Theory of Structures
Sample Problems
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Sample Problems
Cantilever Beams
Situation
Refer to the cantilever beam shown. Assume EI = 10,000 kN-m².
1. Determine the vertical deflection at B.
A. 112.5 mm
B. 95.4 mm
C. 103.7 mm
D. 136.9 mm
2. Determine the vertical deflection at C.
A. 39.7 mm
B. 45.7 mm
C. 56.9 mm
D. 87.4 mm
3. Determine the slope of the beam at C.
A. 0.05429
B. 0.01875
C. 0.03658
D. 0.02025
Problem (Nov. 2018)
A vertical load of ____ is applied at mid-length of a ...
Propped Beams
Propped Cantilever
Problem
Refer to the beam shown. E = 200 GPa, I = 150 x 10⁶ mm⁴. The spring deforms 1 mm in every 500 N load. Determine the vertical reaction at B.
A. 62.34 kN
B. 66.84 kN
C. 85.42 kN
D. 74.98 kN
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Problem
Refer to the beam shown. E = 200 GPa, I = 180 x 10⁶ mm⁴. The spring deforms 1 mm in every 500 N load. Determine the vertical reaction at B.
A. 289.3 kN
B. 187.5 kN
C. 256.8 kN
D. 218.7kN
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Situation
Refer to the beam shown. Assume E = 200 GPa and I = 120 x 10⁶ mm⁴. Determine the following:
1. The vertical reaction at B.
A. 69 kN
B. 52 kN
C. 74 kN
D. 87 kN
2. The bending moment at A.
A. -321 kN-m
B. -425 kN-m
C. -287 kN-m
D. -372 kN-m
3. The vertical deflection at C.
A. 63.58 mm
B. 82.37 mm
C. 96.32 mm
D. 101.25 mm
4. The maximum deflection of the beam.
A. 82.5 mm
B. 96.3 mm
C. 87.9 mm
D. 110.7 mm
Propped Simple Beam
Problem (Nov. 2018)
A simply supported beam has a span of 12 m. The beam carries a uniformly distributed load of ...
Deflection of Simple Beams
Situation
Refer to the beam shown. Assume EI = constant.
Determine the following:
1. The slope at A.
A. 569.87/EI
B. 324.12/EI
C. 456.32/EI
D. 384.92/EI
2. The deflection at B.
A. 720.5/EI
B. 652.4/EI
C. 765.8/EI
D. 810.9/EI
3. The rotation at B.
A. 35.89/EI
B. 29.08/EI
C. 26.58/EI
D. 45.08/EI
Double Integration
Problem
Determine the deflection at B and E in mm using the double integration method. E = 200 GPa, I = 280 x 10⁶ mm⁴.
Three-Moment Equation
Problem
Determine the deflection at B and E in mm using the three-moment equation. E = 200 GPa, I = 280 x 10⁶ mm⁴.
Pattern Loading
Three Spans
Problem (Nov. 2018) - Pattern Loading
Given the following data of the three-span beam...
(Pattern loading)