Verification Example - Composite Steel Beam Design Secondary Member (LRFD & ASD)
Description
This verification example represents the analysis and design of a composite steel beam (secondary member) utilizing Tedds. This example is based on Design Example I.1 of the Companion to the AISC Steel Construction Manual Volume 1: Design Examples Version 15.1 (Pages I-4 through I-14). Comparisons and contrasts are tabularized and discussed regarding the results from Tedds and the AISC Design Example.
Problem statement
Select an appropriate ASTM A992 W-shaped beam and determine the required number of ¾” ⌀ steel headed stud anchors. The beam will not be shored during construction.
Tedds calculation
Composite beam design (AISC360) - Compared using version 1.0.19
Running the example in Tedds
The Tedds verification examples referenced in this document can be run in Tekla Tedds from the Engineering library index, in the Verification Examples\Composite beam design (AISC360) folder.
References
International Building Code (IBC) 2018
AISC Steel Construction Manual 15th ed.
Companion to the AISC Steel Construction Manual Volume 1: Design Examples Version 15.1
ANSI/AISC 360-16: Specification for Structural Steel Buildings
ACI 318-14: Building Code Requirements for Structural Concrete and Commentary
Example information
4-½” normal weight concrete on 3” x 18 ga. (Vulcraft 3VLI-36) composite deck (total slab thickness = 7-½”)
γconcrete = 145 lb/ft3
f’c = 4 ksi
ASTM A992
Fy = 50 ksi
Fu = 65 ksi
¾” ⌀ Steel stud anchors
Fu = 65 ksi
Stud height = 3” + 1-½” = 4-½” (AISC Section I3.2c)
Short-term to long-term concrete elastic modulus = 3:1 (assumed)
Figure 1: Composite beam floor layout with the secondary member to be analyzed
| Applied Loads | ||
|---|---|---|
| Pre-Composite (Construction Stage) | ||
|
Dead Load |
75 lb/ft2 | Composite slab (72-½ lb/ft2 (slab) and 2-½ lb/ft2 (deck)) |
| 50 lb/ft | Self-weight of steel beam | |
| Construction Live Load | 25 lb/ft2 | Light duty (ASCE 37-14 Table 4-4) |
| Post-Composite | ||
| Dead | 10 lb/ft2 | Miscellaneous (HVAC, ceiling, floor covering, sprinklers, etc.) |
| Live | 100 lb/ft2 | Assembly occupancy (non-reducible). Live load is assumed to be 100% long-term, as no information is provided in the Design Example. |
| Serviceability Criteria | ||
|---|---|---|
| Pre-Composite (Construction Stage) | ||
| Concrete (wet) + Self-weight | < L/360 or 1” | AISC Design Guide 3 Ch. 5 recommendations |
| Post-Composite | ||
| Dead+Live | < L/240 | IBC 2018 Table 1604.3 |
| Live | < L/360 | IBC 2018 Table 1604.3 |
| Comparison of Results between Tedds and AISC Example I.1 (LRFD) | |||
|---|---|---|---|
| Component | Tedds Result | AISC Example I.1 | % Difference |
| Pre-Composite (Construction Stage) | |||
| Beam Size | W21x50 | W21x50 | - |
| Flexural Demand (Mu) | 344.25 k-ft | 344 kip-ft | 0.1% |
| Flexural Capacity (φMn) | 412.50 k-ft | 413 kip-fta | 0.1% |
| Shear Demand (Vu) | 30.6 kips | 30.6 kips | 0.0% |
| Shear Capacity (φVn) | 237.1 kips | 237 kips | 0.0% |
| Dead Load Deflection w/ camberb | 2.59” - 2” (camber) = 0.59” | 2.59” - 2” (camber) = 0.59” | 0.0% |
| Post-Composite | |||
| Total number of shear studs | 46 studsc | 46 studs | |
| Flexural Demand (Mu) | 678.37 k-ft | 678 kip-ft | 0.0% |
| Flexural Capacity (φMn) | 769.71 kip-ft | 769 kip-ft | 0.0% |
| Compression Block Depth (a) | 0.946” | 0.946”c | 0.0% |
| Steel Anchor Shear Capacity (∑Qn) | 385.94 kips | 390 kips | 1.0%d |
| % Composite Action | 52.5% | 53.1% | 1.1%d |
| Shear Demand (Vu) | 60.3 kips | 60.3 kips | 0.0% |
| Shear Capacity (φVn) | 237.1 kips | 237 kips | 0.0% |
| Total Deflection | 1.364” = L/396 < L/240 | N/A | |
| Live Load Deflection (based on full design live load) | 1.24” = L/435 < L/360 | 1.26” = L/429 < L/360 | 1.6% |
| Final Beam Design | W21x50 (46) c=2” | W21x50 (46) c=2” | - |
| Comparison of Results between Tedds and AISC Example I.1 (ASD) | |||
|---|---|---|---|
| Component | Tedds Result | AISC Example I.1 | % Difference |
| Pre-Composite (Construction Stage) | |||
| Beam Size | W21x50 | W21x50 | - |
| Flexural Demand (Ma) | 265.78 k-ft | 266 kip-ft | 0.1% |
| Flexural Capacity (Mn/Ω) | 274.45 k-ft | 274 kip-fta | 0.2% |
| Shear Demand (Va) | 23.6 kips | 23.6 kips | 0.0% |
| Shear Capacity (Vn/Ω) | 158.1 kips | 158 kipsa | 0.1% |
| Dead Load Deflection w/ camberb | 2.59” - 2” (camber) = 0.59” | 2.59” - 2” (camber) = 0.59” | 0.0% |
| Post-Composite | |||
| Total number of shear studs | 46 studsc | 46 studs | |
| Flexural Demand (Ma) | 480.94 k-ft | 481 kip-ft | 0.0% |
| Flexural Capacity (M/Ω) | 512.11 kip-ft | 512 kip-ft | 0.0% |
| Compression Block Depth (a) | 0.946” | 0.946”c | 0.0% |
| Steel Anchor Shear Capacity (∑Qn) | 385.65 kips | 390 kips | 1.0%d |
| % Composite Action | 52.5% | 53.1% | 1.1%d |
| Shear Demand (Va) | 42.8 kips | 42.8 kips | 0.0% |
| Shear Capacity (Vn/Ω) | 158.1 kips | 158 kips | 0.1% |
| Total Deflection | 1.36” = L/396 < L/240 | N/A | |
| Live Load Deflection (based on full design live load) | 1.24” = L/435 < L/360 | 1.26” = L/429 < L/360 | 1.6% |
| Final Beam Design | W21x50 (46) c=2” | W21x50 (46) c=2” | - |
Comparison Notes
a AISC Table 3-2
b Tedds calculates the total construction stage deflection including all preconstruction dead loads and construction live loads. The value shown is with the construction live load removed.
c The compression block depth in the AISC Design Example is determined from the required horizontal shear (386 kips) instead of the provided shear strength of 46 anchors (390 kips).
d In Tedds, the maximum number of available ribs to midspan of the beam is (21), so (19) ribs has (1) stud and (2) ribs have (2) studs, which leads to slightly different values of total strength of provided steel anchors and percent of composite action.
Conclusion
Upon reviewing the results above, it is evident that the solutions determined by Tedds match the AISC Design Example I.1 (apart from minor differences due to rounding and precision).