# GATE Ae : Test-II - 10 July 2020

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GATE AE : Structures
10 JULY 2020 - 3:00 pm - Duration : 90 min
Strength of Materials / Aircraft Structures
Topic-II : Transverse members

• 1.

### A cantilever beam OP is connected to another beam PQ with a pin joint as shown in figure. A load of 10 kN is applied at the midpoint of PQ. The magnitude of bending moment (in kN-m) at fixed end O is:

• A.

2.5

• B.

5

• C.

10

• D.

25

C. 10
Explanation
The magnitude of the bending moment at the fixed end O can be determined by analyzing the forces and moments acting on the beam. Since the load of 10 kN is applied at the midpoint of PQ, it will create a bending moment that is equal to half of the load multiplied by the distance between the load and the fixed end O. In this case, the distance is equal to half of the length of PQ. Therefore, the bending moment at the fixed end O is 10 kN-m.

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• 2.

### A simply supported beam of length L is subjected to a varying distributed load q(x) = sin (3πx/L) Nm-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force (in N) at the left support is:

• A.

Zero

• B.

L/3π

• C.

L/2π

• D.

L/π

B. L/3π
Explanation
The magnitude of the vertical reaction force at the left support is L/3Ï€. This can be determined by integrating the distributed load q(x) over the length of the beam. The integral of sin(3Ï€x/L) with respect to x from 0 to L gives -L/3Ï€. Since the beam is simply supported, the sum of the vertical reaction forces at the supports must be zero. Therefore, the magnitude of the vertical reaction force at the left support is L/3Ï€.

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• 3.

### A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross-section with a width of 30mm and height of 100mm. The maximum bending moment occurs at:

• A.

Location B

• B.

2675mm to the right of A

• C.

2500mm to the right of A

• D.

3225mm to the right of A

C. 2500mm to the right of A
Explanation
The maximum bending moment occurs at 2500mm to the right of A because this is the point where the load is the farthest from the support at A. As the load is applied at a distance from the support, it creates a moment that causes bending in the beam. The farther the load is from the support, the greater the bending moment. Therefore, the maximum bending moment occurs at the point where the load is the farthest from the support, which is 2500mm to the right of A.

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• 4.

### In a simply – supported beam loaded as shown below, the maximum bending moment (in Nm) is:

• A.

25

• B.

30

• C.

35

• D.

60

B. 30
Explanation
The maximum bending moment in a simply-supported beam occurs at the center of the beam. In this case, the beam is loaded symmetrically, so the maximum bending moment will be at the midpoint of the beam. Therefore, the maximum bending moment is 30 Nm.

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• 5.

### An overhanging beam of length L is loaded with a UDL of strength 'q' as shown in the figure below. For what value of 'a' will the ratio of bending moment at the middle of the beam to the bending moment at the supports be equal to 3:4?

• A.

L/2

• B.

L/3

• C.

L/4

• D.

L/6

B. L/3
Explanation
The ratio of bending moment at the middle of the beam to the bending moment at the supports is equal to 3:4 when the load is placed at a distance of L/3 from the supports. This is because the bending moment is directly proportional to the load and the distance from the supports. By placing the load at L/3, the bending moment at the middle of the beam will be three times larger than the bending moment at the supports, resulting in a 3:4 ratio.

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• 6.

### A liver is supported by two hinges at A and C. It carries a force of 3kN as shown in the figure. The bending moment at B will be......

• A.

Zero kN-m

• B.

1 kN-m

• C.

2 kN-m

• D.

3 kN-m

B. 1 kN-m
Explanation
The bending moment at point B will be 1 kN-m. This is because the force of 3 kN acting at point C creates a clockwise moment around point B, while the force of 3 kN acting at point A creates a counterclockwise moment around point B. These two moments cancel each other out, resulting in a net bending moment of 1 kN-m at point B.

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• 7.

### Choose the correct option as given in the answer choice:

• A.

(a)

• B.

(b)

• C.

(c)

• D.

(d)

• E.

None of these

A. (a)
• 8.

### A simply supported beam is subjected to a distributed loading as shown in the figure:                                   The ratio of maximum bending moment to maximum shear force for this beam is:

• A.

