Civil Engineering PE Structural Analysis of Trusses 4 — Questions and Answers
Question 1: In the analysis of a space (3D) truss, the determinacy condition is m + r = 3j. A space truss has 30 members, 6 reactions, and 12 joints. The truss is:
- Statically determinate (Correct answer)
- Statically indeterminate to 1st degree
- A mechanism
- Statically indeterminate to 3rd degree
Correct answer: Statically determinate
For a 3D truss: m + r = 30 + 6 = 36 = 3j = 3(12) = 36, confirming the truss is statically determinate.
Question 2: The influence line for the force in a diagonal tension member of a Pratt truss shows that the member carries tension when the live load is placed:
- In the panel where the member is located and extending to one support (Correct answer)
- Only directly over the member
- Across the entire span
- Only at the joint where the member terminates
Correct answer: In the panel where the member is located and extending to one support
For a diagonal tension member in a Pratt truss, the critical live load position occupies the panel containing the member and extends to the nearest support.
Question 3: A composite truss has steel top and bottom chords with timber web members. Under gravity loading, which chord is in compression?
- Top chord (Correct answer)
- Bottom chord
- Both chords simultaneously
- Neither chord; all compression goes to web members
Correct answer: Top chord
Under gravity (downward) loading, the top chord of a simply supported truss acts as a compression element, analogous to the top fiber of a beam.
Question 4: For the Cremona (graphical) method of truss analysis, forces are found by:
- Drawing a force polygon (Maxwell diagram) where member forces close the polygon at each joint (Correct answer)
- Summing moments about strategic cut sections
- Using stiffness matrices at each node
- Applying virtual work to each member independently
Correct answer: Drawing a force polygon (Maxwell diagram) where member forces close the polygon at each joint
The Cremona/Maxwell diagram is a graphical force polygon technique where equilibrium at each joint is satisfied when the force polygon closes.
Question 5: A truss bridge deck girder delivers concentrated loads only at panel points. This is a critical requirement because:
- Loads applied between joints would cause bending in chord members, violating the two-force member assumption (Correct answer)
- Panel points are the strongest locations in the chord
- Diagonal members cannot carry transverse loads
- Bridge codes prohibit mid-panel loading
Correct answer: Loads applied between joints would cause bending in chord members, violating the two-force member assumption
Classical truss analysis assumes members are two-force members (axial only); loading between joints introduces bending moments that the analysis ignores.
Question 6: In a Howe truss under gravity loading, the diagonal members are oriented such that they carry:
- Compression (Correct answer)
- Tension
- Zero force at midspan and tension at ends
- Bending and shear
Correct answer: Compression
In a Howe truss, diagonals slope downward toward the center, causing them to carry compression under gravity loads (opposite of Pratt truss diagonals).
Question 7: A redundant (statically indeterminate) truss requires which additional condition beyond equilibrium to solve member forces?
- Compatibility of deformations (force-deformation relationships) (Correct answer)
- A larger free-body diagram cut
- Additional moment equations about more joints
- Higher safety factors on all member forces
Correct answer: Compatibility of deformations (force-deformation relationships)
Statically indeterminate trusses cannot be solved by equilibrium alone; compatibility equations relating member deformations must also be satisfied.
Civil Engineering PE Structural Analysis of Trusses 4
In the analysis of a space (3D) truss, the determinacy condition is m + r = 3j.
A space truss has 30 members, 6 reactions, and 12 joints.
The truss is: