Maximum Tensile Strength

Question

Given a concrete beam (b = 10 in.; h = 25 in.) with flexural reinforcement at the bottom, the transformed

moment of inertia is It=14,740 in^4, and the location of the neutral axis from top of the beam is y=13.2 in.

Assuming an elastic behavior, what is the maximum tensile stress in the concrete (bottom face) when M =

50 kip-ft?

Answer 1

Hey, thanks for posting the question, this problem is related to Moment equation (M/I)=(\sigma/y)=(E/R); where sigma is the Tensile Stress.

In the given problem, we have to bring all inputs to a consistent unit system (lb and in.)

M= 50kip-ft = 50 x 1000 x 12 = 600,000 lb-in

I=14740in^4

y (or NA from Bottom) = (25 in. - 13.2 in.) = 11.8 in.

So, plugging these numbers in the moment equation, Sigma = (M/I) x y

we get sigma = (600,000/14740) x (11.8) = 480.3 psi.