GPSC Civil Engineering (Combine Exam) Paper Solution (03-05-26) – Page 19

181) A beam of rectangular cross-section (b x d) is subjected to bending moment M. The ratio of maximum bending stress to average bending stress across the depth is

1. 1.0
2. 1.5
3. 2.0
4. 3.0

182) A thin-walled closed cylindrical pressure vessel has internal pressure p, internal radius r and wall thickness t. Which of the following correctly states the hoop (circumferential) stress and longitudinal (axial) stress?

1. σh = pr / t; σL = pr / (2t); σh/σL = 2
2. σh = pr / (2t); σL = pr / t; σh/σL = 0.5
3. σh = 2pr / t; σL = pr / t; σh/σL = 2
4. σh = pr / t; σL = pr / t; σh/σL = 1

183) Consider a state of pure shear where shear stress = τ. The principal stresses are

1. σ1 = +2τ, σ2 = – 2τ, at 45° to the shear planes
2. σ1 = +τ, σ2 = – τ, at 45° to the shear planes
3. σ1 = +τ, σ2 = 0, at 0° to the shear planes
4. σ1 = 0, σ2 = 0, with maximum shear

184) A solid shaft and a hollow shaft have the same material, same length and same weight (hence same volume). The hollow shaft has outer diameter D₀ and inner diameter Dᵢ = 0.6D₀. Compared to the solid shaft, the hollow shaft will have

1. Higher torsional strength and lower weight efficiency
2. Lower torsional strength but higher torsional stiffness
3. Higher polar section modulus and better strength-to-weight ratio
4. The same polar moment of inertia since volumes are equal

185) According to the Maximum Shear Stress Theory (Tresca’s criterion) of failure, yielding begins when

1. The maximum principal stress equals the yield stress in uniaxial tension
2. The distortion strain energy equals that at yield in uniaxial tension
3. The sum of all principal stresses equals the uniaxial yield stress
4. The maximum shear stress equals half the yield stress in uniaxial tension

186) Consider the following statements about the bending of beams:

1. The neutral axis passes through the centroid of the cross-section for homogeneous beams.
2. Bending stress is zero at the neutral axis and maximum at the outermost fibres.
3. Shear stress is maximum at the neutral axis for rectangular sections.
4. The flexure formula σ = My/I is valid only within the elastic limit.

Which of the above statements are correct?

1. 1, 2 and 3 only
2. 2, 3 and 4 only
3. 1, 2, 3 and 4
4. 1 and 4 only

187) The Degree of Static Indeterminacy (DSI) of a propped cantilever beam of span L, fixed at one end and simply supported at the other is

1. 0 (statically determinate)
2. 1
3. 2
4. 3

188) Consider the following statements about Influence Lines:

1. An influence line for a response function gives the variation of that function as a unit load traverses the span.
2. The influence line for bending moment at midspan of a simply supported beam is triangular.
3. Müller-Breslau’s principle states that the influence line for a reaction is the deflected shape caused by a unit displacement or rotation at the point of interest.
4. The maximum live-load moment at a section occurs when the load is placed over the entire span.

Which of the above statements are correct?

1. 1, 2 and 3 only
2. 1 and 2 only
3. 2, 3 and 4 only
4. 1, 2, 3 and 4

189) A two-span continuous beam ABC is analysed using the Three-Moment Theorem (Clapeyron’s equation). For equal spans L, same EI and UDL w on both spans, the support moment at B (intermediate support) is

1. M} = wL² / 8
2. M} = wL² / 10
3. MB = – wL² / 10 (from fixed end moments)
4. MB = – wL² / 8

190) In the Stiffness Method (Direct Stiffness/Matrix Method) of structural analysis, the stiffness matrix [K] for a prismatic beam element of length L, flexural rigidity EI (with 4 DOF: two rotations and two vertical displacements) has the diagonal terms in the order [v₁, θ₁, v₂, θ₂] as

1. 12EI/L³, 4EI/L, 12EI/L³, 4EI/L
2. 6EI/L², 4EI/L, 6EI/L², 4EI/L
3. 12EI/L³, 2EI/L, 12EI/L³, 2EI/L
4. EI/L³, EI/L, EI/L³, EI/L