A simply supported beam has a span of 20 ft and carries a uniformly
distributed load of 2 kip/ft over the entire span. What is the maximum
bending moment?
A) 50 kip-ft
B) 75 kip-ft
C) 100 kip-ft
D) 200 kip-ft
Answer: C
Rationale: For a simply supported beam carrying a uniform load over
the full span, the maximum bending moment occurs at midspan and is
calculated as Mmax=wL2/8M_{max}=wL^2/8. Substituting w=2w=2
kip/ft and L=20L=20 ft gives
Mmax=2(20)2/8=100M_{max}=2(20)^2/8=100 kip-ft. The result
represents the critical positive bending moment at the center of the
beam.
A steel tension member has a gross cross-sectional area of 4.0 in² and
carries an axial tensile force of 80 kips. What is the average gross-
section tensile stress?
Page 1 of 71
,A) 10 ksi
B) 20 ksi
C) 25 ksi
D) 32 ksi
Answer: B
Rationale: Average axial stress is determined by dividing the applied
axial force by the gross cross-sectional area. Using σ=P/A\sigma=P/A,
the stress is 80/4.0=2080/4.0=20 ksi. This calculation represents the
average stress over the gross section and is a basic starting point for
evaluating the strength of a tension member.
A reinforced concrete rectangular beam is subjected to positive
bending. Where is the primary tension reinforcement typically placed?
A) Near the top face
B) At the neutral axis
C) Near the side faces only
D) Near the bottom face
Answer: D
Rationale: Under typical positive bending in a simply supported
reinforced concrete beam, the beam curves downward, placing the
lower portion of the cross section in tension and the upper portion in
compression. Concrete is relatively weak in tension, so reinforcing steel
is placed near the tension face to resist tensile forces and control
cracking. The exact reinforcement arrangement depends on the
structural system and loading condition.
A column has an effective length of 12 ft and a radius of gyration of 3 in.
What is its slenderness ratio KL/rKL/r, assuming K=1.0K=1.0?
Page 2 of 71
,A) 48
B) 36
C) 24
D) 12
Answer: A
Rationale: The slenderness ratio is KL/rKL/r, with all dimensions
expressed in consistent units. The effective length is 12 ft, or 144 in.,
and the radius of gyration is 3 in. Therefore,
KL/r=144/3=48KL/r=144/3=48. Slenderness is important because
increasing slenderness generally increases susceptibility to buckling and
reduces the axial capacity of compression members.
A structural engineer is determining the factored gravity load for a
design situation involving dead load DD and live load LL. Which
expression represents a commonly used strength-level gravity load
combination?
A) D+LD+L
B) 0.9D+L0.9D+L
C) 1.2D+1.6L1.2D+1.6L
D) 1.6D+1.2L1.6D+1.2L
Answer: C
Rationale: A commonly used strength-design gravity load combination
is 1.2D+1.6L1.2D+1.6L. The factors account for uncertainty in the
magnitude of loads and are used when evaluating structural strength
under factored load effects. Engineers must use the applicable
governing building code and project-specific requirements when
selecting load combinations.
Page 3 of 71
, A simply supported beam carries a concentrated load at its center.
Where does the maximum bending moment occur?
A) At the left support
B) At the center of the span
C) At one-quarter of the span
D) At the right support
Answer: B
Rationale: For a simply supported beam with a single concentrated load
located at midspan, the bending moment increases from zero at the
supports to its maximum value directly beneath the applied load. The
supports have zero bending moment for the idealized pin-and-roller
support condition. This behavior follows directly from the beam's shear
and moment relationships.
A steel beam is laterally unsupported over a long length. Which failure
mode may control its flexural capacity?
A) Local concrete crushing
B) Punching shear
C) Bearing failure of timber
D) Lateral-torsional buckling
Answer: D
Rationale: A steel beam subjected to bending can experience lateral-
torsional buckling when the compression flange is insufficiently braced.
The compression flange tends to move laterally while the beam twists
about its longitudinal axis. The unbraced length, section properties,
loading pattern, and support conditions influence the susceptibility and
available flexural strength.
