Civil Engineering PE Structural Analysis of Trusses 5 — Questions and Answers
Question 1: When using virtual work to find the deflection of a truss joint, the virtual work equation is δ = Σ(nNL/AE). In this equation, 'n' represents:
- Member forces due to a unit virtual load applied at the joint of interest (Correct answer)
- Member forces due to the actual applied loads
- Cross-sectional area of each member
- Member length divided by elastic modulus
Correct answer: Member forces due to a unit virtual load applied at the joint of interest
In the virtual work method for trusses, 'n' is the axial force in each member caused by a unit (virtual) load applied at the point and in the direction of the desired deflection.
Question 2: A truss member with cross-sectional area A = 4 in², length L = 10 ft, E = 29,000 ksi, and axial force P = 80 kips has an axial deformation of:
- 0.00828 in (Correct answer)
- 0.0828 in
- 0.828 in
- 8.28 in
Correct answer: 0.00828 in
δ = PL/AE = (80)(10×12)/[(4)(29,000)] = 9,600/116,000 = 0.00828 in.
Question 3: In the stiffness (direct stiffness) method for truss analysis, the global stiffness matrix is assembled by:
- Superimposing member stiffness matrices transformed to global coordinates at shared DOFs (Correct answer)
- Inverting the flexibility matrix directly
- Applying moment distribution to each panel
- Solving the force polygon at every joint iteratively
Correct answer: Superimposing member stiffness matrices transformed to global coordinates at shared DOFs
The direct stiffness method transforms each member's local stiffness matrix to global coordinates and adds contributions to the shared degrees of freedom in the global stiffness matrix.
Question 4: A pin-jointed truss member is slender and subjected to axial compression. The critical buckling load is governed by:
- Euler's formula: Pcr = π²EI/(KL)² (Correct answer)
- The plastic moment capacity: Mp = FyZ
- Shear flow: q = VQ/I
- Torsional warping constant: Cw
Correct answer: Euler's formula: Pcr = π²EI/(KL)²
Slender compression members in a truss buckle elastically per Euler's formula, where KL is the effective length and I is the moment of inertia about the weak axis.
Question 5: A truss experiences differential thermal expansion where the top chord heats up more than the bottom chord. In a statically determinate truss, the effect on member forces is:
- No change in member forces; the truss deforms freely without inducing forces (Correct answer)
- Compression in all members due to thermal expansion
- Tension in the top chord and compression in the bottom chord
- Indeterminate without knowing the temperature gradient
Correct answer: No change in member forces; the truss deforms freely without inducing forces
In a statically determinate structure, thermal deformations can occur freely without inducing additional member forces.
Question 6: An influence line for the reaction at the left support of a simply supported truss spans 60 ft with panels at 10 ft each. The influence line ordinate at a point 20 ft from the left support is:
- 0.667 (Correct answer)
- 0.333
- 1.000
- 0.500
Correct answer: 0.667
The influence line for a left support reaction is linear: ordinate = (L - x)/L = (60 - 20)/60 = 40/60 = 0.667.
Question 7: A truss is analyzed using the flexibility method. The compatibility equation used for a single degree of indeterminacy is:
- δ₁₀ + δ₁₁·X₁ = 0 (Correct answer)
- K·u = F
- ΣFy = 0 with unknown redundant
- δ = PL/AE for each member
Correct answer: δ₁₀ + δ₁₁·X₁ = 0
In the flexibility method, the compatibility equation δ₁₀ + δ₁₁·X₁ = 0 states that the displacement due to applied loads plus the displacement due to the redundant X₁ must satisfy the geometric constraint.
Civil Engineering PE Structural Analysis of Trusses 5
When using virtual work to find the deflection of a truss joint, the virtual work equation is δ = Σ(nNL/AE).
In this equation, 'n' represents: