Find the maximum allowable bending moment and the maximum allowable centre-point load for a beam spanning3.0m?

Question

if the maximum permissible stress is 5.5 N/mm2 and the beam section is 75 mm by 225 mm deep.

Answer 1

It looks like you need to employ the flexure formula.

Sigma=Mc/I

Sigma = stress

M=bending moment

c=distance from neutral axis to beam surface

I=area moment of inertia

The maximum moment occurs at the center of the beam.  Max stress is at the surface (y=c).

Then:

M=FL/2

c=h/2

I=(bh^3)/3

Substitute and solve for F.

Answer 2

The maximum bending moment of a simply supported beam with a concentrated load P at mid-span is;

M = PL/4  

Where;

M = the bending moment in N -m

P = the concentrated load in N

L = unsupported span of the beam

The bending stress of a beam with a rectangular section is;

s =(6M/bd^2)1000

Where;

M = the bending moment in N-m

s = the bending stress in N/mm^2

b = the width of the beam in mm

d = depth of the beam in mm

Thus for the given allowable stress and beam section, The maximum allowable bending moment of the 3 meter beam is;

M= 5.5 x 75 x 225^2/(6 x 1000) = 3480.46875 N-m

The allowable concentrated load placed at mid-span would therefore be;

P = 4M/L = 4 x 3480.46875/3 =4640.625 N