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To solve this problem,
we need to start by remembering the support conditions of the two supports on the beam
the first on the left hand side of the beam is a pin joint at point A and this type of support has both a horizontal
and vertical reaction force,
denoted here by the arrows VA and HA.
On the right end of the beam at point B is a roller support which has only a vertical reaction force denoted by VB
For this problem we required to solve all the reaction forces at the supports and this can be achieved
using equilibrium equations.
The first necessary equilibrium equation states that the sum of all forces in a horizontal direction are equal to zero
So it can be seen that in order to balance the 30 kN force acting in this direction
HA must be equal to 30 kN in the opposite direction.
In a similar way,
it can be seen that in order to balance the 10 kN download force acting on the beam
the sum of VA plus VB
must be equal to 10 kN acting in the opposite direction
Because of the symmetry of the loading and supports, in this case we can assume that VA is equal to VB
Therefore,
2VA
must be equal to 10 kN.
Therefore,
VA = VB
equals 10 kNs divided by 2.
which is equal to five kNs
As a final check and to verify our calculations
we can calculate the sum of moments about any point on the beam and it should be equal to zero.
In this case, lets take the sum of all moments about Point A.
so we have a 10kN force
acting 3.5 m from Point A
and we also have a 5kN force acting 7m from Point A, at the opposite end of the beam
and that's also acting in the opposite direction
so it's got to be negative.
And this equals zero.
When we solve all of this we find that
the moments about Point A are in fact equal to zero,
satisfying the equilibrium equation and confirming that our calculations are likely to be correct.
Congratulations if you were able to do this on your own.
Make sure that you are very familiar with these processes as the use of equilibrium equations in solving support reactions
is used very extensively throughout the applications within this course and even further into your engineering careers.