Page 4 of 71
distributed load of 2 kip/ft over the entire span. What is the maximum
bending moment?
A) 50 kip-ft
B) 75 kip-ft
C) 100 kip-ft
D) 200 kip-ft
Answer: C
Rationale: For a simply supported beam carrying a uniform load over
the full span, the maximum bending moment occurs at midspan and is
calculated as Mmax=wL2/8M_{max}=wL^2/8. Substituting w=2w=2
kip/ft and L=20L=20 ft gives
Mmax=2(20)2/8=100M_{max}=2(20)^2/8=100 kip-ft. The result
represents the critical positive bending moment at the center of the
beam.
A steel tension member has a gross cross-sectional area of 4.0 in² and
carries an axial tensile force of 80 kips. What is the average gross-
section tensile stress?
Page 1 of 71
,A) 10 ksi
B) 20 ksi
C) 25 ksi
D) 32 ksi
Answer: B
Rationale: Average axial stress is determined by dividing the applied
axial force by the gross cross-sectional area. Using σ=P/A\sigma=P/A,
the stress is 80/4.0=2080/4.0=20 ksi. This calculation represents the
average stress over the gross section and is a basic starting point for
evaluating the strength of a tension member.
A reinforced concrete rectangular beam is subjected to positive
bending. Where is the primary tension reinforcement typically placed?
A) Near the top face
B) At the neutral axis
C) Near the side faces only
D) Near the bottom face
Answer: D
Rationale: Under typical positive bending in a simply supported
reinforced concrete beam, the beam curves downward, placing the
lower portion of the cross section in tension and the upper portion in
compression. Concrete is relatively weak in tension, so reinforcing steel
is placed near the tension face to resist tensile forces and control
cracking. The exact reinforcement arrangement depends on the
structural system and loading condition.
A column has an effective length of 12 ft and a radius of gyration of 3 in.
What is its slenderness ratio KL/rKL/r, assuming K=1.0K=1.0?
Page 2 of 71
,A) 48
B) 36
C) 24
D) 12
Answer: A
Rationale: The slenderness ratio is KL/rKL/r, with all dimensions
expressed in consistent units. The effective length is 12 ft, or 144 in.,
and the radius of gyration is 3 in. Therefore,
KL/r=144/3=48KL/r=144/3=48. Slenderness is important because
increasing slenderness generally increases susceptibility to buckling and
reduces the axial capacity of compression members.
A structural engineer is determining the factored gravity load for a
design situation involving dead load DD and live load LL. Which
expression represents a commonly used strength-level gravity load
combination?
A) D+LD+L
B) 0.9D+L0.9D+L
C) 1.2D+1.6L1.2D+1.6L
D) 1.6D+1.2L1.6D+1.2L
Answer: C
Rationale: A commonly used strength-design gravity load combination
is 1.2D+1.6L1.2D+1.6L. The factors account for uncertainty in the
magnitude of loads and are used when evaluating structural strength
under factored load effects. Engineers must use the applicable
governing building code and project-specific requirements when
selecting load combinations.
Page 3 of 71
, A simply supported beam carries a concentrated load at its center.
Where does the maximum bending moment occur?
A) At the left support
B) At the center of the span
C) At one-quarter of the span
D) At the right support
Answer: B
Rationale: For a simply supported beam with a single concentrated load
located at midspan, the bending moment increases from zero at the
supports to its maximum value directly beneath the applied load. The
supports have zero bending moment for the idealized pin-and-roller
support condition. This behavior follows directly from the beam's shear
and moment relationships.
A steel beam is laterally unsupported over a long length. Which failure
mode may control its flexural capacity?
A) Local concrete crushing
B) Punching shear
C) Bearing failure of timber
D) Lateral-torsional buckling
Answer: D
Rationale: A steel beam subjected to bending can experience lateral-
torsional buckling when the compression flange is insufficiently braced.
The compression flange tends to move laterally while the beam twists
about its longitudinal axis. The unbraced length, section properties,
loading pattern, and support conditions influence the susceptibility and
available flexural strength.
Page 4 of 71
