Thread: Bending moment for a Beam

a simply supported beam of a span 8.0m carriers a design load of 30kN/m.

a)write an expression for the bending moment, M, at a section which is at a distance of x from a support

b)Express the engineers bending eqaution as a differential equation relating the vertical deflection, y, of the beam to the bending moment at x.

c)obtain the particular soultion of this equation.

i could do with some help especially part b and c

for the expression i have:

Mx = 120-10x/2

Mx= 120x-5x sqaured this may not be correct.

any help be great thank you

Originally Posted by size

a simply supported beam of a span 8.0m carriers a design load of 30kN/m.

a)write an expression for the bending moment, M, at a section which is at a distance of x from a support

b)Express the engineers bending eqaution as a differential equation relating the vertical deflection, y, of the beam to the bending moment at x.

c)obtain the particular soultion of this equation.

i could do with some help especially part b and c

for the expression i have:

Mx = 120-10x/2

Mx= 120x-5x sqaured this may not be correct.

any help be great thank you

Dear size,

If we denote the shearing force by S and the bending moment by M, using the differential equations for a beam we have,

where w is the weight per unit length.

A is an arbitrary constant.

Also,

Using the boundary conditions



Therefore,

The bending moment and the vertical deflection is related by the Euler-Bernoulli equation,



Substituting the value obtained for M and using the boundary conditions you can obtain,



Hope this will help you.