Structural Analysis

Name: _____________________

Date: _____________________

Instructions: Answer all questions. Write your answers clearly in the space provided.

Question 1:

For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal (i) Of a stiffness matrix must be positive (ii) Of a stiffness matrix must be negative (iii) Of a flexibility matrix must be positive (iv) Of a flexibility matrix must be negative The correct answer is

A. (i) and (iii)
B. (ii) and (iii)
C. (i) and (iv)
D. (ii) and (iv)
Answer: _________
Question 2:

Study the following statements. i) The displacement method is more useful when degree of kinematic indeterminacy is greater than the degree of static indeterminacy. ii) The displacement method is more useful when degree of kinematic indeterminacy is less than the degree of static indeterminacy. iii) The force method is more useful when degree of static indeterminacy is greater than the degree of kinematic indeterminacy. iv) The force method is more useful when degree of static indeterminacy is less than the degree of kinematic indeterminacy. The correct answer is

A. (i) and (iii)
B. (ii) and (iii)
C. (i) and (iv)
D. (ii) and (iv)
Answer: _________
Question 3:

Muller Breslau’s principle for obtaining influence lines is applicable to i) trusses ii) statically determinate beams and frames iii) statically indeterminate structures, the material of which is elastic and follows Hooke’s law iv) any statically indeterminate structure The correct answer is

A. (i), (ii) and (iii)
B. (i), (ii) and (iv)
C. (i) and (ii)
D. Only (i)
Answer: _________
Question 4:

In the slope deflection equations, the deformations are considered to be caused by i) bending moment ii) shear force iii) axial force The correct answer is

A. Only (i)
B. (i) and (ii)
C. (ii) and (iii)
D. (i), (ii) and (iii)
Answer: _________
Question 5:

Select the correct statement

A. Flexibility matrix is a square symmetrical matrix
B. Stiffness matrix is a square symmetrical matrix
C. Both (A) and (B)
D. None of the above
Answer: _________
Question 6:

A simply supported beam deflects by 5 mm when it is subjected to a concentrated load of 10 kN at its centre. What will be deflection in a 1/10 model of the beam if the model is subjected to a 1 kN load at its centre ?

A. 5 mm
B. 0.5 mm
C. 0.05 mm
D. 0.005mm
Answer: _________
Question 7:

The deflection at any point of a perfect frame can be obtained by applying a unit load at the joint in

A. Vertical direction
B. Horizontal direction
C. Inclined direction
D. The direction in which the deflection is required
Answer: _________
Question 8:

Independent displacement components at each joint of a rigid-jointed plane frame are

A. Three linear movements
B. Two linear movements and one rotation
C. One linear movement and two rotations
D. Three rotations
Answer: _________
Question 9:

The thickness of the rectangular plate for the cap or base of a solid round steel columns, is calculated from the formula $${ ext{t}} = sqrt {frac{{9{ ext{W}}}}{{16{{ ext{f}}_{{ ext{bct}}}}}} imes frac{{ ext{D}}}{{{ ext{D}} - { ext{d}}}}} $$ xa0 xa0 where 'd' is

A. The reduced diameter of the column
B. The dimension of the base
C. The diameter of the base
D. The diameter of the top
Answer: _________
Question 10:

While using three moments equation, a fixed end of a continuous beam is replaced by an additional span of

A. Zero length
B. Infinite length
C. Zero moment of inertia
D. None of the above
Answer: _________
Question 11:

The effective length of lacing is the distance

A. Between the inner end rivets of the bar for single lacing
B. 0.7 of the distance between the inner end rivets of the bar for double lacing
C. Between the inner ends of effective lengths of welds connecting the members
D. All the above
Answer: _________
Question 12:

For a two-hinged arch, if one of the supports settles down vertically, then the horizontal thrust

A. Is increased
B. Is decreased
C. Remains unchanged
D. Becomes zero
Answer: _________
Question 13:

For a symmetrical two hinged parabolic arch, if one of the supports settles horizontally, then the horizontal thrust

A. Is increased
B. Is decreased
C. Remains unchanged
D. Becomes zero
Answer: _________
Question 14:

If the main reinforcement of the slab is parallel to a T-beam, the transverse reinforcement at mid span of the slab is provided at least __________ of main reinforcement.

