Test 30 - Moving Loads and Influence Line Fundamentals

Question 1 ప్రశ్న 1

Which statement best defines an influence line for a structural response quantity?

A It shows the variation of bending moment along every section of a structure for one fixed loading condition. B It shows the variation of a specified response at one chosen location as a unit load moves across the structure. C It shows only the deflected shape of a structure under permanent loading. D It shows the variation of material stress with strain.

Question 2 ప్రశ్న 2

Which statement correctly distinguishes an influence line for bending moment at section C from an ordinary bending-moment diagram?

A Both diagrams always represent exactly the same quantity along the beam. B An influence line varies the load position while observing moment at C, whereas a bending-moment diagram shows moment at different beam sections for a specified fixed loading. C An influence line is used only for indeterminate structures, whereas a bending-moment diagram is used only for determinate structures. D A bending-moment diagram is dimensionless, whereas an influence line for moment always has units of force.

Question 3 ప్రశ్న 3

A simply supported beam AB has span L. A downward unit load is at a distance x from support A. What are the influence-line ordinates for vertical reactions RA and RB at that load position?

A RA = x/L and RB = (L-x)/L B RA = (L-x)/L and RB = x/L C RA = RB = 1/2 for every load position D RA = L/x and RB = L/(L-x)

Question 4 ప్రశ్న 4

A simply supported beam has a span of 12 m. At a particular instant, a 40 kN moving point load is 3 m from the left support A. What are the vertical reactions?

A RA = 10 kN and RB = 30 kN B RA = 20 kN and RB = 20 kN C RA = 30 kN and RB = 10 kN D RA = 40 kN and RB = 0

Question 5 ప్రశ్న 5

A single downward point load P moves across a simply supported beam from support A to support B. At what position is the vertical reaction at A maximum?

A When the load is at A B When the load is at midspan C When the load is at B D The reaction at A is independent of load position

Question 6 ప్రశ్న 6

An overhanging beam has supports A at x = 0 and B at x = 6 m, with a right overhang extending to free end C at x = 8 m. A downward unit load is placed at C. What are the vertical support reactions?

A RA = 1/3 upward and RB = 2/3 upward B RA = 0 and RB = 1 upward C RA = 1/3 downward and RB = 4/3 upward D RA = 2/3 downward and RB = 5/3 upward

Question 7 ప్రశ్న 7

A simply supported beam AB has span L. Section C is a distance a from A and b from B, where L = a + b. What is the maximum ordinate of the influence line for bending moment at C?

A ab/L B L/(ab) C a+b D ab/L²

Question 8 ప్రశ్న 8

A simply supported beam has span 8 m, and section C is 3 m from the left support. A moving point load of 60 kN is positioned exactly at C. What bending moment acts at C?

A 75.0 kN·m B 90.0 kN·m C 112.5 kN·m D 150.0 kN·m

Question 9 ప్రశ్న 9

A simply supported beam has span 8 m and section C is 3 m from the left support. A uniformly distributed load of 10 kN/m covers the entire span. Using the influence line for moment at C, what is MC?

A 37.5 kN·m B 60.0 kN·m C 75.0 kN·m D 150.0 kN·m

Question 10 ప్రశ్న 10

A simply supported beam has span 8 m and section C at x = 3 m from the left support. A UDL of 12 kN/m acts only from x = 2 m to x = 6 m. What bending moment acts at C?

A 54 kN·m B 60 kN·m C 66 kN·m D 72 kN·m

Question 11 ప్రశ్న 11

For a simply supported beam of span L, section C is at distance a from the left support and b = L-a from the right support. Define section shear as VC = RA minus the total downward load lying strictly to the left of C. What are the limiting shear influence-line ordinates immediately to the left and immediately to the right of C?

A C-: +b/L and C+: -a/L B C-: -a/L and C+: +b/L C C-: -b/L and C+: +a/L D C-: +a/L and C+: -b/L

Question 12 ప్రశ్న 12

A simply supported beam has span 10 m and section C at 4 m from the left support. Using VC = RA minus downward loads to the left of C, what shear at C is caused by a 50 kN point load placed immediately to the right of C, and what shear is caused when it is immediately to the left?

A +20 kN and -30 kN B +30 kN and -20 kN C +50 kN and -50 kN D +20 kN and +30 kN

Question 13 ప్రశ్న 13

A simply supported beam has span 10 m and section C at 4 m from the left support. A UDL of 8 kN/m covers the entire span. Under the convention VC = RA minus the downward load to the left of C, what is the shear at C?

