The picture shows a two-dimensional free body diagram of a truss with a pin joint at one end.
The free body diagram at the pin joint should show
a. no forces at the joint
b. only parallel force component
c. only perpendicular force component
d. both parallel and force components
No forces at the joint
The correct answer is d. both parallel and force components.
In a free body diagram of a pin joint, we should include both parallel and perpendicular force components. The pin joint allows for forces to act in multiple directions because it can support both parallel and perpendicular forces. Therefore, the free body diagram at the pin joint should show both parallel and perpendicular force components acting on it.
To determine the correct answer, we need to understand the concept of a free body diagram. A free body diagram is a simplified illustration that represents an object or a system and all the external forces acting upon it. It helps us analyze and solve problems related to the equilibrium of forces.
In the case of a truss with a pin joint, a pin is a type of joint that allows rotation but prevents translation in any direction. When drawing a free body diagram at the pin joint, we need to consider the forces acting on the joint to maintain equilibrium.
Now, let's look at the options:
a. No forces at the joint: This answer is incorrect because in a pin joint, there are usually forces acting on it to maintain equilibrium.
b. Only parallel force component: This answer is incorrect because a pin joint does not restrict forces to act only in parallel.
c. Only perpendicular force component: This answer is incorrect because a pin joint does not restrict forces to act only perpendicular to the joint.
d. Both parallel and force components: This answer is correct. A free body diagram at a pin joint should include both parallel and perpendicular force components. This is because in order to maintain equilibrium, forces acting on the pin joint may have both a parallel (along the direction of the truss) and perpendicular (normal to the truss) component.
To create the free body diagram at the pin joint, draw arrows to represent the forces acting on the joint, showing both the parallel and perpendicular components as needed. Ensure that the sum of all forces acting on the joint is equal to zero to maintain equilibrium.
Therefore, the correct answer is d. Both parallel and force components.