Test 7 - SFD and BMD for Point Loads and UDL

Question 1 ప్రశ్న 1

While constructing shear-force and bending-moment diagrams for a statically determinate beam, which procedure is fundamentally correct?

A Draw the expected diagram shapes first and use equilibrium only if a numerical ordinate is required. B Determine support reactions from whole-beam equilibrium, evaluate internal shear and moment from section equilibrium, and then connect the ordinates consistently with the loading. C Determine bending moments first from assumed curvature and obtain reactions from the completed BMD. D Ignore support reactions because the internal-force diagrams depend only on applied loads.

Question 2 ప్రశ్న 2

A simply supported beam of span 8 m carries a 40 kN point load at midspan. What are the support reactions and the maximum bending moment?

A 20 kN at each support and 40 kN·m B 20 kN at each support and 80 kN·m C 40 kN at each support and 80 kN·m D 20 kN at each support and 160 kN·m

Question 3 ప్రశ్న 3

A simply supported beam AB of span 6 m carries a 30 kN point load 2 m from support A. What are the vertical reactions and the maximum bending moment?

A RA = 10 kN, RB = 20 kN and Mmax = 20 kN·m B RA = 20 kN, RB = 10 kN and Mmax = 40 kN·m C RA = 15 kN, RB = 15 kN and Mmax = 30 kN·m D RA = 20 kN, RB = 10 kN and Mmax = 60 kN·m

Question 4 ప్రశ్న 4

A simply supported beam 5 m long carries a UDL of 12 kN/m over its entire span. What are the support reactions and maximum bending moment?

A 30 kN at each support and 37.5 kN·m B 30 kN at each support and 75 kN·m C 60 kN at each support and 37.5 kN·m D 24 kN at each support and 30 kN·m

Question 5 ప్రశ్న 5

A simply supported beam of span 8 m carries a UDL of 6 kN/m over the entire span and a 20 kN downward point load 2 m from the left support. What are the support reactions?

A RA = 29 kN and RB = 39 kN B RA = 34 kN and RB = 34 kN C RA = 39 kN and RB = 29 kN D RA = 48 kN and RB = 20 kN

Question 6 ప్రశ్న 6

A simply supported beam of span 10 m carries a UDL of 4 kN/m over its full span and a 30 kN point load at 6 m from the left support. Where does the maximum bending moment occur and what is its value?

A At 5 m from the left support; 110 kN·m B At the 30 kN load, 6 m from the left support; 120 kN·m C At 6 m from the left support; 180 kN·m D At the right support; 120 kN·m

Question 7 ప్రశ్న 7

A simply supported beam of span 8 m carries a UDL of 10 kN/m over the left-hand 4 m only. At what distance from the left support does the maximum bending moment occur, and what is its value?

A 2 m; 40 kN·m B 3 m; 45 kN·m C 4 m; 40 kN·m D 5 m; 45 kN·m

Question 8 ప్రశ్న 8

A simply supported beam of span 8 m carries a UDL of 10 kN/m over the right-hand 4 m only. At what distance from the left support does the maximum bending moment occur, and what is its value?

A 3 m; 45 kN·m B 4 m; 40 kN·m C 5 m; 45 kN·m D 6 m; 40 kN·m

Question 9 ప్రశ్న 9

A cantilever beam 3 m long carries a downward point load of 18 kN at its free end. Taking sagging bending moment as positive, which pair correctly gives the internal shear-force magnitude and the fixed-end bending moment?

A 18 kN and -54 kN·m B 18 kN and +54 kN·m C 54 kN and -18 kN·m D 6 kN and -54 kN·m

Question 10 ప్రశ్న 10

A cantilever beam 4 m long carries a UDL of 7 kN/m over the entire span. Taking sagging bending moment as positive, what are the fixed-end shear-force magnitude and bending moment?

A 14 kN and -28 kN·m B 28 kN and -56 kN·m C 28 kN and +56 kN·m D 56 kN and -112 kN·m

Question 11 ప్రశ్న 11

A cantilever 5 m long carries a UDL of 4 kN/m over its entire length and a 20 kN downward point load located 3 m from the fixed end. What are the vertical fixed-support reaction magnitude and fixed-end bending-moment magnitude?

A 40 kN and 110 kN·m B 20 kN and 60 kN·m C 40 kN and 100 kN·m D 60 kN and 110 kN·m

Question 12 ప్రశ్న 12

A cantilever beam is 6 m long and carries a UDL of 5 kN/m only over the outermost 2 m adjacent to the free end. What are the fixed-end shear-force magnitude and bending-moment magnitude?

A 10 kN and 20 kN·m B 10 kN and 50 kN·m C 20 kN and 50 kN·m D 30 kN and 90 kN·m

Question 13 ప్రశ్న 13

A cantilever beam 6 m long carries a UDL only over the first 2 m measured from the fixed support, while the remaining 4 m up to the free end is unloaded. What are the shear force and bending moment at a section 3 m from the fixed support?

