Forging new generations of engineers Loads and Structural

Forging new generations of engineers

Loads and Structural Members

Purpose Stability Strength Economic Value

Types of Loads Dead Live Wind Impact/Shock/Vibration Seismic

Loads and Load Paths Snow, Movable Furniture, and Occupancy = LL Permanent Fixtures and Weight of Structural Materials = DL Ground Reaction

Structural Efficiency Dead Load Live Load

Factor of Safety Live Loads * 1. 7 Dead Loads * 1. 4

Beam Types Simple Continuous Cantilever Moment fixed at one end

Supports Pin Connection Roller Connection Fixed Support

Load Distribution Uniform Loading Concentrated Loading Combination Loading

Columns F (External) Designed for compression. WCOL (External) Additional loads can cause bending in the columns. WFTG (External) RSoil (External)

Building Design Problem A Steel Framed Retail Building with Concrete Floors and Flat Roof

Steps in Design Process Plan/ Layout Structural Grid Establish loads Size the members Evaluate and Compare to preliminary design Redesign

Structural Elements Interior Beams Exterior Beam Girders Footing Column

Framing with Foundation Plan Design Area

Tributary or Contributing Area Beam C. 2 -3 Tributary Area Girder 2 AD Column A-2 6’- 0” Tributary Width

Roof Beam C. 2 -3 Data Dead Load=(DL) 1/8” thick steel plate Roofing material Suspended Ceiling Mechanical/ Electrical Items Total DL 10 lb/ft 2 2 lb/ft 2 10 lb/ft 2 32 lb/ft 2 Total LL 20 lb/ft 2 Total 16 lb/ft Tributary width Total 6’- 0” Span = L Total 16’- 0” Live Load=(LL) Snow Assumed Beam Weight per ft. W 12 x 16

Interior Roof Beam C. 2 -3 Calculations Load = (DL + LL) x Tributary width (32 lb/ft 2 + 20 lb/ft 2 ) x 6. 0 ft = 312. 0 lb/ft Add the Assumed Beam Weight of 16 lb/ft Total Uniform Load (W 1) = Load + Beam Weight per ft. 312. 0 lb/ft + 16 lb/ft = 328. 0 lb/ft Use 328. 0 lb/ft for Uniform Load (W 1)

Interior Roof Beam C. 2 -3 Calculations End Reaction Forces of Beam C. 2 -3 (W 1 x L) / 2 = R 3 328. 0 lb/ft x 16 ft / 2 = 2, 624. 0 lb Maximum Moment Force of Beam C. 2 -3 (W 1 x (L)2) / 8 = Mmax 328. 0 lb/ft x 162 ft 2 / 8 = 10, 496. 0 ft-lb Use 10, 496. 0 ft-lb for Moment (M)

Roof Beam C. 2 -3 Moment and Shear Diagram Moment Diagram

Exterior Beam A. 2 -3 Calculations Beam Load W = (DL + LL)½(Trib. width) W = (52 lb)1/2(6 ft) = 156 lb/ft Total Uniform Load on Exterior Beam W = Load + Beam weight per ft. W = 156 lb/ft + 16 lb/ft = 172. 0 lb/ft

Exterior Beam A. 2 -3 Calculations Reaction Forces (W)(L)/8 = R 2 =R 3 (172. 0 lb/ft)(16 ft)/2 = RA 3 = 1376. 0 lb Shear Diagram

Allowable Bending Stress = Fb Fb = (Yield Strength) A 36 Structural Steel – 36, 000 psi Fb = (36, 000 psi) = 24, 000 psi

Section Modulus (S) = M = 10, 496 ft-lb SRequired = Fb = 24, 000 psi 10, 496 ft-lb x 12 in/ft 24, 000 lb/in 2 SRequired = 5. 248 in 3

MDSolids Design Roof Beam C. 2 -3

MDSolids Design Roof Beam C. 2 -3

Beam C. 2 -3 Deflection limited to: (16 ft)(12 in/ft) 360 =. 533 in.

Beam C. 2 -3 Comparisons Beam Sz (in 3) Deflection (inches) W 6 X 9 5. 6 1. 017 W 8 X 10 7. 8 0. 5415 W 6 X 12 7. 3 0. 7547 W 10 X 12 10. 9 0. 3100 W 4 X 13 5. 5 1. 476 W 8 X 13 9. 9 0. 4212 SELECT

Girder 2 AD Data Girder 2 AD Span Length is 18 feet. Concentrated Load = 5248 lb Uniform Load = 24 lb/ft

Girder 2 AD Calculations End Reaction Forces of Girder 2 AD P 1 + (W x L) / 2 = RA =RD 5248 lb + (24 lb/ft x 18 ft) / 2 = 5464 = RA = RD 5, 464 lb

Girder 2 AD Calculations Maximum Moment Force of Girder 2 AD (W 1 x L 2) / 8 + P 1 d = M 24. 0 lb/ft x 182 ft 2 / 8 + 5248 lb x 6 ft = 32, 460 ft-lb Use 32, 460. 0 ft-lb for Moment (M)

Girder 2 AD Moment and Shear Diagram Moment Diagram

Girder Section Modulus (S) = M = 32, 460 ft-lb SRequired = Fb = 24, 000 psi 32, 460 ft-lb x 12 in/ft 24, 000 lb/in 2 SRequired = 16. 23 in 3

Girder 2 AD Section Modulus (S)

Design Results Deflection Limit = = (18’) X (12)in. ft 360 Deflection Limit = 0. 6” Girder Sz (in 3) Deflection (inches) W 10 X 19 18. 8 0. 6925 W 12 X 19 21. 3 0. 5130

Loads on Column and Footing Roof Loads Column A-2 Soil Bearing Reaction

Loads on Column - Footing Column Self Weight 15 ft x 20 lb/ft (estimated) = Girder Reaction Force = Ext. Beams x 2 = 2(1, 376 lb) = Total Use 9, 000 lbs 300 lb 5, 464 lb 2, 752 lb 8, 516 lb

Available Soil Bearing Capacity Footing wt. = (1 ft)(150 lb/ft 3) = 150 lb/ft 2 Allowable Soil Bearing Capacity = 3000 lb/ft 2 Soil Capacity Available = 3000 lb/ft 2 - 150 lb/ft 2 = 2850 lb/ft 2 = qnet

Sizing the Footing Load Column = 9, 000 lbs Soil Capacity Available = 2850 lb/ft 2 = qnet Area = 9000 lb 2850 lb/ft 2 =1. 78 ft Use 2’- 0” x 2’- 0” Square Footing

The Solutions: Beam C. 2 -3 W 10 x 12 Girder 2 AD Column A-2 Footing W 12 x 19 W 12 x 22 2’ x 2’

Steps in Design Process Plan/ Layout Structural Grid Establish loads Size the members Evaluate and Compare to preliminary design Redesign

Structural Layout for our building

References: Examples Morrow, H. W. (1998). Statics and Strength of Materials, Upper Saddle River, NJ: Prentice Hall

Credits: Writer: Gary Platt Content Editor: Sam Cox & Wes Terrell Production Work: CJ Amarosa Publisher: CJ Amarosa – Project Lead The Way Virtual Academy for Professional Development – www. pltw. org