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

Question 14 ప్రశ్న 14

Several concentrated moving loads Pi occupy known positions xi on a structure. If yi is the influence-line ordinate for a particular response at each load position, how is that response calculated?

A By ΣPi yi with the algebraic signs of the ordinates retained B By ΣPi/yi C By multiplying the total load by the largest ordinate regardless of load positions D By Σyi without using the load magnitudes

Question 15 ప్రశ్న 15

A simply supported beam has span 10 m and section C at 4 m from the left support. Two point loads, 40 kN and 20 kN, maintain a spacing of 2 m and may move across the beam in either order. What is the maximum bending moment at C?

A 112 kN·m B 120 kN·m C 128 kN·m D 144 kN·m

Question 16 ప్రశ్న 16

A simply supported beam has span 12 m. At one instant, a 30 kN moving load is 2 m from support A and a 50 kN load is 7 m from A. What is the reaction at A?

A 34.17 kN B 40.00 kN C 45.83 kN D 55.00 kN

Question 17 ప్రశ్న 17

A simply supported beam has span 10 m and section C at 4 m from A. A movable UDL of intensity 10 kN/m can be placed over whichever favorable part of the span is required. What are the maximum positive and maximum negative shear values at C under the convention VC = RA minus the load to the left of C?

A +18 kN and -8 kN B +30 kN and -20 kN C +8 kN and -18 kN D +20 kN and -30 kN

Question 18 ప్రశ్న 18

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

A 2.0 m on each side; MC = 72.0 kN·m B 1.6 m to the left and 2.4 m to the right; MC = 76.8 kN·m C 2.4 m to the left and 1.6 m to the right; MC = 76.8 kN·m D All 4 m to the right; MC = 64.0 kN·m

Question 19 ప్రశ్న 19

Which statement best expresses the Müller-Breslau principle for an influence line?

A Remove the restraint associated with the required response and impose a unit displacement in its positive direction; the resulting compatible displaced shape is proportional to the influence line. B Draw the ordinary bending-moment diagram and divide every ordinate by EI. C Place all moving loads simultaneously at midspan. D Replace the structure by a free body having no supports.

Question 20 ప్రశ్న 20

To obtain qualitatively the influence line for the vertical reaction at support A of a determinate beam using the Müller-Breslau principle, what is done?

A Release the vertical restraint at A and impose a positive unit vertical displacement there. B Insert an internal hinge at every beam section. C Remove support B and apply a unit moment at A. D Keep all restraints unchanged and apply a unit axial force.

Question 21 ప్రశ్న 21

To construct qualitatively the influence line for bending moment at an interior section C using the Müller-Breslau principle, which operation is appropriate?

A Release the bending-moment restraint at C by inserting a hinge and impose a positive unit relative rotation corresponding to MC. B Remove the entire beam from both supports. C Apply a unit vertical translation at C without releasing the moment. D Cut the beam at C and impose only an axial displacement.

Question 22 ప్రశ్న 22

For the shear influence line at an interior section C of a simply supported beam, which feature is expected when a moving unit load crosses C?

A A unit jump in the influence-line ordinate B A perfectly smooth curve with zero slope at C C No change of ordinate at C D An infinite ordinate at C

Question 23 ప్రశ్న 23

What are the usual dimensions of influence-line ordinates for a support reaction, section shear and section bending moment when the moving load is treated as a unit force?

A Reaction and shear ordinates are dimensionless, while bending-moment ordinates have dimensions of length. B All three ordinates have dimensions of force. C Reaction ordinates have dimensions of length, while moment ordinates are dimensionless. D All influence-line ordinates have dimensions of force times length.

Question 24 ప్రశ్న 24

Consider the following statements about a simply supported beam and a fixed interior section C:
1. The influence line for a support reaction is linear over the span.
2. The bending-moment influence line at C reaches its peak when the unit load is at C.
3. The shear influence line at C is continuous as the unit load crosses C.
4. The response to several concentrated moving loads is found by summing each load multiplied by its influence-line ordinate.

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 influence-line concept with its correct description:
1. Influence line for RA of a simply supported beam
2. Influence line for moment at section C
3. Influence line for shear at section C
4. Response to a UDL over a specified portion of the beam

P. Has a unit jump at C under the stated shear convention
Q. Load intensity multiplied by the algebraic area under the influence line over the loaded length
R. Straight line from ordinate 1 at A to 0 at B
S. Piecewise linear triangle with its vertex at C

Which matching is correct?

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

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