Test 32 - Influence Lines for UDL and Combined Moving Loads

Question 1 ప్రశ్న 1

A uniformly distributed moving load of intensity w covers a specified portion of a beam. If y(x) is the influence-line ordinate for a required response, how is the response obtained?

A By multiplying w by the algebraic area under the influence line over the loaded length B By multiplying w only by the maximum influence-line ordinate C By dividing the loaded length by the total influence-line area D By multiplying the total beam span by the support reaction

Question 2 ప్రశ్న 2

If a distributed moving load has variable intensity w(x) rather than a constant intensity, which expression gives its effect on a structural response having influence-line ordinate y(x)?

A Response = ∫w(x)y(x) dx over the loaded region B Response = wmax times the total beam span C Response = ∫y(x) dx without using w(x) D Response = w(x)/y(x) at the section only

Question 3 ప్రశ్న 3

A simply supported beam has span 12 m and carries a UDL of 8 kN/m over the entire span. Using the influence line for the reaction at the left support A, what is RA?

A 24 kN B 48 kN C 72 kN D 96 kN

Question 4 ప్రశ్న 4

A simply supported beam has span 12 m. A UDL of 6 kN/m acts only from support A to a point 4 m from A. What is the reaction at A?

A 12 kN B 16 kN C 20 kN D 24 kN

Question 5 ప్రశ్న 5

For the beam and partial UDL described in the previous question, what is the reaction at support B?

A 4 kN B 8 kN C 12 kN D 20 kN

Question 6 ప్రశ్న 6

A simply supported beam has span 10 m, and section C is 4 m from support A. A UDL of 8 kN/m covers the entire span. What is the bending moment at C?

A 48 kN·m B 72 kN·m C 96 kN·m D 120 kN·m

Question 7 ప్రశ్న 7

A simply supported beam has span 10 m and section C at 4 m from A. A UDL of 10 kN/m acts only from x = 2 m to x = 7 m, where x is measured from A. What bending moment acts at C?

A 70 kN·m B 80 kN·m C 90 kN·m D 100 kN·m

Question 8 ప్రశ్న 8

A simply supported beam has span 10 m and section C at 4 m from A. Define positive shear as VC = RA minus the downward load lying to the left of C. A UDL of 8 kN/m covers the entire span. What is VC?

A -8 kN B 0 C +8 kN D +16 kN

Question 9 ప్రశ్న 9

For the same 10 m beam with section C at 4 m, a movable UDL of 10 kN/m can cover any favorable portion of the span. What is the maximum positive shear at C?

A 8 kN B 12 kN C 18 kN D 24 kN

Question 10 ప్రశ్న 10

For the same beam and section, what is the maximum negative shear at C produced by a movable UDL of 10 kN/m?

A -4 kN B -8 kN C -12 kN D -18 kN

Question 11 ప్రశ్న 11

A simply supported beam has span 10 m and section C at 4 m from A. A movable UDL of 10 kN/m has a fixed loaded length of 4 m. For maximum bending moment at C, how should the UDL be positioned, and what is the resulting MC?

A 2 m on each side of C; 72.0 kN·m B 1.6 m to the left and 2.4 m to the right of C; 76.8 kN·m C 2.4 m to the left and 1.6 m to the right of C; 76.8 kN·m D All 4 m to the right of C; 64.0 kN·m

Question 12 ప్రశ్న 12

A simply supported beam has span 10 m and section C at 4 m from A. A movable UDL of 8 kN/m has a fixed loaded length of 6 m. What is the maximum bending moment at C?

A 72.00 kN·m B 76.80 kN·m C 80.64 kN·m D 96.00 kN·m

Question 13 ప్రశ్న 13

A simply supported beam has span 10 m and section C at 4 m from A. A full-span UDL of 6 kN/m acts together with a 30 kN concentrated load located exactly at C. What is the bending moment at C?

A 108 kN·m B 120 kN·m C 132 kN·m D 144 kN·m

Question 14 ప్రశ్న 14

A simply supported beam has span 10 m and section C at x = 4 m. A UDL of 5 kN/m acts from x = 2 m to x = 6 m, and a 20 kN concentrated load acts at x = 8 m. What is MC?