A. 40%
B. 50%
C. 60%
D. 70%
Answer: _________
Question 15:

The deformation of a spring produced by a unit load is called

A. Stiffness
B. Flexibility
C. Influence coefficient
D. Unit strain
Answer: _________
Question 16:

The number of independent equations to be satisfied for static equilibrium of a plane structure is

A. 1
B. 2
C. 3
D. 6
Answer: _________
Question 17:

To generate the j th column of the flexibility matrix

A. A unit force is applied at coordinate j and the displacements are calculated at all co-ordinates
B. A unit displacement is applied at co-ordinate j and the forces are calculated at all co-ordinates
C. A unit force is applied at coordinate j and the forces are calculated at all co-ordinates
D. A unit displacement is applied at co-ordinate j and the displacements are calculated at all co-ordinates
Answer: _________
Question 18:

The three moments equation is applicable only when

A. The beam is prismatic
B. There is no settlement of supports
C. There is no discontinuity such as hinges within the span
D. The spans are equal
Answer: _________
Question 19:

The Castigliano's second theorem can be used to compute deflections

A. In statically determinate structures only
B. For any type of structure
C. At the point under the load only
D. For beams and frames only
Answer: _________
Question 20:

Bending moment at any section in a conjugate beam gives in the actual beam

A. Slope
B. Curvature
C. Deflection
D. Bending moment
Answer: _________
Question 21:

A load W is moving from left to right support on a simply supported beam of span T. The maximum bending moment at 0.4 1 from the left support is

A. 0.16 Wl
B. 0.20 Wl
C. 0.24 Wl
D. 0.25 Wl
Answer: _________
Question 22:

Effects of shear force and axial force on plastic moment capacity of a structure are respectively to

A. Increase and decrease
B. Increase and increase
C. Decrease and increase
D. Decrease and decrease
Answer: _________
Question 23:

The principle of virtual work can be applied to elastic system by considering the virtual work of

A. Internal forces only
B. External forces only
C. Internal as well as external forces
D. None of the above
Answer: _________
Question 24:

Pick up the correct statement for the web stiffeners.

A. Vertical stiffeners are spaced at a distance not greater than 1.5 d and not less than 0.33 d
B. d is the distance between flange angles or the clear distance between flanges
C. For horizontal stiffeners, d is the clear distance between the horizontal stiffener and the tension flange
D. All the above
Answer: _________
Question 25:

Number of unknown internal forces in each member of a rigid jointed plane frame is

A. 1
B. 2
C. 3
D. 6
Answer: _________
Question 26:

The number of independent displacement components at each joint of a rigid-jointed space frame is

A. 1
B. 2
C. 3
D. 6
Answer: _________
Question 27:

The slenderness effect of a wall is considered if the effective height of the wall exceeds the thickness

A. 8 times
B. 10 times
C. 12 times
D. 16 times
Answer: _________
Question 28:

The test strength of the sample is taken as the average of the strength of

A. 2 specimens
B. 3 specimens
C. 4 specimens
D. 5 specimens
Answer: _________
Question 29:

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
Answer: _________
Question 30:

If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin-jointed plane frame is given by

A. m + r + 2j
B. m - r + 2j
C. m + r - 2j
D. m + r - 3j
Answer: _________
Question 31:

The minimum horizontal distance between two parallel main reinforcing bars, is

A. The diameter of the bar if their diameters are same
B. The diameter of the longer bar if their diameters are unequal
C. 5 mm more than nominal maximum size of the coarse aggregate
D. Greatest value of the above
Answer: _________
Question 32:

A single rolling load of 8 kN rolls along a girder of 15 m span. The absolute maximum bending moment will be

A. 8 kN-m
B. 15 kN-m
C. 30 kN-m
D. 60 kN-m
Answer: _________
Question 33:

If in a pin-jointed plane frame (m + r) > 2j, then the frame is (Where ‘m’ is number of members, ‘r’ is reaction components and ‘j’ is number of joints)

A. Stable and statically determinate
B. Stable and statically indeterminate
C. Unstable
D. None of the above
Answer: _________
Question 34:

