# Truss Analysis Problem

In this case, L, theta and P are given, there will be 4 reactions at the wall? (2 horizontal and 2 vertical).

\begin{align} \sum F_v &= 0 \therefore F_{v,B} + F_{v,A} = P \\ \sum F_h &= 0 \therefore F_{h,B} = F_{h,A} \end{align}

What will be the tensile stresses along AB and AC?

However, I do not know how to obtain the other 2 equations to solve all the reaction forces at the wall and the tensile stresses? Can anyone please help? One of those equations are from the moment?

As member AB is orthogonal to Point C it cannot impart any vertical reaction, hence Point B provides the only vertical support, and hence has to have a vertical reaction equal to P.

to find point B horizontal reaction, we set the sum of moments about point C equal to zero.

\begin{align} \sum M_C &=0 \\ -PL +F_{h_{B}}H &=0 \\ F_{h_{B}} &= PL/H\text{ pointing left} \\ \therefore F_{h_{C}}&=PL/H\text{ pointing right} \end{align}

tensile stress along AB is: \begin{align} T&=\dfrac{\sqrt{F_{h_{B}}^2+ F_{v_{b}}^2}}{A} \\ &= \dfrac{\sqrt{(PL/H)^2+P^2}}{A} \end{align} And I let you do the stress on AC.

• @AndyT, please! sometimes we just miss the other guys' point. As you may know there is many guys who may not have clue and once I saw first you mistook the annotation for supports, I thought you where one of them, my apologies. May 30 '19 at 2:52

@AndyT and @kamran explained how to technically solve this question. I would like to add a short comment about the thing seemed to confuse you the most.

Indeed, there are 4 reactions in this problem. If the triangle was made of a solid body, you would deal with a statically indeterminate problem and find it quite hard to resolve those reactions. However, since we are dealing with a truss, you should examine carefully whether its statically determinate or not:

• The number of unknowns is 6 - the above mentioned 4 reactions + axial forces along the truss members
• The number of equation is also 6 - 3 pin joints, each has 2 equilibrium equations (in X and Y directions)
• Since the number of unknown equals the number of equations - you deal with statically determinate problem and can resolve all the reactions without dealing with the truss stiffness

Resolve at point A, remembering that in a truss the members only carry axial loads:

• Vertically P = FAB * sin theta
• Horizontally FAB * cos theta + FAC = 0

This gives you the member forces without even needing to worry about the reactions (though they're pretty trivial once you've worked out the member forces).