# Thread: Bending moment for a Beam

1. ## 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

2. 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,

$\frac{dS}{dx}=w$ where w is the weight per unit length.

$\frac{dS}{dx}=30\Rightarrow s=30x+C$ A is an arbitrary constant.

Also, $\frac{dM}{dx}=-S\Rightarrow \frac{dM}{dx}=-30x-C\Rightarrow M=\frac{-30x^2}{2}-Cx+D$

Using the boundary conditions $x=0;~M=0\Rightarrow D=0$

$x=8;~M=0\Rightarrow C=-120$

Therefore, $M=-15x^2+120$

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

$M=(EI)\frac{d^{2}y}{dx^2}$

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

$y=\frac{1}{(EI)}\left(-\frac{5x^4}{4}+20x^3-640x\right)$