A 46 kN·m B 50 kN·m C 54 kN·m D 60 kN·m

Question 15 ప్రశ్న 15

A simply supported beam has span 12 m. A full-span UDL of 4 kN/m acts together with a 30 kN concentrated load located 3 m from support A. What is the reaction at A?

A 40.5 kN B 43.5 kN C 46.5 kN D 52.5 kN

Question 16 ప్రశ్న 16

A simply supported beam has span 12 m. A 30 kN moving point load and a movable UDL of 5 kN/m having fixed length 4 m may be positioned independently to maximize reaction RA. What is the maximum RA?

A 40.00 kN B 43.33 kN C 46.67 kN D 50.00 kN

Question 17 ప్రశ్న 17

A simply supported beam has span 10 m and section C at 4 m from A. A 30 kN point load and a 4 m long UDL of 5 kN/m may be positioned independently to maximize bending moment at C. What is the maximum combined MC?

A 96.0 kN·m B 102.4 kN·m C 110.4 kN·m D 120.0 kN·m

Question 18 ప్రశ్న 18

An overhanging beam has supports A at x = 0 and B at x = 6 m, with a right overhang extending to x = 8 m. A UDL of 6 kN/m acts only over the overhang from x = 6 m to x = 8 m. What are the support reactions?

A RA = 2 kN upward and RB = 10 kN upward B RA = 2 kN downward and RB = 14 kN upward C RA = 6 kN downward and RB = 18 kN upward D RA = 0 and RB = 12 kN upward

Question 19 ప్రశ్న 19

A simply supported beam has span 12 m. A movable UDL of 6 kN/m has fixed length 5 m. What is the maximum reaction at support A?

A 18.75 kN B 21.00 kN C 23.75 kN D 30.00 kN

Question 20 ప్రశ్న 20

A 4 m long UDL of 5 kN/m moves together with a 30 kN concentrated load located at the right-hand end of the UDL. This combined system moves across a simply supported beam of span 12 m. What is the maximum reaction at support B?

A 36.67 kN B 40.00 kN C 43.33 kN D 46.67 kN

Question 21 ప్రశ్న 21

A simply supported beam has span 10 m and section C at 4 m from A. A 20 kN point load is placed immediately to the right of C, and a UDL of 4 kN/m extends for 3 m from C toward B. Using VC = RA minus loads strictly to the left of C, what is VC?

A 12.0 kN B 14.7 kN C 17.4 kN D 21.0 kN

Question 22 ప్రశ్న 22

For a simply supported beam, the influence line for bending moment at an interior section is positive throughout the span. If a movable UDL has no restriction on loaded length other than remaining on the beam, where should it be placed to maximize the positive bending moment at that section?

A Over the entire span B Only over the left half of the span C Only over the right half of the span D Only over the negative influence-line region

Question 23 ప్రశ్న 23

Consider the following statements about moving UDLs and influence lines:
1. The response to a UDL equals its intensity multiplied by the algebraic influence-line area under the loaded region.
2. To maximize positive shear at a section using an unrestricted movable UDL, the load should occupy the positive region of the shear influence line.
3. A fixed-length UDL producing maximum moment at an interior section must always be centred geometrically about that section.
4. Negative influence-line areas must retain their signs when distributed-load responses are calculated.

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 24 ప్రశ్న 24

Match each influence-line application with its correct principle:
1. Full or partial UDL response
2. Maximum positive section shear under unrestricted movable UDL
3. Fixed-length UDL for maximum moment at an interior section
4. Several combined moving load components

P. Position the fixed loaded length so that its end ordinates on the moment influence line are equal
Q. Add the separate responses by linear superposition
R. Load the positive portion of the shear influence line
S. Multiply load intensity by the relevant algebraic influence-line area

Which matching is correct?

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

Question 25 ప్రశ్న 25

A simply supported beam has span 10 m and section C at 4 m from A. Define VC = RA minus the downward loads strictly to the left of C. A UDL of 6 kN/m acts from x = 0 to x = 2 m, while another UDL of 4 kN/m acts from x = 6 m to x = 10 m. What is VC?

A -2 kN B 0 C +2 kN D +4 kN

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