Test 24 - Yield Line Theory of RCC Slabs

Question 1 ప్రశ్న 1

Which statement best describes yield-line analysis of reinforced concrete slabs?

A It is a linear-elastic method used primarily to calculate service-load deflections B It is a plastic-collapse method in which an assumed kinematically admissible yield-line mechanism gives an upper-bound estimate of collapse load C It is a method for determining only punching-shear strength D It assumes that the slab remains completely uncracked up to collapse

Question 2 ప్రశ్న 2

What is meant by a positive yield line in a conventionally reinforced RCC slab subjected to downward gravity loading?

A A line along which only concrete compression failure occurs B A line at which the top reinforcement yields under hogging moment C A line associated with positive or sagging bending, with principal flexural tension at the bottom face D A construction joint having zero bending resistance

Question 3 ప్రశ్న 3

Which description correctly identifies a negative yield line in an RCC slab?

A It is associated with hogging bending and yielding of reinforcement near the top face B It is always located at the centre of a simply supported slab C It represents a region having zero bending moment D It can occur only in an unreinforced slab

Question 4 ప్రశ్న 4

When is a set of yield lines considered to form a collapse mechanism?

A As soon as the first flexural crack appears anywhere in the slab B When every reinforcement bar in the entire slab reaches yield simultaneously C When the concrete compression zone disappears everywhere D When enough yield lines have formed to divide the slab into segments that can undergo compatible rigid-body rotations consistent with the supports

Question 5 ప్రశ్న 5

Which two methods are commonly used to determine collapse loads in classical yield-line analysis?

A Slope-deflection method and moment-distribution method B Virtual-work method and segmental-equilibrium method C Conjugate-beam method and moment-area method D Hardy Cross method and column-analogy method

Question 6 ప్రశ్న 6

What equation expresses the virtual-work principle at collapse in yield-line analysis?

A Elastic strain energy must be zero B External work must always exceed internal work C External work done by the collapse loads equals internal work dissipated along the yield lines D Support reaction work alone equals the dead-load work

Question 7 ప్రశ్న 7

A straight yield line has constant plastic moment resistance m per unit length, length L and relative rotation theta across it. What is its contribution to internal work?

A mLtheta B mL/theta C mtheta/L D mL squared theta

Question 8 ప్రశ్న 8

For a uniformly distributed load w acting over a slab area A, how is the external virtual work generally obtained in yield-line analysis?

A By multiplying w by the maximum slab displacement only B By multiplying w by the slab perimeter C By using only the displacement at the supports D By integrating the load multiplied by the compatible virtual displacement over the loaded slab area

Question 9 ప్రశ్న 9

An isotropically reinforced square slab of side L is simply supported along all four edges and carries a uniformly distributed collapse load w. For the standard symmetric X-shaped yield-line mechanism with positive plastic moment resistance m per unit length, which relation is obtained?

A w = 8m/L squared B w = 24m/L squared C w = 48m/L squared D w = 12m/L squared

Question 10 ప్రశ్న 10

A 5 m by 5 m isotropically reinforced slab is simply supported on all four edges. Assuming the standard symmetric X-shaped mechanism and positive plastic moment resistance m = 30 kN·m/m, what uniformly distributed collapse load is obtained?

A 14.4 kN/m² B 24.0 kN/m² C 28.8 kN/m² D 36.0 kN/m²

Question 11 ప్రశ్న 11

A square slab is fixed along all four edges and is assumed to collapse in the symmetric mechanism consisting of positive diagonal yield lines and negative yield lines along all four fixed edges. If the positive and negative plastic moment capacities are m+ and m- respectively, which collapse-load relation follows for a uniformly distributed load?

A w = 24(m+ + m-)/L squared B w = 8(m+ - m-)/L squared C w = 24m+/L squared only D w = 48(m+ + m-)/L squared

Question 12 ప్రశ్న 12

A 5 m square slab fixed on all four edges has positive plastic moment capacity m+ = 25 kN·m/m and negative plastic moment capacity m- = 15 kN·m/m. Assuming the standard symmetric fixed-edge mechanism under UDL, what collapse load is obtained?

A 24.0 kN/m² B 28.8 kN/m² C 32.0 kN/m² D 38.4 kN/m²

Question 13 ప్రశ్న 13

An isotropically reinforced square slab is simply supported along all four edges and is subjected to a single concentrated load at its centre. For the symmetric X-shaped yield-line mechanism, the positive plastic moment resistance is 22 kN·m/m. What collapse point load is predicted?

A 88 kN B 176 kN C 264 kN D 352 kN

Question 14 ప్రశ్న 14

Consider a one-way slab strip of span L, simply supported at both ends and carrying a uniformly distributed collapse load w. If a positive yield line forms across the full strip width at midspan with plastic moment resistance m per unit width, what collapse-load relation is obtained?

