roof Framing and Roof Deck are not shown

3 D View of Retail Building Steel Framing and 1 st Floor Slab Shown

Steps in Calculation 1. Analysis of structural members, designing for Moment and checking for Deflection 2. Evaluate and compare to preliminary design 3. 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 Girder Carry the girder reactions to the column and then down to the footing

FOUNDATION PLAN

Design Area Partial 2 nd FLOOR FRAMING PLAN

Column B-3 Beam B. 3 Girder 3 BC 6’-8” Width Partial 2 nd FLOOR FRAMING PLAN Tributary or Contributing Area for Beam B. 3 is shown

Column B-3 Partial Roof FLOOR FRAMING PLAN

Steps for Calculating Beam Loading 1. 2. 3. 4. 5. 6. 7. Find weights of building elements Compute weight carried per linear foot of beam and multiple by Tributary Width Assume weight of beam per lineal foot Add beam weight to superimposed dead load to get Total Dead Load (DL) Select Design Live Load (LL) use applicable building codes Combine DL + LL, this will be the Uniform Load on Beam, w Calculate any Concentrated Loads on Beam

Steps for Calculating Beam Loading continued 8. 9. 10. 11. 12. 13. Use MD Solids to set up Beam Loading and generate the Moment, Shear and End Reactions for the beam Select Member Shape using the Standard Steel Shapes Define Stress Limits (set Steel Yield Stress Fy=36 ksi or 50 ksi) Compare Beam Design to Allowable Deflection Limits ( L/360) Select most economical beam ( typically the lightest beam weight) Deflection may control beam size

Beam and Girder Calculations Second Floor

2 nd Floor Loading for Beam B. 3 - Dead Load Span Length 18’-0” Dead Load 4” thick concrete slab Flooring- Ceramic Tile Partitions (Drywall with metal stud) Suspended Ceiling Mechanical/ Electrical Items Total DL Assumed Dead Load Weight of Beam 50 lb/ft 2 10 lb/ft 2 8 lb/ft 2 2 lb/ft 2 10 lb/ft 2 80 lb/ft 2 20 lb/ft

2 nd Floor Loading for Beam B. 3 - Live Load Retail Space 80 lb/ft 2 Total Load DL + LL (per lineal foot of beam) [80 lb/ft 2 + 80 lb/ft 2 ] 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

2 nd Floor Loading for Beam B. 3 Uniform Load w= 1090 lb/ft Assume: Simple Beam Loading Condition Span Length is 18 feet. Uniform Load w = 1090 lb/ft

2 nd Floor Beam B. 3 - Shear and Moment Shear Moment Max. Moment = 44, 145 lb-ft Max. Shear = 9, 810 lb

Design Results for Beam B. 3 Note: Beams were sized using MD Solids By Limiting the Deflection to L /360 Where L = 18 ft x 12 in/ft = 216 inches Limit Deflection = L/360 = 216/360 = 0. 60 inches

Design Results for Beam B. 3 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. 66 Fy For Fy=36, 000 psi Fb= 24, 000 psi For Fy=50, 000 psi Fb=33, 000 psi

Design Results for Beam B. 3 SRequired = M/Fb M=44, 145 ft-lbs SRequired = (44, 145 ft-lb)(12 in/ft) / 24, 000 lb/in 2 SRequired = 22. 07 in 3 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.

Design Results for Beam B. 3 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 this Limit Deflection to L/360 where L is in inches Moment 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 (in 4) Deflection (inches) W 10 x 22 23. 2 0. 7523 W 12 x 22 25. 4 0. 5691 W 14 x 22 29. 0 0. 4461 W 10 x 26 27. 9 0. 6165 W 12 x 26 33. 4 0. 4352 W 14 x 26 33. 5 0. 3624 SELECT Limiting Deflection to L/360 This most likely will control the beam design.

2 nd Floor Loading for Girder 3 -BC Uniform Load w= 50 lb/ft (Estimated weight of Girder) P 1 = P 2 =19, 620 lb. These are the reactions from each beam similar to Beam B. 3 that rest on the Girder

2 nd Floor Shear and Moment Girder 3 BC Max. Moment = 133, 365 lb-ft Max. Shear = 20, 120. 0 lb

Design Results for Girder 3 BC The following standard steel shapes will be acceptable for the specified bending moment and shear force. W 16 x 45 Sz= 72. 7 in 3 Deflection=0. 5773” W 18 x 46 Sz= 78. 8 in 3 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-3 Use Allowable Soil Bearing Capacity = 3000 psf Loads transferred to footing are generated from: n n Dead and Live Loads from structural elements above ( 2 nd Floor and Roof ) Columns Dead Load ( Self Weight) Loads from 1 st 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 Mechanical Equipment Steel Deck Insulation Roof Membrane and Gravel Roof Framing Total 2 lb/ft 2 10 lb/ft 2 5 lb/ft 2 2 lb/ft 2 6 lb/ft 2 10 lb/ft 2 35 lb/ft 2

Roof Loads continued Snow Load Rochester, NY Total Load on Roof DL + SL = 35 lb/ft 2 55 lb/ft 2 + 55 lb/ft 2 = 90 lb/ft 2 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 ft 2 DL + SL = 90 lb/ft 2 (DL+SL)( Trib. Area)=(90 lb/ft 2)(360 ft 2)=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 2 nd Floor • Additionally, the self weight of the column and footing will also be added to the total load used to Size the Footing Soil Bearing Reaction Roof Loads COLUMN 2 nd Floor Loads 1 st Floor/ Slab Loads

Column B-3 2 nd Floor Partial Plan

Loads on Column and Footing Loads on the Column 2 nd Floor Girder x 2 = (20, 120 lb) 2 = 40, 240 lb Beams x 2 = (9, 810 lb) 2 = 19, 620 lb 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, 000 lb The Soil is capable of resisting a total bearing pressure of force of 3000 lb/ft 2 Using the following formula: Pressure = Load /Area q= P/A q = 3000 lb/ft 2 is the allowable bearing capacity of the soil

Soil Bearing Capacity Available Pressure = Load /Area q= P/A 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/ft 2 = footing weight in lb/ft 2 Weight of Footing = 150 lb/ft 2 Soil Capacity Available = 3000 lb/ft 2 - 150 lb/ft 2 Soil Capacity Available = 2850 lb/ft 2 = qnet

Sizing the Footing for Column B-3 Soil Capacity Available = 2850 lb/ft 2 = qnet Total Load of Footing = 94, 000 lb Pressure = Load /Area q= P/A Rearranging the formula so that we can get the required Area of the footing P/ q net = Area 94, 000 lb / 2850 lb/ft 2 = 32. 98 ft 2 = 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. (2 nd ed. ). Saddle River, NJ: Pearson Education, Inc – Shaeffer, R. E. , (2002). Elementary Structures for Architects and Builders (4 th ed. ). Columbus, OH: Prentice Hall. – Manual of Steel Construction, (8 th 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