Shear Forces and Bending Moments in Beams

[mit_hacker]

Homework Statement

(Q) A beam 4m long is supported at the left hand side by a hinge support and on the right by a roller support. It is under a non-uniform load intensity throughout by a load intensity given by:

w = 25Cos(pi x/8)kN/m.

Write equations for the shear force and the bending moments for any section of the beam.

Homework Equations

F= -∫▒w
M=-∫▒F

The Attempt at a Solution

I can easily apply the above formulas and integrate.

The shear force comes to -200/π Sin(πx/8).
Similarly, the Moments come to -400/π^2 Cos(πx/8)

But at the back of the book, there is also the constant term along with the term obtained by the integration.

Can someone please help me to calculate them. How did they come about?

 

[PhanthomJay]

Homework Statement

(Q) A beam 4m long is supported at the left hand side by a hinge support and on the right by a roller support. It is under a non-uniform load intensity throughout by a load intensity given by:

w = 25Cos(pi x/8)kN/m.

Write equations for the shear force and the bending moments for any section of the beam.

Homework Equations

F= -∫▒w
M=-∫▒F

The Attempt at a Solution

I can easily apply the above formulas and integrate.

The shear force comes to -200/π Sin(πx/8).
Similarly, the Moments come to -400/π^2 Cos(πx/8)

But at the back of the book, there is also the constant term along with the term obtained by the integration.

Can someone please help me to calculate them. How did they come about?

You've got to look at the boundary conditions to get the constants. What do you know about the bending moment at each support?

 

[mit_hacker]

Ahhhhhhhhh!

That was so simple?:rofl:

I can't believe that I didn't see it! Thanks a lot for your help PhantomJay!