A w = 4m/L squared B w = 16m/L squared C w = 8m/L squared D w = 24m/L squared

Question 15 ప్రశ్న 15

A one-way simply supported slab strip has span 4 m and positive plastic moment resistance m = 24 kN·m/m. Assuming the standard midspan yield-line mechanism under uniform loading, what collapse load is obtained?

A 12 kN/m² B 18 kN/m² C 24 kN/m² D 48 kN/m²

Question 16 ప్రశ్న 16

A one-way slab strip is fixed at both ends and collapses with one positive yield line at midspan and negative yield lines at both supports. If the positive and negative plastic moment capacities are m+ and m- respectively, which collapse-load relation applies under uniform loading?

A w = 8m+/L squared B w = 16m-/L squared C w = 4(m+ + m-)/L squared D w = 8(m+ + m-)/L squared

Question 17 ప్రశ్న 17

A one-way slab strip fixed at both ends has span 4 m, positive plastic moment resistance m+ = 20 kN·m/m and negative plastic moment resistance m- = 15 kN·m/m. What uniformly distributed collapse load follows from the standard three-yield-line mechanism?

A 12.5 kN/m² B 17.5 kN/m² C 25.0 kN/m² D 35.0 kN/m²

Question 18 ప్రశ్న 18

Which statement correctly distinguishes isotropically and orthotropically reinforced slabs in yield-line analysis?

A An isotropic slab has zero moment capacity in one reinforcement direction B An orthotropic slab must have identical plastic moment resistance in all directions C In an isotropically reinforced slab the relevant plastic moment capacity is direction-independent, whereas an orthotropic slab has different capacities associated with its principal reinforcement directions D The distinction concerns only concrete grade and not reinforcement

Question 19 ప్రశ్న 19

For an orthotropically reinforced slab, use the supplied relation m(alpha) = mx cos²(alpha) + my sin²(alpha). If mx = 30 kN·m/m, my = 15 kN·m/m and the yield line makes alpha = 60 degrees with the x-axis, what value of m(alpha) is obtained?

A 18.75 kN·m/m B 22.50 kN·m/m C 26.25 kN·m/m D 30.00 kN·m/m

Question 20 ప్రశ్న 20

Three different kinematically admissible yield-line mechanisms for the same slab predict collapse loads of 42 kN/m², 37 kN/m² and 40 kN/m². According to the upper-bound character of yield-line analysis, which value should govern among these mechanisms?

A 42 kN/m² because the largest value is always safest B 40 kN/m² because the mean mechanism should be selected C 39.67 kN/m² because the predictions should be averaged D 37 kN/m² because the lowest admissible upper-bound collapse load is the critical one among those examined

Question 21 ప్రశ్న 21

Which statement most accurately distinguishes yield-line analysis from ordinary elastic slab analysis?

A Yield-line analysis determines only elastic deflection while elastic analysis determines collapse load B Yield-line analysis investigates an ultimate plastic collapse mechanism, whereas elastic analysis evaluates pre-yield force and deformation distributions based on elastic stiffness assumptions C Both methods necessarily give identical bending-moment distributions at every load level D Yield-line theory eliminates the need for all serviceability checks

Question 22 ప్రశ్న 22

How does changing an edge from simply supported to fully rotationally restrained affect a typical yield-line collapse mechanism, assuming adequate top reinforcement is present?

A The restrained edge can develop a negative yield line and contribute additional internal plastic work B The edge can no longer transmit any bending moment C All positive yield lines necessarily disappear D The collapse load must remain identical because support restraint has no influence on yield-line analysis

Question 23 ప్రశ్న 23

Which requirement is essential for an assumed yield-line pattern to be kinematically admissible?

A Every slab segment must remain horizontal during collapse B The pattern must give the maximum possible collapse load C The slab segments must undergo compatible motions while satisfying the displacement restraints imposed by the supports D All yield lines must be parallel to one another

Question 24 ప్రశ్న 24

A yield line has plastic moment resistance m = 30 kN·m/m, length 4.0 m and compatible relative rotation 0.020 rad. What internal work is dissipated along this yield line?

A 0.60 kN·m B 1.20 kN·m C 1.50 kN·m D 2.40 kN·m

Question 25 ప్రశ్న 25

An isotropically reinforced 6 m by 6 m square slab is simply supported on all four edges and is assumed to collapse in the standard symmetric X-shaped mechanism. If its positive plastic moment resistance is 18 kN·m/m, what uniformly distributed collapse load follows from virtual work?

A 6 kN/m² B 9 kN/m² C 12 kN/m² D 18 kN/m²

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