### Analysis and Design of Structures - multiple choice questions from AMIE exams (Summer 2020)

Multiple Choice Questions (10 x 2)

1. Thickened part of a flat slab over its supporting column, is technically known as
(a) Drop panel*
(b) Capital
(d) None of these

2. Side face reinforcement shall be provided in the beam when the depth of the web in a beam exceeds
(a) 50 cm
(b) 75 cm
(c) 100 cm
(d) 120 cm

3. For the initial estimate for a beam design, the width is assumed
(a) 1/15th of span
(6) 1/20th of span
(c) 1/25th of span
(d) 1/30th of span

4. In a slab, the pitch of the main reinforcement should not exceed its effective depth
(a) Three times
(b) Four times
(c) Five times
(d) Two times

5. The Young’s modulus of elasticity of steel is
(a) 150 KN/mm²
(b) 200 KN/mm²
(c) 250 KN/mm²
(d) 275 KN/mm²

6. Which of the following methods of structural analysis is a force method?
(a) Slope deflection method
(b) Column analogy method
(c) Moment distribution method
(d) None of the above

7. If in a rigid-jointed space frame. (6m + r) < 6j, then the frame is
(a) Unstable
(b) Stable and statically determine
(c) Stable and statically indeterminate
(d) None of the above

8. The fixed support in a real beam becomes in the conjugate beam a
(a) Roller support
(b) Hinged support
(c) Fixed support
(d) Free end

9. In the moment distribution method, the sum of distribution factors of all the members meeting at any joint is always
(a) Zero
(b) Less than I
(c) 1
(d) Greater than 1

10. Degree of kinematic indeterminacy of a pin-jointed plane frame is given by
(a) 2j - r
(b) j - 2r
(c) 3j - r
(d) 2j + r

1. (a) Drop panels are the rectangular portion provided above the column and below the slab in order to restrict the slab from getting sheared and undergoing rupture. Drop panel increases the contact surface area between the column and slab, which will enable a better distribution of load from slab to column. Thus, it will reduce the chance of slab failure due to unbalanced moments.

2. (b) Side face reinforcement shall be provided as per CI. 26.5.1.3 and 26.5.17(6) of IS 456:2000
• Beam depth > 450 mm (if beam subjected to torsion)
• Beam depth > 750 mm (if beam not subjected to torsion)
• Provide @ 0.1% of web area and distribute it equally on both side faces
3. (d) For the initial estimate for a beam design, as per the thumb rule the width is assumed to be the 1/30th of the span. In the early stage of a design, designers do not have an idea about the dimension of a structure. So during that phase thumb rules of design are preferred.

4. (a) The pitch of the main bars shall not exceed the following: (i) three times the effective depth of the slab, and (ii) 300 mm.

5. (b) The Young’s modulus of steel (also referred to as modulus of elasticity of steel) is between 190 – 210 GPa at room temperature.

6. (b) Column analogy method: It is a method used to analyze indeterminate structures specifically fixed beams, frames, and arches. It is ideally suited for computing stiffness and carryover factor in beams and frames having variable cross-sections.
See the following table which compares force methods and displacement methods.

7. (a) The degree of static indeterminacy of a rigid-jointed space frame is
D = (6m + r) - 6j
Where, m = number of members in the joint, r = number of equilibrium equations and j = number of joints
When,
D = 0, then the truss is stable and determinate, such trusses are called perfect trusses.
D > 0, then the truss is stable but indeterminate or over stiff
D < 0, then the truss is unstable or deficient.
Hence, D = (6m + r) - 6j < 0, the truss is unstable.

8. (d) Conjugate Beam Theorem
• Theorem 1: The slope at a point in the real beam is numerically equal to the shear at the corresponding point in the conjugate beam.
• Theorem 2: The displacement of a point in the real beam is numerically equal to the moment at the corresponding point in the conjugate beam.

9. (c) The DF for a member at a joint is the ratio of the stiffness (or relative stiffness) of the member to the total stiffness (or total relative stiffness) of all the members meeting at a joint.
The summation of DF for all the members at a joint is one.
DF is a property of rigid joint, it is not the property of hinge joint. So, the DF of a hinge joint is always zero.

10. (a) D = 2j –r for a pin-jointed frame. D = 3j –r for a rigid jointed frame. Here j number of joints and r number of reactions.

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