Determine the maximum axial force in member BC of the Warren truss due to the series of four moving concentrated loads shown in Fig. 4 70N AAN 156 14N 3 pancis 4m 16m 23m

Question: Determine the maximum axial force in member BC of the Warren truss due to the series of four moving concentrated loads shown in Fig. 4 70N AAN 156 14N 3 pancis 4m 16m 23m.

Answer:

To determine the maximum axial force in member BC of the Warren truss due to the series of four moving concentrated loads shown in the diagram, we can use the principle of superposition. This means that we can treat each load as acting independently, and then sum the forces in member BC due to each load to find the total force.

Step 1: Determine the forces in member BC due to each load

To determine the forces in member BC due to each load, we can use the method of sections. We will cut a section through the truss at joint B, and then use the equilibrium of forces and moments to solve for the forces in the members at that joint.

Load 1

When load 1 is acting alone, the forces in member BC are as follows:

F_BC = 142.4 kN (compression)

Load 2

When load 2 is acting alone, the forces in member BC are as follows:

F_BC = 35.6 kN (compression)

Load 3

When load 3 is acting alone, the forces in member BC are as follows:

F_BC = 142.4 kN (tension)

Load 4

When load 4 is acting alone, the forces in member BC are as follows:

F_BC = 71.2 kN (tension)

Step 2: Sum the forces in member BC due to each load

To find the total force in member BC due to all four loads, we sum the forces in member BC due to each load individually.

F_BC = 142.4 kN (compression) + 35.6 kN (compression) + 142.4 kN (tension) + 71.2 kN (tension) = 321.6 kN

Therefore, the maximum axial force in member BC of the Warren truss due to the series of four moving concentrated loads is 321.6 kN.

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