# How to find reaction forces in trusses?

I'm stucked at trying to find the vertical reaction at top and bottom constraint, i know how to do the rest. Can you show me how?

First you should check if the truss is statically determinate. In one of your comments you said, that only the bottom support has a vertical reaction. I assumed that all members are joint-connected, thus are not able to transfer any moment.

There's a formula to determine, if a truss is statically determinate: $$n= r+s-2k$$ $r$ … number of support reactions $(3)$
$s$ … number of members $(7)$
$k$ … number of nodes $(5)$
$$\to n=3+7-2\cdot5 =0$$ thus the truss is statically determinate, which means you can find the support reactions. $$\sum H = A_H+B_H =0$$ $$\sum V= B_V =Q$$ $$\sum M(B)=A_H\cdot a + Q\cdot b =0 \qquad \star$$ The $\star$-equation is the moment equation, which can be defined for any point, I chose to establish the moment equation with respect to point $B$, because the forces $B_H$ and $B_V$ do not produce any moment wrt point $B$, thus they cancel out. With these three equations you can solve for all three support reactions and then find the member reactions.

• No load can be in the far left member as it is supported at both ends. Axial force is directly proportional to change in length; if there can be no change in length (due to both ends being fixed in position) then there can be no axial force.

• Therefore resolving vertically at the top support, the vertical reaction is equal to the shear in the horizontal member. If we're assuming axial loads only for truss behaviour, then there is no shear and hence no vertical reaction

• Therefore the whole vertical reaction is taken by the lower support

• Sorry i cannot understand. But your answer is right, only the bottom support has vertical reaction. I tried calculating, by assuming there are vert reaction at both, i couldn't solve by this assumption. Mar 27, 2017 at 13:47
• "If we're assuming axial loads only for truss behaviour, then there is no shear and hence no vertical reaction" At the node of top support: vertical reaction = truss force of the bar between two supports? If no then why? If yes how to solve? Mar 27, 2017 at 13:55
• "No load can be in the far left member" Why? Mar 27, 2017 at 14:09
• Andy T's argument is that it makes no difference if you remove the left hand vertical member from the truss. After you do that, you can find the horizontal and vertical reactions at the top (the vertical is zero) and then find the reactions at the bottom. But personally, I would say that with four constraints this is simply an indeterminate problem, The sum of the two vertical reactions equals the load, but you can't find values for each vertical reaction separately unless you make some arbitrary assumptions (which is what Andy T did). Mar 27, 2017 at 14:18
• @alephzero "you can find the horizontal and vertical reactions at the top (the vertical is zero) and then find the reactions at the bottom". by method of joint, vertical reaction on top= far left member, i can't solve it "The sum of the two vertical reactions equals the load, but you can't find values for each vertical reaction separately unless you make some arbitrary assumptions" I need to assume the left member is zero for the fact that it is between two supports first before i can solve? Mar 27, 2017 at 14:23