Verification Example - Composite Steel Beam Design Main Member (LRFD & ASD)
Description
This verification example represents the analysis and design of a composite steel girder (main member) utilizing Tedds. This example is based on Design Example I.2 of the Companion to the AISC Steel Construction Manual Volume 1: Design Examples Version 15.1 (Pages I-15 through I-33). 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 girder and determine the required number of ¾” ⌀ steel headed stud anchors. The girder will not be shored during construction.
Tedds calculation
Composite beam design (AISC360) - Compared using version 1.0.16
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)
Secondary beams are W21x50 composite beams spaced at 10’-0” o.c.
Figure 1: Composite beam floor layout with girder to be analyzed and designed
Figure 2: Composite girder stud layout (AISC Example I.2)
Figure 3: Composite girder stud layout (Tedds output)
| 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 secondary steel beams | |
| 76 lb/ft | Self-weight of girder | |
| 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) |
| 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.2 (LRFD) | |||
|---|---|---|---|
| Component | Tedds Result | AISC Example I.2 | % Difference |
| Pre-Composite (Construction Stage) | |||
| Beam Size | W24x76 | W24x76 | - |
| Flexural Demand (Mu) | 621.1 k-ft | 624 kip-ft | 0.5%a |
| Flexural Capacity (φMn) | 677.2 k-ft | 677 kip-ftb | 0.0% |
| Shear Demand (Vu) | 62.57 kips | N/A | - |
| Shear Capacity (φVn) | 315.5 kips | N/A | - |
| Dead Load Deflection w/ camberc | 1” - ¾” (camber) = 0.25” | 1” - ¾” (camber) = 0.25” | 0.0% |
| Post-Composite | |||
| Total number of shear studsd | 55 studs | 55 studs | |
| Flexural Demand (Mu) | 1,215.1 k-ft | 1,220 kip-ft | 0.4% |
| Flexural Capacity (φMn) | 1,267.3 kip-ft | 1,280 kip-ft | 1.0% |
| Compression Block Depth (a) | 1.83” | 1.83” | 0.0% |
| Steel Anchor Shear Capacity (∑Qn) | 559.96 kips | 560 kips | 0.0% |
| % Composite Action | 50% | 50% | 0.0% |
| Shear Demand (Vu) | 121.97 kips | 122 kips | 0.0% |
| Shear Capacity (φVn) | 315.48 kips | 315 kips | 0.0% |
| Total Deflectione | 0.94” = L/383 < L/240 | N/A | - |
| Live Load Deflection (based on full design live load)e | 0.623” = L/578 < L/360 | 0.543” = L/663 < L/360 | 14.7% |
| Final Beam Design | W24x76 (55) c=¾” | W24x76 (55) c=¾” | - |
| Comparison of Results between Tedds and AISC Example I.2 (ASD) | |||
|---|---|---|---|
| Component | Tedds Result | AISC Example I.2 | % 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 Deflectione | 2.05” = L/263 < L/240 | N/A | |
| Live Load Deflection (based on full design live load)e | 1.329” = L/406 < L/360 | 1.26” = L/429 < L/360 | 5.5% |
| Final Beam Design | W21x50 (46) c=2” | W21x50 (46) c=2” | - |
Comparison Notes
aThe design example used a trial girder weight of 80 lb/ft, while Tedds used the final beam size weight of 76 lb/ft, leading to the small difference.
bAISC Table 3-2
cTedds calculates the total construction stage deflection which includes all preconstruction dead loads and construction live loads. The value shown is with the construction live load removed.
cTedds calculates the total construction stage deflection which includes all preconstruction dead loads and construction live loads. The value shown is with the construction live load removed.
dSee Figures 2 and 3 for girder stud layout.
eIn Tedds, the effective moment of inertial for the partially composite beam is calculated using a reduction factor of 0.75, consistent with AISC 360-10. It is understood that the commentary in AISC 360-16 states that this factor could not be substantiated, and to use the lower-bound approach. Tedds is currently implementing this alternate design approach to calculate deflection for composite members.
fWhen the composite girder is designed using the ASD method, a W24x76 beam is not suitable for pre- or post-composite loading. However, the AISC design example continues the design using a W24x76 girder. To follow suit, the Tedds calculations provide results for a W24x76 composite girder.
Conclusion
Upon reviewing the results above, it is evident that the solutions determined by Tedds match the AISC Design Example I.2 (apart from minor differences due to rounding and precision).