The simply supported notched bar is subjected to two forces

The simply supported notched bar is subjected to two forces P. Determine the largest magnitude of P that can be applied without causing the material to yield. The material is A-36 steel. Each notch has a radius of r = 0.125 in.

Solution

force = P (force)

Maximum bending moment M in the bar= P*20 (force.in)

bar crossection area at notch= 1.25² * pi /4 = 1.227 (in²)

bar section modulus = 1.25³ * pi / 32 = 0.1917 (in³)

yield strength of A36 at room temp= s (force/in²) = 36000 PSI

Nominal stress due to bending = M/Z = 20P/0.1917 = 104.33P (force/in²)

Now to stress concenntration factor K_t from the table of round bar in bending case for the given size of bar & notch = 1.95

So, actual stress at notch = Nominal stress * 1.95 = 104.33P * 1.95 = 203.4435P (force/in²)

Largest magnitude of P that can be applied without yielding = s / 203.4435 = 36000/203.4435 = 176.95 pound