A rigid-jointed plane frame is stable and statically determinate if (where m is number of members, r is reaction components and j is number of joints)

A. (m + r) = 2j
B. (m + r) = 3j
C. (3m + r) = 3j
D. (m + 3r) = 3j
Answer: _________
Question 35:

A pin-jointed plane frame is unstable if (where m is number of members, r is reaction components and j is number of joints)

A. (m + r) < 2j
B. (m + r) = 2j
C. (m + r) > 2j
D. None of the above
Answer: _________
Question 36:

The degree of static indeterminacy of a pin-jointed space frame is given by (where m is number of unknown member forces, r is unknown reaction components and j is number of joints)

A. m + r - 2j
B. m + r - 3j
C. 3m + r - 3j
D. m + r + 3j
Answer: _________
Question 37:

The degree of static indeterminacy up to which column analogy method can be used is

A. 2
B. 3
C. 4
D. Unrestricted
Answer: _________
Question 38:

When a load crosses a through type Pratt truss in the direction left to right, the nature of force in any diagonal member in the left half of the span would

A. Change from compression to tension
B. Change from tension to compression
C. Always be compression
D. Always be tension
Answer: _________
Question 39:

Pick up the incorrect statement from the following:

A. The gross section of the web of rolled I-beams is the depth of the beam multiplied by the web thickness
B. The gross section of the web of channels is the depth of the web multiplied by its thickness
C. The gross section of the web of plate girders is the depth of the web plate multiplied by its thickness
D. None of these
Answer: _________
Question 40:

The number of independent equations to be satisfied for static equilibrium in a space structure is

A. 2
B. 3
C. 4
D. 6
Answer: _________
Question 41:

For a single point load W moving on a symmetrical three hinged parabolic arch of span L, the maximum sagging moment occurs at a distance x from ends. The value of x is

A. 0.211 L
B. 0.25 L
C. 0.234 L
D. 0.5 L
Answer: _________
Question 42:

If in a rigid-jointed space frame, (6m + r) < 6j, then the frame is

A. Unstable
B. Stable and statically determinate
C. Stable and statically indeterminate
D. None of the above
Answer: _________
Question 43:

Pick up the correct statement applicable to cased columns.

A. Single I-beam or channels back with or without flange plates may be used
B. The overall dimensions of the steel section do not exceed 750 × 450 mm over plate if used
C. The column is unpainted and is solidly encased in ordinary dense concrete with 10 mm aggregates having a minimum of cube strength 160 kg/cm 2 at 28 days
D. The surface and edges of the steel column should be provided a concrete cover not less than 50 mm
Answer: _________
Question 44:

In column analogy method, the area of an analogous column for a fixed beam of span L and flexural rigidity E$$I$$ is taken as

A. $$frac{{ ext{L}}}{{{ ext{E}}I}}$$
B. $$frac{{ ext{L}}}{{2{ ext{E}}I}}$$
C. $$frac{{ ext{L}}}{{3{ ext{E}}I}}$$
D. $$frac{{ ext{L}}}{{4{ ext{E}}I}}$$
Answer: _________
Question 45:

For under water concreting.

A. At least 10 percent more cement is required as compared to dry conditions
B. The volume of coarse aggregates shall not be less than one and half times and not more than twice that of fine aggregate
C. De-watering by pumping is not done or until 24 hours thereafter
D. All the above
Answer: _________
Question 46:

In moment distribution method, the sum of distribution factors of all the members meeting at any joint is always

A. 0
B. Less than 1
C. 1
D. Greater than 1
Answer: _________
Question 47:

Which of the following is not the displacement method?

A. Equilibrium method
B. Column analogy method
C. Moment distribution method
D. Kani's method
Answer: _________
Question 48:

Which of the following methods of structural analysis is a displacement method?