A Shear = 10 kN and moment = 10 kN·m B Shear = 10 kN and moment = 20 kN·m C Shear = 0 and moment = 0 D Shear = 0 and moment = 10 kN·m

Question 14 ప్రశ్న 14

A simply supported beam of span 9 m carries a 20 kN point load at x = 3 m and a 30 kN point load at x = 6 m from the left support. What is the maximum bending moment?

A 60 kN·m B 70 kN·m C 80 kN·m D 90 kN·m

Question 15 ప్రశ్న 15

A simply supported beam 8 m long carries two equal point loads of 25 kN located 2 m and 6 m from the left support. What is the structural response between the two loads?

A Shear force is zero and bending moment is constant at 50 kN·m. B Shear force is 25 kN and bending moment increases linearly from 0 to 100 kN·m. C Shear force is zero and bending moment is zero. D Shear force varies linearly and bending moment is parabolic.

Question 16 ప్రశ్న 16

A simply supported beam 6 m long carries point loads of 15 kN at 1.5 m and 25 kN at 4.5 m from the left support. What is the maximum bending moment?

A 22.5 kN·m B 26.25 kN·m C 33.75 kN·m D 45.0 kN·m

Question 17 ప్రశ్న 17

A simply supported beam 10 m long carries a UDL of 8 kN/m over its entire span. Define the shear-force ordinate V at a section as the algebraic sum of vertical forces to the left of that section, taking upward forces as positive, and take sagging bending moment as positive. What are V and M at a section 3 m from the left support?

A V = +16 kN and M = +84 kN·m B V = +24 kN and M = +96 kN·m C V = +16 kN and M = +120 kN·m D V = -16 kN and M = +84 kN·m

Question 18 ప్రశ్న 18

A simply supported beam of span 12 m carries a UDL of 6 kN/m over the full span. At what section is the shear force zero, and what is the bending moment there?

A x = 3 m; M = 81 kN·m B x = 6 m; M = 108 kN·m C x = 6 m; M = 216 kN·m D x = 9 m; M = 81 kN·m

Question 19 ప్రశ్న 19

Over a 6 m beam interval, the shear force decreases linearly from +24 kN to -12 kN. Adopt dV/dx = -w and dM/dx = V, with downward load intensity w taken as positive. What uniform load intensity acts over the interval and what is the net change in bending moment?

A w = 4 kN/m and ΔM = 36 kN·m B w = 6 kN/m and ΔM = 36 kN·m C w = 6 kN/m and ΔM = 72 kN·m D w = 12 kN/m and ΔM = 18 kN·m

Question 20 ప్రశ్న 20

At a concentrated downward point load, the shear-force ordinate changes from +14 kN immediately to the left of the load to -26 kN immediately to its right. What is the magnitude of the point load, assuming there is no support reaction at that same point?

A 12 kN B 26 kN C 40 kN D 52 kN

Question 21 ప్రశ్న 21

Over a 2 m beam segment, the shear force is constant at +15 kN and the bending moment at the left end of the segment is +20 kN·m. Using dM/dx = V, what is the bending moment at the right end?

A -10 kN·m B +20 kN·m C +35 kN·m D +50 kN·m

Question 22 ప్రశ్న 22

The same downward point load P is applied first at the free end of a cantilever of length L and then at a point L/2 from the fixed support. How do the fixed-end shear-force magnitude and fixed-end bending-moment magnitude compare between the two cases?

A Both fixed-end shear and moment are halved when the load is moved to L/2. B Fixed-end shear is unchanged, while fixed-end moment is halved. C Fixed-end shear is halved, while fixed-end moment is unchanged. D Both quantities remain unchanged.

Question 23 ప్రశ్న 23

A simply supported beam 6 m long carries a UDL of 4 kN/m over its full span together with an 18 kN downward point load at midspan. What is the maximum bending moment?

A 36 kN·m B 45 kN·m C 54 kN·m D 63 kN·m

Question 24 ప్రశ్న 24

Consider the following statements for beams carrying only point loads and uniformly distributed loads:
1. Between concentrated loads, a region having no distributed load has constant shear force.
2. Under a constant UDL, the shear-force diagram is linear and the bending-moment diagram is parabolic.
3. A point load causes a finite jump in bending moment even when no concentrated couple is applied there.
4. A zero-shear point at which shear changes sign corresponds to a local extremum of bending moment.

Which statements are correct?

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

Question 25 ప్రశ్న 25

Match each beam-loading case with its characteristic shear-force and bending-moment behaviour:
1. Simply supported beam with a single central point load
2. Simply supported beam with a full-span UDL
3. Cantilever with a free-end point load
4. Cantilever with a full-span UDL

P. Constant shear and linearly varying bending moment over the span
Q. Linear shear and parabolic bending moment, both reaching their largest magnitudes at the fixed end
R. Shear is piecewise constant with a jump at midspan and bending moment is piecewise linear with its maximum at midspan
S. Shear varies linearly across the span and bending moment is parabolic with its maximum at midspan

Which matching is correct?

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

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