Q. 11: What is relation between the maximum tensile stress and the maximum compressive stress in any section of beam?
Sol.: Let us assume inverted angle section of the beam as shown below:
In case of beam, the maximum compressive stress will be set up in the topmost layer, and maximum tensile stress will be set up in the bottom most layer due to bending.
σc = maximum compressive stress
σt = maximum tensile stress
yC = distance of topmost layer from neutral axis N-A
yt = distance of bottommost layer from neutral axis N-A.
Then, according to the bending equation,
M/I = σ /y
σ = maximum bending stress,
y = distance of the layer at which the maximum bending stress occurs, distance being measured from neutral axis,
M = maximum moment of resistance
= maximum B.M.
I = Moment of inertia (M.I.) of the section of the beam about the neutral axis.
Equate both we get;