Find the design moment capacity of the concrete beam

The beam is 14 inches wide and 20 inches in height. It does have a dimension given 2.5 inches to the reinforcement and it has number 5 bars.

Concrete specified strength = 3000 PS

Yield strength = 60000 PS

Ø_b is the bending reduction factor

We have to know the M_n where M_n is the nominal moment capacity.

M_n = A_s x Yield strength x (d – a/2)

[Where, a = A_s x Yield strength/ 0.85 x specified strength of concrete x width (b)

Area of steel = 4 x 0.31 in² x 60000 PS1/ 0.85 x 3000PS1 x 14 inches = 2.08 inches]

M_n = (4) (.31 inches²) x 60000(17.5 – 2.08/2)  

M_n = 1225 inch.K

When Divided it by 12 inches per foot, it gives M_{n ­}= nominal capacity = 102.1 foot K

We are going to assume that Ø_b is equal to 0.9

Then, Ø_b M_n = 0.9 x 102.1 = 91.9 Foot K

Validate Ø_b = 0.9

In order for that to be true, strain ε_s > 0.005

We can really calculate that, ε_s = ε_c (d – c)/c

Where c = a/ β₁ = 2.08/0.85 = 2.45

Then, ε_s = 0.003(17.5 – 2.45)/2.45 = 0.018 > 0.005

And therefore, our assumption is true.

Other things to check are ρ_max and ρ_min    

Watch the following video for more details.

Video Source: Gladys Jean