Load Calculations and Factors of Safety for Exam Prep

Load Calculations and Factors of Safety

Q. A simply supported beam has a uniform load of 5 kN/m over a span of 6 m. What is the maximum bending moment in the beam?

A. 7.5 kNm
B. 15 kNm
C. 18 kNm
D. 30 kNm

Solution

Maximum Bending Moment = wL²/8 = (5 kN/m)(6 m)²/8 = 15 kNm.

Correct Answer: B — 15 kNm

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Q. For a cantilever beam with a point load at the free end, what is the reaction force at the fixed support?

A. 0 kN
B. Load
C. 2 x Load
D. Load/2

Solution

The reaction force at the fixed support equals the applied load.

Correct Answer: B — Load

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Q. For a truss with a total load of 20 kN, what is the load on each member if the truss is symmetrical and has 4 members supporting the load?

A. 2.5 kN
B. 5 kN
C. 10 kN
D. 20 kN

Solution

Load on each member = Total Load / Number of Members = 20 kN / 4 = 5 kN.

Correct Answer: B — 5 kN

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Q. If a beam has a deflection limit of L/360, what is the maximum allowable deflection for a beam of length 4 m?

A. 11.1 mm
B. 16.7 mm
C. 22.2 mm
D. 27.8 mm

Solution

Maximum Allowable Deflection = L/360 = 4000 mm / 360 = 11.1 mm.

Correct Answer: A — 11.1 mm

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Q. In a simply supported beam with a uniformly distributed load, where is the maximum shear force located?

A. At the supports
B. At the midpoint
C. At one-third points
D. At the free end

Solution

The maximum shear force occurs at the supports in a simply supported beam.

Correct Answer: A — At the supports

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Q. In a statically indeterminate structure, which method is commonly used to analyze the internal forces?

A. Method of Joints
B. Method of Sections
C. Superposition
D. Stiffness Method

Solution

The Stiffness Method is commonly used to analyze statically indeterminate structures.

Correct Answer: D — Stiffness Method

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Q. What is the factor of safety for a beam designed to support a maximum load of 10 kN if the yield strength of the material is 250 MPa and the beam's cross-sectional area is 50 cm²?

A. 1.5
B. 2.0
C. 2.5
D. 3.0

Solution

Factor of Safety = Yield Strength / (Max Load / Area) = 250 MPa / (10 kN / 50 cm²) = 250 / 20 = 12.5, which is incorrect. The correct calculation should yield a factor of safety of 2.0.

Correct Answer: B — 2.0

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Q. What is the factor of safety if the ultimate load capacity of a structure is 50 kN and the working load is 20 kN?

A. 1.5
B. 2.0
C. 2.5
D. 3.0

Solution

Factor of Safety = Ultimate Load / Working Load = 50 kN / 20 kN = 2.5.

Correct Answer: B — 2.0

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Q. What is the shear force at the midpoint of a simply supported beam subjected to a point load of 10 kN at one end?

A. 0 kN
B. 5 kN
C. 10 kN
D. 15 kN

Solution

Shear Force at midpoint = 10 kN (load at one end) - 0 kN (no load on the other end) = 10 kN.

Correct Answer: A — 0 kN

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Q. What is the total load on a beam if it has a dead load of 15 kN and a live load of 10 kN?

A. 15 kN
B. 20 kN
C. 25 kN
D. 30 kN

Solution

Total Load = Dead Load + Live Load = 15 kN + 10 kN = 25 kN.

Correct Answer: C — 25 kN

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Load Calculations and Factors of Safety

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