EI Structural Analysis & Design 1 — Questions and Answers
Question 1: A simply supported beam of length 10 ft carries a concentrated load of 500 lb at its midpoint. What is the vertical reaction at each support?
- 500 lb
- 250 lb (Correct answer)
- 125 lb
- 1000 lb
Correct answer: 250 lb
By symmetry, each support carries half the total load: 500/2 = 250 lb.
Question 2: Which condition must be satisfied for a structure to be in static equilibrium?
- The sum of all forces equals zero only
- The sum of all moments equals zero only
- Both the sum of all forces and the sum of all moments equal zero (Correct answer)
- The sum of all forces equals the sum of all moments
Correct answer: Both the sum of all forces and the sum of all moments equal zero
Static equilibrium requires ΣF = 0 (in all directions) and ΣM = 0 about any point simultaneously.
Question 3: For a cantilever beam of length L with a uniform distributed load w, what is the maximum bending moment?
- wL²/8
- wL²/4
- wL²/2 (Correct answer)
- wL²
Correct answer: wL²/2
The maximum moment in a cantilever with UDL occurs at the fixed support and equals wL²/2.
Question 4: In the method of joints for truss analysis, which equilibrium equations are applied at each joint?
- ΣFx = 0 and ΣFy = 0 (Correct answer)
- ΣM = 0 only
- ΣFx = 0, ΣFy = 0, and ΣM = 0
- ΣFz = 0 only
Correct answer: ΣFx = 0 and ΣFy = 0
At each pin joint, members are concurrent so ΣM = 0 is automatically satisfied; only ΣFx = 0 and ΣFy = 0 are needed.
Question 5: Euler's critical buckling load for a column with both ends pinned and length L is given by which formula?
- Pcr = π²EI / (4L²)
- Pcr = π²EI / L² (Correct answer)
- Pcr = 2π²EI / L²
- Pcr = π²EI / (2L²)
Correct answer: Pcr = π²EI / L²
For a pin-pin column, the effective length equals L and Pcr = π²EI/L², known as Euler's formula.
Question 6: A steel rod with cross-sectional area of 2 in² is subjected to a tensile force of 60,000 lb. What is the axial stress?
- 15,000 psi
- 30,000 psi (Correct answer)
- 60,000 psi
- 120,000 psi
Correct answer: 30,000 psi
Axial stress σ = P/A = 60,000 lb / 2 in² = 30,000 psi.
Question 7: The factor of safety (FS) is defined as which of the following?
- Working stress divided by ultimate stress
- Ultimate (or yield) stress divided by allowable stress (Correct answer)
- Allowable load divided by applied load
- Elastic modulus divided by applied strain
Correct answer: Ultimate (or yield) stress divided by allowable stress
FS = Failure stress (ultimate or yield) / Allowable stress, ensuring that the design stress remains well below the failure point.
EI Structural Analysis & Design 1
A simply supported beam of length 10 ft carries a concentrated load of 500 lb at its midpoint.
What is the vertical reaction at each support?