Concept explainers
Find the forces in the members of the truss.
Explanation of Solution
Given information:
Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.
- For summation of forces along x-direction is equal to zero
- For summation of forces along y-direction is equal to zero
- For summation of moment about a point is equal to zero
Method of joints and section.
The negative value of force in any member indicates compression (C) and the positive value of force in any member indicates Tension (T).
Calculation:
Show the free body diagram of the truss as shown in Figure 1.
Refer Figure 1.
Consider the horizontal and vertical reactions at A are
Consider the vertical reaction at E is
Take the sum of the forces in the horizontal direction as zero.
Take the sum of the forces in the vertical direction as zero.
Take the sum of the moment about point A as zero.
Substitute
Calculate the value of the angle
Consider a section a-a passing through the members BC, CG, and JK.
Show the portion of the truss to the left of the section a-a as shown in Figure 2.
Refer Figure 2.
Take the sum of the moment about C as zero.
JOINT A.
Show the joint as shown in Figure 3.
Refer Figure 3.
For Equilibrium of forces,
JOINT J.
Show the joint as shown in Figure 4.
Refer Figure 4.
For Equilibrium of forces,
Substitute
JOINT F.
Show the joint as shown in Figure 5.
Refer Figure 5.
For Equilibrium of forces,
JOINT G.
Show the joint as shown in Figure 6.
Refer Figure 6.
For Equilibrium of forces,
JOINT E.
Show the joint as shown in Figure 7.
Refer Figure 7.
For Equilibrium of forces,
JOINT K.
Show the joint as shown in Figure 8.
Refer Figure 8.
For Equilibrium of forces,
Add Equation (3) and (4).
Subtract Equation (4) and (3).
JOINT I.
Show the joint as shown in Figure 9.
Refer Figure 9.
For Equilibrium of forces,
JOINT H.
Show the joint as shown in Figure 10.
Refer Figure 10.
For Equilibrium of forces,
Add Equation (5) and (6).
Subtract Equation (5) from Equation (6).
JOINT B.
Show the joint as shown in Figure 11.
Refer Figure 11.
For Equilibrium of forces,
JOINT D.
Show the joint as shown in Figure 12.
Refer Figure 12.
For Equilibrium of forces,
Show the forces in the members of the truss as shown in Table 1.
| Member | Force (k) |
| DC | |
| BC | |
| HD | |
| HC | |
| IH | |
| ID | |
| KH | |
| KI | |
| ED | |
| EI | |
| GB | |
| GC | |
| FG | |
| FB | |
| JF | |
| JG | |
| AB | |
| AF | |
| JK |
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