A. Moment distribution method
B. Column analogy method
C. Three moment equation
D. None of the above
Answer: _________
Question 49:

The carryover factor in a prismatic member whose far end is fixed is

A. 0
B. $$frac{1}{2}$$
C. $$frac{3}{4}$$
D. 1
Answer: _________
Question 50:

The degree of kinematic indeterminacy of a pin-jointed space frame is (where m, r and j have their usual meanings)

A. 2j - r
B. 3j - r
C. j - 2r
D. j - 3r
Answer: _________
Question 51:

The degree of static indeterminacy of a rigid-jointed space frame is (where m, r and j have their usual meanings)

A. m + r - 2j
B. m + r - 3j
C. 3m + r - 3j
D. 6m + r - 6j
Answer: _________
Question 52:

Castigliano’s first theorem is applicable

A. For statically determinate structures only
B. When the system behaves elastically
C. Only when principle of superposition is valid
D. None of the above
Answer: _________
Question 53:

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
Answer: _________
Question 54:

Principle of superposition is applicable when

A. Deflections are linear functions of applied forces
B. Material obeys Hooke's law
C. The action of applied forces will be affected by small deformations of the structure
D. None of the above
Answer: _________
Question 55:

The effective and actual lengths of a cantilever are same if continuous at the support,

A. Unstrained against torsion at the support and free at the end
B. With partial restraint against torsion of the support and free at the end
C. Restrained against torsion at the support and free at the end
D. None of these
Answer: _________
Question 56:

When a uniformly distributed load, longer than the span of the girder, moves from left to right, then the maximum bending moment at mid section of span occurs when the uniformly distributed load occupies

A. Less than the left half span
B. Whole of left half span
C. More than the left half span
D. Whole span
Answer: _________
Question 57:

Degree of static indeterminacy of a rigid-jointed plane frame having 15 members, 3 reaction components and 14 joints is

A. 2
B. 3
C. 6
D. 8
Answer: _________
Question 58:

For heavily reinforced concrete member, the nominal maximum size of the aggregates should be restricted to

A. 5 mm less than the minimum clear distance between the main bars
B. 5 mm less than the minimum cover to the reinforcement
C. Smaller of A and B
D. Greater of A and B
Answer: _________
Question 59:

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
Answer: _________
Question 60:

When a series of wheel loads crosses a simply supported girder, the maximum bending moment under any given wheel load occurs when

A. The centre of gravity of the load system is midway between the centre of span and wheel load under consi-deration
B. The centre of span is midway between the centre of gravity of the load system and the wheel load under consideration
C. The wheel load under consideration is midway between the centre of span and the centre of gravity of the load system
D. None of the above
Answer: _________
Question 61:

The maximum bending moment due to a train of wheel loads on a simply supported girder

A. Always occurs at centre of span
B. Always occurs under a wheel load
C. Never occurs under a wheel load
D. None of the above
Answer: _________
Question 62:

When a uniformly distributed load, shorter than the span of the girder, moves from left to right, then the conditions for maximum bending moment at a section is that

A. The head of the load reaches the section
B. The tail of the load reaches the section
C. The load position should be such that the section divides it equally on both sides
D. The load position should be such that the section divides the load in the same ratio as it divides the span
Answer: _________
Question 63:

In the displacement method of structural analysis, the basic unknowns are

A. Displacements
B. Force
C. Displacements and forces
D. None of the above
Answer: _________
Question 64:

If the specified thickness of a footing is 100 cm, the depth of the form work may be tolerated from

A. -2 mm to +2 mm
B. -3 mm to +3 mm
C. -4 mm to +4 mm
D. -5 mm to +5 mm
Answer: _________
Question 65:

For the stability of a structural part, the weight or anchorage should be

A. 1.2 times the minimum overturning moment due to dead load
B. 1.4 times the minimum overturning moment due to dead load
C. Sum of (A) and (B)
D. None of these
Answer: _________
Question 66:

The width of the analogous column in the method of column analogy is

A. $$frac{2}{{{ ext{E}}I}}$$
B. $$frac{1}{{{ ext{E}}I}}$$
C. $$frac{1}{{2{ ext{E}}I}}$$
D. $$frac{1}{{4{ ext{E}}I}}$$
Answer: _________