L/3

• B.

L/6

• C.

L/4

• D.

L/12

B. L/6
Explanation
The ratio of maximum bending moment to maximum shear force for a simply supported beam with a distributed loading is L/6. This can be determined by analyzing the shear force and bending moment diagrams for the beam. The maximum bending moment occurs at the midpoint of the beam, where the shear force is zero. Therefore, the ratio of the maximum bending moment to the maximum shear force is L/6.

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• 9.

### A simply supported beam at its ends carries a central concentrated load, and maximum bending moment is M. If the same load be uniformly distributed over the length of the beam, what is the maximum bending moment?

• A.

M

• B.

M/2

• C.

M/4

• D.

2M

B. M/2
Explanation
When the load is uniformly distributed over the length of the beam, the bending moment is halved compared to when the load is concentrated at the center. This is because the load is now evenly distributed along the beam, resulting in a more balanced distribution of forces and moments. Therefore, the maximum bending moment is M/2.

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• 10.

• A.

40 kNm

• B.

-80 kNm

• C.

58 kNm

• D.

116 kNm

A. 40 kNm
• 11.

### A uniformly distributed load is acting over a 3m long cantilever beam. The shear force at the midpoint of the beam is 6kN, what is the bending moment at this point?

• A.

3 kNm

• B.

4 kNm

• C.

4.5 kNm

• D.

2.25 kNm

• E.

9 kNm

C. 4.5 kNm
Explanation
The bending moment at the midpoint of a cantilever beam can be calculated using the equation M = (wL^2)/8, where M is the bending moment, w is the uniformly distributed load, and L is the length of the beam. In this case, the load is not given, but since the shear force at the midpoint is 6kN, we can use the relationship between shear force and bending moment, V = dM/dx, where V is the shear force, M is the bending moment, and x is the distance from the support. By integrating this equation, we can find that the bending moment at the midpoint is 4.5 kNm.

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• 12.

### A pin jointed uniform rigid rod of weight W and length L is supported horizontally with a force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is:

• A.

Zero

• B.

W/4

• C.

W/2

• D.

W

B. W/4
Explanation
When the force F is suddenly removed, the rod will start to rotate about the pin joint. At the instant of force removal, the rod will be in equilibrium, meaning that the sum of the torques acting on the rod must be zero. The weight W of the rod exerts a clockwise torque about the pin joint, while the vertical reaction at the support exerts an equal and opposite counterclockwise torque. Since the rod is uniform, the weight is evenly distributed along its length. Therefore, the vertical reaction at the support must be W/4 in order to balance the torque and maintain equilibrium.

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• 13.

### Beam ABCD represents a reinforced-concrete foundation beam that supports a uniform load of intensity     q1= 3500 lb/ft (see figure). Assume that the soil pressure on the underside of the beam is uniformly distributed with intensity q2.                                                Find the ratio of bending moment at point B to the bending moment at the midpoint of the beam:-

• A.

2:9

• B.

9:2

• C.

3:7

• D.

7:3

C. 3:7
Explanation
The ratio of bending moment at point B to the bending moment at the midpoint of the beam is 3:7. This means that the bending moment at point B is 3 parts and the bending moment at the midpoint is 7 parts. This ratio indicates that the bending moment is higher at the midpoint compared to point B, suggesting that the beam experiences higher stress and bending at the midpoint due to the load distribution.

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• 14.

### A beam ABC with an overhang at one end supports a uniform load of intensity 12 kN/m and a concentrated load of magnitude 2.4 kN (see figure). For this beam, the point of contraflexure lies at what distance to the left of point C?

• A.

1.92 m

• B.

2.08 m

• C.

2.24 m

• D.

2.40 m

C. 2.24 m
Explanation
The point of contraflexure in a beam occurs where the bending moment changes sign. In this case, the bending moment is positive to the left of the point of contraflexure and negative to the right. The concentrated load at point C creates a positive bending moment, while the uniform load creates a negative bending moment. By calculating the moments caused by the concentrated and uniform loads, we can determine the point of contraflexure. The correct answer, 2.24 m, is the distance to the left of point C where the bending moment changes sign.

