Composite Sections and Steel Beam Design. Composite Design. Steel Beam Selection - ASD Composite Sections Analysis Method

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1 Architecture 324 Structures II Composite Sections and Steel Beam Design Steel Beam Selection - ASD Composite Sections Analysis Method Photo by Mike Greenwood, Used with permission University of Michigan, TCAUP Structures II Slide 1/15 Composite Design Steel W section with concrete slab attached by shear studs. The concrete slab acts as a wider and thicker compression flange. Strength increase by 33% to 50% Deflection reduced by 70% to 80% Can attain either longer spans or smaller members more economical in long spans Smaller floor depth, therefore reduced overall building heights and weights Reduced DL of system, reduction of other material vertically (façade, walls, plumbing, wiring, etc.) University of Michigan, TCAUP Structures II Slide 2/15

2 Shear Studs Also called Nelson studs after the company that originated them. From AISC DigiLib Can be spot welded through light gage decking onto W section University of Michigan, TCAUP Structures II Slide 3/15 Effective Flange Width, b eff Slab on both sides: b eff is the least total width : Total width: ¼ of the beam span Overhang: 8 x slab thickness Overhang: ½ the clear distance to next beam (i.e. b eff is the web on center spacing) University of Michigan, TCAUP Structures II Slide 4/15

3 Effective Flange Width, b eff Slab on one side: b eff is the least total width (i.e. overhang + steel flange) : Total width: 1/12 of the beam span Overhang: 6 x slab thickness Overhang: ½ the clear distance to next beam University of Michigan, TCAUP Structures II Slide 5/15 Analysis Procedure (ASD - Elastic) 1. Define effective flange width, b eff Find actual stress 2. Calculate n = Ec/Es Use steel as base. (concrete scales narrower) 3. Transform concrete: width = n b eff 4. Find centroid and neutral axis. 5. Calculate transformed I tr do NOT include concrete in tension. Find load capacity 6. If load is known, calculate stress or 7. If finding maximum load, use allowable stresses. The lesser M will determine which material controls the section. University of Michigan, TCAUP Structures II Slide 6/15

4 Non-composite vs. Composite Sections Given: DL slab = 62.5 psf DL beam = 135 plf LL =? n = E conc /E steel = 1/9 F steel = 24 ksi ( Fy = 36 ) F conc = 1.35 ksi For this example, floor capacity is found for two different floor systems: 1. Find capacity of steel section independent from slab 2. Find capacity of steel and slab as a composite section University of Michigan, TCAUP Structures II Slide 7/15 Part 1 Non-composite Analysis (ASD) Find section modulus, S x in the steel W-section chart. Assume an allowable stress, F b. Determine the total moment capacity of the section, M = F b S x Subtract the DL moment to find the remaining LL moment. Calculate LL capacity in PSF. University of Michigan, TCAUP Structures II Slide 8/15

5 Part 2 - Composite Analysis (ASD) 1. Determine effective width of slab. (using 90 y92 ) 2. Find n=ec/es (1/9) 3. Draw transformed section. (transform the concrete) 4. Calculate Transformed I x : Locate neutral axis. Consider only the concrete above the N.A. (compression). Use parallel axis theorem. University of Michigan, TCAUP Structures II Slide 9/15 Effective Flange Width, b eff Slab on both sides: b eff is the least total width : Total width: ¼ of the beam span Overhang: 8 x slab thickness Overhang: ½ the clear distance to next beam (i.e. b eff is the web on center spacing) University of Michigan, TCAUP Structures II Slide 10/15

6 Composite Analysis cont. 4. Calculate Transformed I x : Use parallel axis theorem. Neglect concrete in tension! (if any) I a = Σ I g + Σ A d 2 University of Michigan, TCAUP Structures II Slide 11/15 Composite Analysis cont. 5. Calculate moment capacity for steel and concrete, each assuming full allowable stress level. 6. Choose the smaller moment. It will control capacity. University of Michigan, TCAUP Structures II Slide 12/15

7 Composite Analysis cont. 7. Subtract the DL moment to find the remaining LL moment. 8. Calculate the LL in PSF based on the M LL. University of Michigan, TCAUP Structures II Slide 13/15 Example of Transformed Section with N.A. in Concrete 1. Determine parameters as before: For: W12x19 Slab: h = 9 b eff = 63 n = Determine centroid as before. In this case the centroid falls within the slab University of Michigan, TCAUP Structures II Slide 14/15

8 tr with NA in Concrete (cont) 3. Find the moment of inertia, tr, using the steel and compression concrete University of Michigan, TCAUP Structures II Slide 15/15

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