Here is a question from structures 2 but i'm sure first years will get it right.
Question: Which BMD is the correct for the cantilever beam shown?
Solution: Lets start from the point where the load is applied. It might help if you sketch the problem and mark a line across the structure showing the direction of the applied load
- The bending moment will increases linearly when we move away from the load ( we are moving left) - all diagrams show this!
- As we move down the vertical member on the left hand-side the moment is constant as we are always the same perpendicular distance from the direction of the load.
- Note that at the corner the BMD are both on the outside as there is tension on this face.
- As we move along the bottom beam ( left to midpoint) we get closer and closer to the direction of the applied load so the moment decreases linearly
- As we go past the midpoint on the bottom beam the bottom beam we get further away form the direction of the applied load and hence the moment increases linearly-only diagrams C & D show this.
- If we move up the vertical member on the right hand side we stay a constant perpendicular distance form the direction of load and so the moment is constant - the moment is on the inside of the member as this is the face where we have tension. – Only diagram D shows this.
Lastly as we move along the top beam (right to left) the moment must become less negative and reach zero at the point where we are inline with the direction of load, when we have travelled past this towards the support the moment the moment increases and becomes positive indicating a region of hogging bending ( tension on top face) near the support