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• 15.

### For the simply supported beam of length L, subjected to a uniformly distributed moment 'M' kN–m per unit length as shown in the figure, the bending moment (in kN–m) at the mid-span of the beam is:

• A.

Zero

• B.

M

• C.

M/L

• D.

M/2

A. Zero
Explanation
The bending moment at the mid-span of a simply supported beam subjected to a uniformly distributed moment per unit length is zero. This is because the beam is supported at both ends, causing the moments to cancel out at the midpoint. Therefore, there is no bending moment at the mid-span of the beam.

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• 16.

### Numerical Answer Type: Two people weighing 50kg each are sitting on a plank of length 10m floating on water at 2.5m from either end. Neglecting the weight of the plank ,the bending moment at the center of plank is equal to __________kNm. [Take g = 10m/s2] (Type the correct numerical answer in the space below)

0, 0.0, 0.00
Explanation
The bending moment at the center of the plank can be calculated by multiplying the weight of each person by their distance from the center of the plank. Since both people weigh 50kg and are sitting at a distance of 2.5m from the center, the bending moment for each person is (50kg * 2.5m) = 125kgm. Since the plank is symmetrical, the bending moments from both people will cancel each other out, resulting in a net bending moment of 0kNm at the center of the plank. Therefore, the correct answer is 0, 0.0, 0.00.

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• 17.

### Numerical Answer Type: A simply supported beam of length 3 m with varying distributed load of 3 kN/m is shown in the figure below. The maximum bending moment (in kNm) in the beam is __________.                                       [Type the answer correct to two decimals in the space below]

1.732, 1.7, 1.73, 1.74
• 18.

### Numerical Answer Type: The shear force diagram of a loaded beam is shown in the figure. What is the maximum bending moment (in kNm) of the beam? (Type the correct numerical answer in the space below)

16, 16.0, 16.00
Explanation
The maximum bending moment of the beam can be determined by finding the point on the shear force diagram where the slope changes sign. In this case, the shear force diagram shows a positive slope until it reaches a value of 16 kN, and then the slope becomes negative. Therefore, the maximum bending moment of the beam is 16 kNm.

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• 19.

### Numerical Answer Type: A simply supported beam of length 10 m carries a uniformly varying load whose intensity varies from a maximum value of 5 kN/m at both ends to zero at the center of the beam. It is desired to replace the beam with another simply supported beam which will be subjected to the same maximum 'bending moment’ and ‘shear force' as in the case of the previous one. Determine the rate of loading (in kN/m) for the second beam if it is subjected to a uniformly distributed load over its whole length. (Type the answer correct to two decimals in the space below)

3.75
Explanation

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• 20.

### Numerical Answer Type: For the beam loaded as shown in the figure, the ratio of the maximum bending moment to the bending moment at point B is __________. (Type the answer correct to one decimal place in the space below)

1.5
Explanation
The ratio of the maximum bending moment to the bending moment at point B is 1.5.

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• 21.

### Numerical Answer Type: For the loaded beam as shown in the figure, find the maximum magnitude of the bending moment (in kNm) in the portion of the beam where shear force is -35 kN :- (Type the answer correct to one decimal place in the space below)

67.5, 67.50
Explanation
The maximum magnitude of the bending moment occurs at the point where the shear force changes sign. In this case, the shear force changes from positive to negative, indicating a point of maximum bending moment. Therefore, the maximum magnitude of the bending moment in the portion of the beam where the shear force is -35 kN is 67.5 kNm.

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• 22.

### Numerical Answer Type: Find the bending moment (in kNm) at the midpoint of the beam loaded as shown in the figure below:                                                    (Type the correct numerical answer in the space below)

45, 45.0, 45.00
• 23.

### Numerical Answer Type: An overhanging beam ABC with uniformly distributed load beam is shown in the figure below. The point of contraflexure is __________ inches from the end A.                                       (Type the correct numerical answer in the space below)

40, 40.0, 40.00

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• Mar 22, 2023
Quiz Edited by
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• Jul 08, 2020
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