Structures at Bath

Keeping the concepts fresh

Topic: ST1

Question 18

📥  Beams, ST1

Here is a question from  structures 2 but i'm sure  first years will  get it  right.

question18

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

  1. The  bending moment will increases  linearly when we move away from the load ( we are moving  left) - all  diagrams  show  this!
  2. 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.
  3. 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
  4. 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.
  5. 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

 

Question 17

📥  Beams, ST1

Okay,  this is definitely a simple question to start with.

Picture1

Question:  If x= L/3 what is the vertical reaction at support A?

Solution: To solve this  we  need to take moment about  a  point that we know  the  moment for. Point  B  is a pin  support for must have  zero moment.

  1. So taking  moments about B we  have acting clockwise the moment  generated  by the vertical reaction A (Va * L).
  2. This must be equal to the anticlockwise moments  generated  by  the  applied   loads, which are  equal to
  • P*(2L/3) for the moment from the point  load
  • (wL/2)*(L/4) for the uniform loading - the first  term in brackets is the total load the  second term is the lever arm to the centre of the load.

3. equating  clockwise and  anticlockwise and dividing  by L we get Va=(2P/3) +(wL/8)