# Bending moments

1. Mar 30, 2008

### LiamFermoylel

For a light 5m beam carrying a central
point load of 20 kN, calculate:

a) the maximum shear force (iv got that)
b) " " bending moment

im stuck on the bending moment, i cant remember how to work it out.

2. Mar 30, 2008

### Staff: Mentor

See if this example helps -
http://physics.uwstout.edu/StatStr/statics/Beams/bdsne47b.htm [Broken]

http://physics.uwstout.edu/StatStr/statics/Beams/beam41.htm#Topic%204.1%20Shear%20Forces%20I [Broken]

Last edited by a moderator: Apr 23, 2017 at 11:54 AM
3. Apr 3, 2008

### handsomecat

If you've worked out the expression of the Shear Force, just integrate it with a minus sign outside to get the Bending Moment.

$$M_{xz} = - \int F_{xy} dx$$

To double-check your answer, usually textbooks that describe beam theory will provide solutions to standard beam deflection problems. You can differentiate the expression for the deflection twice to get the expression for the bending moment.

$$M_{xz} = EI \frac{d^2v}{dx^2}$$

4. Apr 4, 2008

### brentoat

if the beam is simply supported, just solve for the reactions and multiply by half by the beams length. In your case it will be 10x5/2 = +25kNm

5. Apr 6, 2008

### LiamFermoylel

thanks iv got it. =)