Civil Engineering PE Structural Analysis of Trusses Questions and Answers — Questions and Answers
Question 1: Which of the following is NOT a standard assumption made in the analysis of an ideal truss?
- Members are connected by rigid, moment-resisting joints. (Correct answer)
- Members are connected by frictionless pins.
- All loads and support reactions are applied only at the joints.
- The weight of the individual members is negligible.
Correct answer: Members are connected by rigid, moment-resisting joints.
The fundamental assumption for an ideal truss is that members are connected by frictionless pins, which cannot resist moments. This simplifies the analysis by ensuring that members are only subjected to axial forces (tension or compression). Rigid, moment-resisting joints are characteristic of frame structures, not ideal trusses.
Question 2: For the truss shown, which member is a zero-force member? (Note: A is a pin support, E is a roller support). [Image of a standard Fink roof truss with a vertical load at joint B. Joints are labeled A-G from left to right, bottom to top. Bottom chord: A, F, G, E. Top Chord: A, B, C, D, E. Webbing: BF, BG, CG, CD, DG, DH. Load is at B. A is pin, E is roller.]
- Member AB
- Member FG
- Member CG
- Member DH (Correct answer)
Correct answer: Member DH
A zero-force member can be identified by inspection using two primary rules. Rule 2 applies at joint H: If three members form a joint at which no external load is applied, and two of the members are collinear, then the third member (the non-collinear one) is a zero-force member. At joint H, members GH and HE are collinear, and no external load is applied. Therefore, member DH is a zero-force member.
Question 3: An engineer needs to determine the force in member CD of the Pratt truss shown below. The truss is subjected to several vertical loads on its top chord. Which analysis method is generally the most direct and efficient for finding the force in only member CD? [Image of a multi-panel Pratt truss with vertical loads on the top chord.]
- Method of Joints
- Virtual Work Method
- Method of Sections (Correct answer)
- Moment Distribution Method
Correct answer: Method of Sections
The Method of Sections is the most efficient technique when the forces in only a few specific members, particularly those near the center of a large truss, are required. By making a vertical cut through members CD, CJ, and IJ, the engineer can treat the left or right portion as a rigid body and use the equations of equilibrium (specifically, summing moments about joint J) to solve directly for the force in member CD without analyzing every joint.
Question 4: A planar truss is composed of 13 members (m) and is supported by a pin at one end and a roller at the other. The truss has 8 joints (j). Based on the relationship m + r = 2j, how would this truss be classified?
- Statically indeterminate to the first degree
- Statically determinate and stable (Correct answer)
- Unstable
- Statically indeterminate to the second degree
Correct answer: Statically determinate and stable
The formula for the static determinacy of a planar truss is m + r = 2j, where m is the number of members, r is the number of reaction forces, and j is the number of joints. In this case, m = 13. A pin support provides 2 reactions, and a roller provides 1 reaction, so r = 3. The number of joints is j = 8. Plugging these values into the formula: 13 + 3 = 16. For the other side of the equation: 2 * 8 = 16. Since 16 = 16 (or m + r = 2j), the truss is statically determinate and stable, assuming it is properly arranged.
Question 5: In the Warren truss shown, a single vertical downward load is applied at joint G. Which of the following statements is most likely true regarding the forces in the top and bottom chord members?
- Top chord members (BC, CD) are in tension; bottom chord members (FG, GH) are in compression.
- Both top and bottom chord members are in tension.
- Both top and bottom chord members are in compression.
- Top chord members (BC, CD) are in compression; bottom chord members (FG, GH) are in tension. (Correct answer)
Correct answer: Top chord members (BC, CD) are in compression; bottom chord members (FG, GH) are in tension.
For a simply supported truss subjected to downward vertical loads, the overall behavior mimics that of a simple beam. The top of the 'beam' (the top chord) experiences compression, while the bottom of the 'beam' (the bottom chord) experiences tension. Therefore, the top chord members will be in compression, and the bottom chord members will be in tension to resist the bending effect of the load.
Question 6: An engineer is analyzing a simple truss using the Method of Joints. After solving for the external support reactions, they begin analyzing forces at a specific joint. What is the maximum number of unknown member forces that can be present at the joint to solve for them directly using the equations of static equilibrium (ΣFx=0, ΣFy=0)?
- 1
- 3
- 2 (Correct answer)
- 4
Correct answer: 2
The Method of Joints analyzes the equilibrium of each pin connection. In a 2D planar truss, there are two available equations of static equilibrium for each joint: the sum of forces in the x-direction equals zero (ΣFx=0) and the sum of forces in the y-direction equals zero (ΣFy=0). Therefore, you can only solve for a maximum of two unknown forces at any single joint.
Civil Engineering PE Structural Analysis of Trusses Questions and Answers
Which of the following is NOT a standard assumption made in the analysis of an ideal truss?