# Verification Example - RC Two-Way Slab Design

## Description

This verification example represents the analysis and design of a reinforced concrete
two-way slab utilizing Tekla Tedds. This example is based on the Two-way Slab
Example 1 of the *ACI Reinforced Concrete Design Handbook, A Companion to ACI
318-19, Volume 1: Member Design *(Pages 96 through 113). Comparisons and
contrasts are tabularized and discussed regarding the results from Tedds and the ACI
Design Example.

## Problem statement

Design the reinforced concrete two-way slab shown in Figure E1.1 of the ACI Design Example. The interior strip along Grid B will be designed. See Figures E1.10 and E1.11 of the ACI Design Example for designed slab reinforcement.

## Tedds calculation

RC two way slab design (ACI318) - Compared using version 1.3.07

## 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\RC two-way slab design (ACI318) folder.

## References

*ACI Reinforced Concrete Design Handbook, A Companion to ACI 318-19, Volume 1:
Member Design*

*ACI 318-19: Building Code Requirements for Structural Concrete and
Commentary*

## Example information

Concrete:

γ_{concrete }= 150
lb/ft^{3}

*f’c* = 5.0 ksi

f_{y} = 60 ksi

` `

Uniform Loads:

Superimposed dead load, D = 15 psf

Live load, L = 100 psf

` `

Column dimensions: 24” x 24”

` `

Concrete cover to reinforcement:

Top clear cover: ¾”

Bottom clear cover: ¾”

## Notes and assumptions

- Analysis and design of the two-way slab will only be performed in the X-direction, matching the ACI design example.
- Bars running in the X-direction are the outer bars in the slab.
- The slab does not contain beams or drop panels
- Lateral loads are resisted by shear walls, so the slab is designed for gravity loads only.
- Diaphragm design is not considered in this example.
- The design utilizes the Direct Design Method, which details have been removed in ACI 318-19, but the method can still be used per Section 8.2.1
- Governing load combination for slab design: 1.2D + 1.6L

Comparison of Results between
Tedds and ACI Example 1 |
|||
---|---|---|---|

Component |
Tedds Result |
ACI Example 1 |
% Difference |

Minimum slab thickness for deflection control | 5.82” | 5.8” | 0.3% |

Flexural
results |
|||

Total panel moment (M_{O}) |
126.8 kip-ft | 127 kip-ft | 0.2% |

Moment distribution of interior panel, negative moment
(M_{u}^{-}) |
82.4 kip-ft | 83 kip-ft | 0.7% |

Moment distribution of interior panel, positive moment
(M_{u}^{+}) |
44.4 kip-ft | 45 kip-ft | 1.3% |

Column strip design moment, negative moment
(M_{x}^{-}) |
61.8 kip-ft |
63 kip-ft |
1.9% |

Column strip design moment, positive moment
(M_{x}^{+}) |
26.6 kip-ft | 27 kip-ft | 1.5% |

Middle strip design moment, negative moment
(M_{x}^{-}) |
20.6 kip-ft | 20 kip-ft | 3.0% |

Middle strip design moment, positive moment
(M_{x}^{+}) |
17.8 kip-ft | 18 kip-ft | 1.1% |

Required
steel area based on strength |
|||

Column strip negative (As_{x,col,neg}) |
0.342 in^{2} / ft |
0.373 in^{2} / ft |
8.3%^{a} |

Column strip positive (As_{x,col,pos}) |
0.144 in^{2} / ft |
0.156 in^{2} / ft |
8.3%^{a} |

Middle strip negative (As_{x,mid,neg}) |
0.111 in^{2} / ft^{} |
0.116 in^{2} / ft |
4.5%^{a} |

Middle strip positive (As_{x,mid,pos}) |
0.096 in^{2} / ft |
0.104 in^{2} / ft |
7.7%^{a} |

Required
steel area including consideration of maximum bar spacing, assuming
No. 5 bars |
|||

Column strip negative (As_{x,col,neg}) |
0.342 in^{2} / ft |
0.373 in^{2} / ft |
8.3%^{a} |

Column strip positive (As_{x,col,pos}) |
0.266 in^{2} / ft |
0.266 in^{2} / ft |
0.0% |

Middle strip negative (As_{x,mid,neg}) |
0.266 in^{2} / ft^{} |
0.266 in^{2} / ft |
0.0% |

Middle strip positive (As_{x,mid,pos}) |
0.266 in^{2} / ft |
0.266 in^{2} / ft |
0.0% |

Slab
Reinforcement |
|||

Column strip negative | #5 @ 9” o.c. | ||

Column strip positive | #5 @ 14” o.c. | ||

Middle strip negative | #5 @ 14” o.c. | ||

Middle strip positive | #5 @ 14” o.c. | ||

Two-way shear
strength |
|||

Shear force (V_{u}) |
69.6 kips | 70 kips | 0.6% |

Design concrete shear strength (φV_{c}) |
137.8 kips | 137.4 kips^{b} |
0.3% |

One-way shear
strength |
|||

Shear force (V_{u}) |
N/A | 32 kips | 0.6% |

Design concrete shear strength (φV_{c}) |
N/A | 88.5 kips | 0.3% |

## Comparison Notes

** ^{a}**Since the bars running in the X-direction are on the outside, the
depth, d = 7” - 0.75” - ⅝”/2 = 5.93”. The ACI example uses the average effective
depth,

*d*, of 5.6”, which should only be used when reviewing shear. This leads to the discrepancies in the results.

** ^{b}**The design example provides the shear stress, so once the stress
is multiplied by the effective depth,

*d*, and the perimeter of the critical section,

*b*the shear strength is displayed.

_{o}## Conclusion

Upon reviewing the results above, the analysis of the reinforced concrete two-way slab within Tedds matches the ACI Design Example 1 (apart from minor differences due to rounding and precision).