Test 8 - SFD and BMD for Overhangs, UVL and Applied Moments

Question 1 ప్రశ్న 1

A triangular distributed load varies linearly from zero at end A to 12 kN/m at end B over a length of 6 m. What are the magnitude and location of its equivalent concentrated load measured from A?

A 36 kN acting 2 m from A B 36 kN acting 4 m from A C 72 kN acting 3 m from A D 24 kN acting 4 m from A

Question 2 ప్రశ్న 2

A trapezoidal distributed load varies linearly from 4 kN/m at A to 10 kN/m at B over a 6 m length. What are the magnitude and approximate location of its resultant measured from A?

A 42 kN at 3.00 m B 36 kN at 3.43 m C 42 kN at 3.43 m D 48 kN at 4.00 m

Question 3 ప్రశ్న 3

An isolated concentrated couple is applied at an interior point of a beam, and there is no concentrated transverse force at that same point. Which local SFD/BMD behaviour is correct?

A The shear-force diagram has a finite jump and the bending-moment diagram remains continuous. B The bending-moment diagram has a finite jump equal in magnitude to the applied couple, while the shear-force diagram has no corresponding force jump. C Both shear force and bending moment must become zero at the couple. D Both diagrams have finite jumps of equal numerical magnitude.

Question 4 ప్రశ్న 4

A beam is supported at A and B, 6 m apart, and overhangs 2 m beyond B to C. A downward point load of 20 kN acts at C. Taking upward reactions as positive and sagging moment as positive, what are RA, RB and the bending moment at B?

A RA = +6.67 kN, RB = +13.33 kN and MB = +40 kN·m B RA = -6.67 kN, RB = +26.67 kN and MB = -40 kN·m C RA = +10 kN, RB = +10 kN and MB = 0 D RA = -3.33 kN, RB = +23.33 kN and MB = -20 kN·m

Question 5 ప్రశ్న 5

A beam is simply supported at A and B, 6 m apart, and has a 2 m overhang BC. A UDL of 10 kN/m acts only over the overhang BC. What are the reactions at A and B and the bending moment at B, taking sagging as positive?

A RA = -3.33 kN, RB = +23.33 kN and MB = -20 kN·m B RA = +3.33 kN, RB = +16.67 kN and MB = +20 kN·m C RA = 0, RB = 20 kN and MB = -10 kN·m D RA = -6.67 kN, RB = +26.67 kN and MB = -40 kN·m

Question 6 ప్రశ్న 6

A beam has 2 m overhangs at both ends, with supports A and B located 6 m apart. A 10 kN downward load acts at the left free end and a 20 kN downward load acts at the right free end. What are the upward reactions RA and RB?

A RA = 15 kN and RB = 15 kN B RA = 6.67 kN and RB = 23.33 kN C RA = 23.33 kN and RB = 6.67 kN D RA = -6.67 kN and RB = 36.67 kN

Question 7 ప్రశ్న 7

A simply supported beam of span 8 m carries a triangular UVL varying from zero at the left support to 12 kN/m at the right support. At what distance from the left support does the maximum bending moment occur, and what is its approximate value?

A 4.00 m and 48.0 kN·m B 4.62 m and 49.27 kN·m C 5.33 m and 64.0 kN·m D 6.00 m and 48.0 kN·m

Question 8 ప్రశ్న 8

A simply supported beam of span 6 m carries a triangular UVL varying from 15 kN/m at the left support to zero at the right support. What is the approximate location and magnitude of the maximum bending moment?

A 2.54 m from the left support and 34.64 kN·m B 3.00 m from the left support and 45.00 kN·m C 2.00 m from the left support and 30.00 kN·m D 3.46 m from the left support and 34.64 kN·m

Question 9 ప్రశ్న 9

A simply supported beam 6 m long carries a trapezoidal load varying linearly from 4 kN/m at the left support to 10 kN/m at the right support. What is the approximate location and value of the maximum bending moment?

A 3.00 m and 30.0 kN·m B 3.21 m and 31.66 kN·m C 3.43 m and 42.0 kN·m D 4.00 m and 36.0 kN·m

Question 10 ప్రశ్న 10

A cantilever of length 6 m carries a triangular load varying from 12 kN/m at the fixed end to zero at the free end. What are the magnitudes of the fixed-end shear force and bending moment?

A 36 kN and 72 kN·m B 36 kN and 144 kN·m C 72 kN and 216 kN·m D 24 kN and 72 kN·m

Question 11 ప్రశ్న 11

A cantilever of length 6 m carries a triangular load varying from zero at the fixed end to 12 kN/m at the free end. What are the magnitudes of the fixed-end shear force and bending moment?

A 36 kN and 72 kN·m B 36 kN and 108 kN·m C 36 kN and 144 kN·m D 72 kN and 144 kN·m

Question 12 ప్రశ్న 12

A beam is supported at A and B, 6 m apart, and overhangs 2 m to C. A UDL of 6 kN/m acts over AB and an 18 kN downward point load acts at C. Taking sagging moment as positive, where is the interior point of contraflexure in AB and what is the maximum positive bending moment?

A Contraflexure at 2 m from A; maximum positive moment 24 kN·m B Contraflexure at 4 m from A; maximum positive moment 12 kN·m C Contraflexure at 5 m from A; maximum positive moment 18 kN·m D No point of contraflexure occurs in AB

Question 13 ప్రశ్న 13

A simply supported beam 6 m long is subjected only to a clockwise concentrated couple of 30 kN·m at an interior point. Taking upward reactions as positive, what are RA and RB?

