Reinforced Concrete Beam Design Example

Statement

A single reinforced rectangular beam has a width of 11” and effective depth of 18”. If f’c = 3ksi and fy is 40ksi. Calculate the moment capacity Mn, if As = 5in2

Given

1. Width of beam = b = 11”
2. Effective depth of reinforced concrete beam = d = 18”
3. f’c = 3 Ksi
4. Fy = 40 ksi
5. A= 5in2

Required

Moment capacity of the reinforced concrete beam = ?

Solution

Given problem is the analysis case. For understanding the solution, one must should have ACI 318M-08 building code.

find steel ratio by using formula defined by ACI 318M-08

Ρ = AS/bd = 5/(11*18) =  0.025

Now find respective value of “R”  from Graph A.1a (Moment capacity of Rectangular beam)

Steel ratio vs R graph (Design Aids)

$R = frac{M_{n}}{bd^{2}}$

R = 800 Psi

$M_{n} = {bd^{2}}*{R}$

Mn =2851.2 K-in.

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