Question

Draw moment and shear diagrams for the structures shown below. q= 1.0km q=1.0km Mo=12.0k-ft 8 ft 4 t2 RB 4 ft Rc 150 lb Tt 300 Ib -ft -12 ft 4. 500 lb/

Answer 1

The tension in the cable and the force at the axle of a crane's boom can be calculated using the free-body diagram and static equilibrium conditions, taking into account the weight of the load and the boom.

Step-by-step explanation:

To calculate the tension in the cable and the force at the axle for a crane's boom lifting a load, it is essential to consider the forces and moments acting on the system. We start with the static equilibrium conditions which state that the sum of forces and moments for a body at rest must be zero.

Analysis for Tension (T)

Consider the boom AB with a 12.0-m length and a 3000-kg load at its end. Assuming gravity acts downward at 9.81 m/s², the force due to the load is F = m x g = 3000 kg x 9.81 m/s². The center of gravity of the boom, which weighs 1000 kg, is located in the middle at 6.0 m from point A. Thus its force is also F = m x g = 1000 kg x 9.81 m/s². For the system to be in equilibrium, the tension in the cable must balance out these forces.

Force at Axle A

To calculate the force at axle A, one must consider the torques around a pivot point, typically chosen at the point where the tension or the force at the axle is being calculated. By summing the moments around axle A and setting them equal to zero, you can solve for the unknowns. The force of the weight of the boom and the load creates a counterclockwise moment, while the tension creates a clockwise moment.

By using these principles and the appropriate free-body diagrams, the calculations will yield the values for the tension T in the cable and the force at the axle A.

Answer 2

To draw the moment and shear diagrams for the given structure, analyze the forces and torques acting on the structure. The moment is the area under the shear diagram, and the shear is the sum of the forces to the left of a point. There are two point loads and a distributed load in the structure.

Step-by-step explanation:

To draw the moment and shear diagrams for the given structure, we need to analyze the forces and torques acting on the structure.

First, let's start with the moment diagram. The moment at any point is the area under the shear diagram up to that point. We can see that there are two point loads at 8ft and 12ft from the left support. The moment at the left support is zero. Between the two point loads, the moment is constant. After the second point load, the moment decreases linearly until it reaches zero at the right support.

Next, let's move to the shear diagram. The shear at any point is equal to the sum of the forces to the left of that point. We can see that there are two point loads and a distributed load. The shear at the left support is zero. Between the two point loads, the shear increases linearly. At the first point load, there is a sudden drop in shear due to the load. Between the two point loads, the shear remains constant. At the second point load, there is another sudden drop, and after that, the shear is zero until the right support.