I was wondering if anyone could help explain how the Vertical reactions for the following structure were calculated.
I am able to calculate the Horizontal reactions. It is the vertical reactions that I am struggling with.
I do the following:-
Sum Vertical Reactions = 0
Va + Vd - 230 = 0
If I take moments about D I get:-
Sum of Moments about Support D = 0
(5.4*230) + (Ha*1.8) = 0
Ha = -690kN
I just don't know how to calculate 230kN at support A.
How to Calculate Reactions at Supports?
1. Let the sum of moments about a reaction point equal to ZERO (ΣM = 0)
All we need to know about moments at this stage is that they are equal to the force multiplied by the distance from a point (i.e. the force x distance from a point).
Consider a simple example of a 4m beam with a pin support at A and roller support at B. The free-body diagram is shown below where Ay and By are the vertical reactions at the supports:
We firstly want to consider the sum of moments about point B and let it equal zero. We have chosen point B to prove this can be done at either end of the beam (provided it is pin supported). However, you could just as easily work from point A. So, now we sum the moments about point B and let the sum equal 0:
NOTE: The sign convention we have chosen is that counter-clockwise moments are positive and clockwise moments are negative. This is the most common sign convention but it is up to you. You must ALWAYS use the same sign convention throughout the whole problem. Always use the same sign convention from the start. We now have our first equation. We need to solve another equation in order to find By (the vertical reaction force at support B).
2. Let the sum of vertical forces equal to 0 (ΣFy = 0)
Sum the forces in the y (vertical) direction and let the sum equal zero. Remember to include all forces including reactions and normal loads such as point loads. So if we sum the forces in the y-direction for the above example, we get the following equation:
NOTE: Again we stuck to a sign convention which was to take upward forces (our reactions) as positive and downward forces (the point load) as negative. Remember the sign convention is up to you but you must ALWAYS use the same sign convention throughout the whole problem.
So there we have it, we have used the two above equations (sum of moments equals zero and sum of vertical forces equals zero) and calculated that the reaction at support A is 10 kN and the reaction at support B 10kN. This makes sense as the point load is right in the middle of the beam, meaning both supports should have the same vertical forces (i.e. it is symmetric).