Equilibrium in roof trusses refers to the balance of forces acting on the truss structure. In order for a truss to be stable and able to support the weight of the roof, all the forces acting on it must be in equilibrium. This means that the sum of all the forces acting on the truss must be equal to zero.
To answer your first question, we need to analyze the forces acting on each member of the truss. In this case, we have three members: AB, BC, and AC. Each member will have a force acting on it, either in tension or compression. Tension is a pulling force, while compression is a pushing force. The direction of the force acting on a member will depend on its orientation in the truss.
To determine which members are in tension and compression, we can use the method of joints. This method involves analyzing the forces acting at each joint in the truss. Starting at joint A, we can see that there are two forces acting on it: the force in member AB and the force in member AC. Since the truss is in equilibrium, the sum of these forces must be equal to zero. This means that the force in member AB must be equal and opposite to the force in member AC. Since we know that the force in member AB is acting downwards, the force in member AC must be acting upwards, making it a compression force.
Moving on to joint B, we can see that there are three forces acting on it: the force in member AB, the force in member BC, and the force from the roof. Again, using the principle of equilibrium, we can determine that the force in member AB is equal and opposite to the force in member BC. Since the force in member AB is acting downwards, the force in member BC must be acting upwards, making it a compression force. The force from the roof is acting downwards, making it a tension force.
Finally, at joint C, we can see that there are two forces acting on it: the force in member BC and the force in member AC. Using the same method, we can determine that the force in member BC is acting downwards, making it a compression force, and the force in member AC is acting upwards, making it a tension force.
To answer your second question, we need to find the magnitude of the force in member AC. This can be done using the equations of equilibrium, which state that the sum of all the forces