A RA = +5 kN and RB = +5 kN B RA = -5 kN and RB = +5 kN C RA = +5 kN and RB = -5 kN D RA = -10 kN and RB = +10 kN

Question 14 ప్రశ్న 14

A simply supported beam 8 m long carries a UDL of 4 kN/m over the full span and a clockwise applied couple of 16 kN·m at midspan. Taking sagging bending moment as positive, what is the maximum positive bending moment?

A 24 kN·m immediately to the left of midspan B 32 kN·m at midspan C 40 kN·m immediately to the right of the applied couple D 48 kN·m at the right support

Question 15 ప్రశ్న 15

A distributed load varies according to w(x) = kx over a beam interval, where k is constant and no concentrated loads or couples occur inside that interval. What are the general polynomial forms of the shear-force and bending-moment variations?

A Shear is constant and bending moment is linear. B Shear is linear and bending moment is parabolic. C Shear is quadratic and bending moment is cubic. D Shear is cubic and bending moment is quadratic.

Question 16 ప్రశ్న 16

Over a 4 m beam interval, a triangular downward load varies from zero to 8 kN/m. If the shear-force ordinate at the beginning of the interval is +10 kN, what is the shear-force ordinate at the end?

A +6 kN B 0 kN C -6 kN D -22 kN

Question 17 ప్రశ్న 17

Over a 5 m beam interval, the shear-force diagram varies linearly from +20 kN at the left end to -10 kN at the right end. Using dM/dx = V, what is the net change in bending moment across the interval?

A -25 kN·m B +25 kN·m C +50 kN·m D +75 kN·m

Question 18 ప్రశ్న 18

Why can the bending moment at a simple support located inside a continuous overhanging beam be non-zero even though a pin or roller support itself does not resist an external moment reaction?

A Because every simple support secretly provides a fixed-end moment. B Because the beam section over the support can transmit internal bending moment generated by loads on the overhang, even though the support reaction itself has no moment component. C Because shear force must always be zero at a simple support. D Because an overhang converts the simple support into a fixed support.

Question 19 ప్రశ్న 19

A trapezoidal downward load varies linearly from 6 kN/m at the left end to 18 kN/m at the right end over 8 m. What are the resultant magnitude and its location measured from the left end?

A 96 kN at 4.00 m B 96 kN at approximately 4.67 m C 72 kN at approximately 5.33 m D 192 kN at approximately 4.67 m

Question 20 ప్రశ్న 20

A cantilever 4 m long carries a trapezoidal downward load varying from 4 kN/m at the fixed end to 10 kN/m at the free end. What are the magnitudes of the fixed-end shear force and bending moment?

A 28 kN and 56 kN·m B 28 kN and 64 kN·m C 24 kN and 64 kN·m D 56 kN and 128 kN·m

Question 21 ప్రశ్న 21

A beam is supported at A and B, 5 m apart, and overhangs 2 m beyond B to C. A 20 kN downward point load acts 3 m from A and a 10 kN downward point load acts at C. Taking sagging moment as positive, which pair correctly gives the bending moment at B and the interior point of contraflexure between the 20 kN load and B?

A MB = -20 kN·m and contraflexure at x = 3.75 m from A B MB = +20 kN·m and contraflexure at x = 4.00 m from A C MB = -10 kN·m and contraflexure at x = 3.50 m from A D MB = 0 and no contraflexure occurs

Question 22 ప్రశ్న 22

The bending-moment ordinates immediately on the two sides of an interior point differ in magnitude by 25 kN·m, while the shear-force diagram has no jump at that point. Which localized external action is consistent with this observation?

A A 25 kN concentrated transverse force B A 25 kN·m concentrated couple C A 25 kN/m UDL acting over an infinitesimal length D A simple support reaction of 25 kN

Question 23 ప్రశ్న 23

Consider the following statements about advanced SFD and BMD construction:
1. The resultant of a triangular distributed load acts at one-third of its base measured from the higher-intensity end.
2. An applied concentrated couple produces a jump in the bending-moment diagram but no corresponding concentrated-force jump in the shear-force diagram.
3. A point of contraflexure requires the bending moment to pass through zero and change sign.
4. For a linearly varying distributed load, shear varies linearly and bending moment varies parabolically.

Which statements are correct?

A 1 and 2 only B 1, 2 and 3 only C 2, 3 and 4 only D 1, 2, 3 and 4

Question 24 ప్రశ్న 24

Match each loading feature with the corresponding SFD/BMD implication:
1. Triangular UVL
2. Trapezoidal UVL
3. Concentrated couple
4. Loaded overhang beyond a simple support

P. May create a non-zero hogging internal moment at the adjacent support
Q. Can be decomposed conveniently into rectangular and triangular load components
R. Produces a quadratic shear variation and cubic bending-moment variation over the loaded region
S. Produces a finite bending-moment jump without a transverse-force jump

Which matching is correct?

A 1-R, 2-Q, 3-S, 4-P B 1-Q, 2-R, 3-P, 4-S C 1-S, 2-P, 3-Q, 4-R D 1-P, 2-S, 3-R, 4-Q

Question 25 ప్రశ్న 25

A beam is supported at A and B, 6 m apart, and overhangs 2 m to C. A triangular distributed load acts over AB, varying from zero at A to 9 kN/m at B, and a 12 kN downward point load acts at C. Taking sagging moment as positive, which pair correctly gives the bending moment at B and the interior point of contraflexure in AB?

A MB = -12 kN·m and contraflexure at 3.16 m from A B MB = -24 kN·m and contraflexure at approximately 4.47 m from A C MB = +24 kN·m and contraflexure at approximately 4.47 m from A D MB = -24 kN·m and no interior contraflexure occurs

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