Answer Key

1: A
2: D
3: A
4: A
5: C
6: A
7: D
8: B
9: A
10: A
11: D
12: C
13: B
14: C
15: B
16: C
17: A
18: C
19: B
20: C
21: C
22: D
Solution: Plastic Moment Capacity: This is the maximum bending moment a structural section can withstand before it starts to deform permanently. Shear Force: Shear force acts parallel to the cross-section of a structural member. Effect of Shear Force: When shear force is present, it reduces the area available to resist bending. Think of it like some part of the section is already 'busy' resisting shear, so it can't contribute as much to resisting bending. Therefore, the plastic moment capacity decreases . Axial Force: Axial force acts along the longitudinal axis of a structural member (either tension or compression). Effect of Axial Force: Axial force also reduces the area available to resist bending. If there's compressive axial force, some of the material is already stressed in compression, leaving less capacity for resisting compressive stresses from bending. If there's tensile axial force, it can similarly reduce the effective area for resisting bending. Therefore, the plastic moment capacity decreases . In summary, both shear force and axial force reduce the plastic moment capacity of a structure.
23: C
24: D
25: C
26: D
27: C
28: B
29: A
30: C
31: D
32: C
33: B
34: C
35: A
36: B
37: B
38: A
39: D
Solution: All the given statements are correct definitions related to the gross sectional area of webs in different structural members . Option A: The gross section of the web of rolled I-beams is accurately calculated as the depth of the beam multiplied by the web thickness. Option B: For channel sections, the gross area of the web is indeed obtained by multiplying the depth of the web by its thickness. Option C: In the case of plate girders, the gross section of the web is correctly given by the product of the web plate depth and its thickness. Since none of the given statements are incorrect, the correct answer is Option D: None of these .
40: D
41: A
42: A
43: N/A
44: A
45: D
46: C
Solution: In the moment distribution method, the sum of distribution factors of all the members meeting at any joint is always 1 . Distribution factors are calculated for each member connected to a joint, based on their stiffness relative to the stiffness of all other members connected to the same joint. The distribution factors determine how the unbalanced moments at the joint will be distributed among the connected members. Since the total moment at the joint is distributed among the connected members, the sum of all distribution factors must equal 1, ensuring that the entire moment is accounted for.
47: B
48: A
49: B
50: B
51: D
52: C
53: B
54: A
Solution: The principle of superposition is applicable when the deflections in a structure are linear functions of the applied forces. This principle holds when the relationship between force and displacement is directly proportional, meaning that the total displacement caused by multiple forces is the sum of the displacements due to each force acting individually. For this to be valid, the material must behave elastically and within its linear range, which is often governed by Hooke's law.
55: C
56: D
57: C
Solution: To determine the degree of static indeterminacy (Ds) for a rigid-jointed plane frame, use the formula:

Ds = (3m + R) - (3j + A) where: m = number of members, R = number of reaction components, j = number of joints, A = number of internal hinges (A = 0 in this case). Given: m = 15 (members), R = 3 (reaction components), j = 14 (joints), A = 0 (no internal hinges). Substitute these values into the formula: Ds = (3 * 15 + 3) - (3 * 14 + 0) Ds = (45 + 3) - (42) Ds = 48 - 42 = 6 Thus, the degree of static indeterminacy is 6.
58: C
Solution: The nominal maximum size of the aggregates in heavily reinforced concrete members is determined to ensure proper compaction and minimal voids in the structure. 1. To avoid interference with the reinforcement, the size of the aggregate should be restricted to 5 mm less than the minimum clear distance between the main bars. 2. Similarly, to maintain adequate cover, the size of the aggregate should also be restricted to 5 mm less than the minimum cover to the reinforcement. 3. Therefore, the nominal maximum size of the aggregates should be the smaller of these two criteria to satisfy both conditions. This ensures proper placement and compaction of the concrete mix around the reinforcement.
59: D
60: B
61: B
Solution: 1. Wheel Load: When a train of wheel loads moves over a simply supported girder, the bending moment changes depending on the position of the wheel loads. 2. Influence Line: The influence line for bending moment indicates that the maximum bending moment occurs when the wheel load is at a specific point on the span. 3. Critical Position: For the maximum bending moment to occur, the critical position of the wheel load is generally at a distance from the support, calculated based on the span and the load distribution. 4. Conclusion: Hence, the maximum bending moment due to a train of wheel loads on a simply supported girder always occurs under a wheel load. Therefore, the correct answer is Option B: Always occurs under a wheel load.
62: D
63: A
64: D
65: C
66: B