# 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”)

γ_{concrete }= 145
lb/ft^{3}

*f’c* = 4 ksi

ASTM A992

F_{y} = 50 ksi

F_{u} = 65 ksi

¾” ⌀ Steel stud anchors

F_{u} = 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)

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Applied Loads |
||
---|---|---|

Pre-Composite (Construction
Stage) |
||

Dead Load |
75 lb/ft^{2} |
Composite slab (72-½ lb/ft^{2} (slab) and 2-½ lb/ft^{2}
(deck)) |

50 lb/ft | Self-weight of secondary steel beams | |

76 lb/ft | Self-weight of girder | |

Construction Live Load | 25 lb/ft^{2} |
Light duty (ASCE 37-14 Table 4-4) |

Post-Composite |
||

Dead | 10 lb/ft^{2} |
Miscellaneous (HVAC, ceiling, floor covering, sprinklers, etc.) |

Live | 100 lb/ft^{2} |
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 (M_{u}) |
621.1 k-ft | 624 kip-ft | 0.5%^{a} |

Flexural Capacity (φM_{n}) |
677.2 k-ft | 677 kip-ft^{b} |
0.0% |

Shear Demand (V_{u}) |
62.57 kips | N/A | - |

Shear Capacity (φV_{n}) |
315.5 kips | N/A | - |

Dead Load Deflection w/ camber^{c} |
1” - ¾” (camber) = 0.25” | 1” - ¾” (camber) = 0.25” | 0.0% |

Post-Composite |
|||

Total number of shear studs^{d} |
55 studs | 55 studs | |

Flexural Demand (M_{u}) |
1,215.1 k-ft | 1,220 kip-ft | 0.4% |

Flexural Capacity (φM_{n}) |
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 (∑Q_{n}) |
559.96 kips | 560 kips | 0.0% |

% Composite Action | 50% | 50% | 0.0% |

Shear Demand (V_{u}) |
121.97 kips | 122 kips | 0.0% |

Shear Capacity (φV_{n}) |
315.48 kips | 315 kips | 0.0% |

Total Deflection^{e} |
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 (M_{a}) |
265.78 k-ft | 266 kip-ft | 0.1% |

Flexural Capacity (M_{n}/Ω) |
274.45 k-ft | 274 kip-ft^{a} |
0.2% |

Shear Demand (V_{a}) |
23.6 kips | 23.6 kips | 0.0% |

Shear Capacity (V_{n}/Ω) |
158.1 kips | 158 kips^{a} |
0.1% |

Dead Load Deflection w/ camber^{b} |
2.59” - 2” (camber) = 0.59” | 2.59” - 2” (camber) = 0.59” | 0.0% |

Post-Composite |
|||

Total number of shear studs | 46 studs^{c} |
46 studs | |

Flexural Demand (M_{a}) |
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 (∑Q_{n}) |
385.65 kips | 390 kips | 1.0%^{d} |

% Composite Action | 52.5% | 53.1% | 1.1%^{d} |

Shear Demand (V_{a}) |
42.8 kips | 42.8 kips | 0.0% |

Shear Capacity (Vn/Ω) | 158.1 kips | 158 kips | 0.1% |

Total Deflection^{e} |
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

** ^{a}**The 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.

** ^{b}**AISC Table 3-2

** ^{c}**Tedds 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.

** ^{c}**Tedds 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.

** ^{d}**See Figures 2 and 3 for girder stud layout.

** ^{e}**In 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.

** ^{f}**When 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).