Solving a Slab Design for Proper Thickness & Reinforcement

[raiderUM]

1. Homework Statement [

Here is the question that I am struggling with. I am told that my answers are not correct, but I do not know where I went wrong? Any suggestions would help greatly! I attached a paper with all my work shown. Thanks!


A solid one-way, continuous slab is used to span as a floor in a manufacturing facility. The structure is designed with columns creating 25’ by 50’ bays. Concrete girders span the 50’ direction and 18” wide concrete beams span the 25’ direction. The beams frame into the columns and into the girders at 1/4 points - center to center. The structure has a superimposed live load of 150 psf and a dead load of 52.5 psf in addition to the dead load of the slab. Given the following data: f y = 60 ksi f c' = 4,000 psi
Use a/d revised = 0.400

a. Determine the slab thickness -- use actual thickness -- No rounding.

b. Determine the spacing of the #4 reinforcing steel at midspan location in the typical interior span. Moment coefficient = + 1/16

b. What is the area of temperature steel required per foot of slab width?

c. Draw a sketch showing the placement of the reinforcing you specified.


Slab thickness “t” ( actual calculated – NO roundoff ) ____5.5______”

Size and spacing of midspan--interior span reinforcing # 4 @ __13___ “ c/c

Area of temperature steel __.1782_____ in2 / foot of width # 3 @ ___7___ ‘” c/c

Homework Equations

The Attempt at a Solution

View attachment question2.pdf

 

[KataKoniK]

First, I started by calculating the tributary area for each bay, which is 25’ x 25’. Then, I calculated the total dead load for each bay by multiplying the tributary area by the dead load of 52.5 psf. This gave me a dead load of 65,625 lbs for each bay. Next, I calculated the total live load for each bay by multiplying the tributary area by the live load of 150 psf. This gave me a live load of 187,500 lbs for each bay.

Using the given data, I calculated the required moment capacity for the beams at midspan using the equation M = (wL^2)/8, where M is the moment capacity, w is the total load, and L is the span length. This gave me a required moment capacity of 1,171,875 ft-lbs for each bay.

Next, I calculated the required moment capacity for the girders at midspan using the equation M = (wL^2)/12, where M is the moment capacity, w is the total load, and L is the span length. This gave me a required moment capacity of 1,757,812.5 ft-lbs for each bay.

To find the required slab thickness, I used the equation t = (M/bd^2)(1/(0.85f'c))^(1/2), where t is the slab thickness, M is the required moment capacity, b is the width of the beam, d is the effective depth of the slab, and f'c is the compressive strength of the concrete. Using the given data and a/d revised = 0.400, I calculated a slab thickness of 5.5 inches.

To determine the spacing of the reinforcing steel at midspan, I used the equation s = (0.9fyAs)/(0.85f'cbd), where s is the spacing, fy is the yield strength of the steel, As is the area of steel required, f'c is the compressive strength of the concrete, b is the width of the beam, and d is the effective depth of the slab. Using the given data, I calculated a spacing of 13 inches for #4 reinforcing steel.

The area of temperature steel required per foot of slab width can be calculated using the equation As = (0.0018bt)/s, where As is the area