theory of structures.pdf

Objective Type Questions Rotation contribution at the fixed end of a member is *(a) 0.5 (6) 0.75 (c ) zero (d) 1.00.

(b) force method (c) stress function method (d) displacement field method.

3.8.

In the E u le r's theory of colum n, direct stress is assumed e.i) negligible z e ro (cl not act ing at a il id) h illy. The rail track is an example of beam (.71 fixed at intervals (l>) of continuous type (c) on elastic supports

(c) fictitious structure (d) all of the above.

3.9.

'// ofsimplysupportedtype. Deficient frames are same as a) redundant frames b) perfect frames c) portal frames d) none of the above.

3.10.

(d) none of the above. The frame shown in Fig. 1. is

b / 6 (c) ? < b / 6 (d ) e = b/3 . 3 .1 8 . 'Boom ' is a com pression m em ber related to

structure at a railway pla crane building frame shuttering.

3.22.

N

Bt

________ c ] ____ * —b/

-H

Fig. 3. (a) moment at B reaches the limit (b) moment at C reaches the limit (c) both of the above (d) none of the above.

Theory of Structures □ □ 3.83 (a) 38.5 t-m, 38.5 t-m Sw ay an alysis of a p o rtal fram e becomes essentials when (b) 3.85 t-m, 3.85 t-m a) loading is non-symmetric (c) 53.8 t-m, 53.8 t-m (d) 43.2 t-m, 43.2 t-m. d iffe re n t ty p es o f jo in ts at 3.28. The B.M at C w ill be equal to support occurs (a) 5.14 t-m (b) 7.71 t-m id) all of the above. (c) 2.57 t-m (d ) 1.28 t-m. A three hinged semicircular arch of 3.29. Reactions w ill be equal at (a) A and E (b) B and D radius V is subjected to u.d.l. of w per unit length on the whole span. (c) A and C (d) A and B. The horizontal thrust w ill be given 3.30. R e a c tio n at B as co m p ared to by reaction at A w ill be (a) w / 2 (b) w r / 2 (a) less (c) zvr (d) zol (b) more (c) equal A three-hinged parabolic arch has (d) cannot be predicted. left and right hinges at hx and h2 (h > h^) d is ta n c e s re s p e c tiv e ly 3.31. R eaction at the extrem e supports will be below the crow n. A concentrated load 'P' a cts on the crow n . (a) 4.71 t (b) 9.42 t Horizontal distance of left and right (c) 14.13 t (d) 2.35 t. hinges from the crown are L] and 3.32. A structural m em ber elongates by L; (L, + L2 = L = span) respectively. 5L under axial tension of 'P '. The Value of Lj w ill be external work done will be (a) P . 5L (b) P . 8L/4 (a) L 4 h / ( 4 h + 4 h 2) (b) 4 h / { 4 h + 4 k i )

3.33. tc) L

+

V ^ / (V ^ + V ^ )2A continuous beam ABCDE is 12 meters long, and contains 4 spans of 3 m eters each. Beam is loaded with u .d.l of 4000 kg/m throughout its length. The bending moments at A and E w ill be equal (a) zero

(b) 12000 kgf-m

(c) 6000 kgf-m (d) 3000 kgf-m. The B.M . at B and D w ill be respectively

A portal frame of uniform flexural rigidity is show n in Fig. 4. Using p rin cip al of least w ork, find the horizontal reaction at D in tonnes.

3.84

□ □ Civil Engineering (Objective Type)

(a) (b) (c) (d) 3.34.

4.5 leftward 4.5 rightw ard 90 leftward 90 rightw ard.

The fixed and moment at the end A of the beam shown in Fig. 5, will be

3.38.

3.39.

3.40. (a) (b) (c) (d)

W qL2/30 W 0L2/12 W 0L2/24 W 0L2/10.

3.35.

If the triangular load covers the left half of the span in Fig. 5, the fixing moment at B will be (a) W 0L2/160 (b) 3 W 0L2/40 (c) 3 W0L2/160 (d) W0L2/40.

3.36.

"B.M . at any section of an arch is p ro p o rtio n a l to the o rd in ate b e tw e e n g iv e n arch and lin e a r arch". This statement relates to the principal of (a) Eddy's theorem (b) Bette's theorem (c) Reciprocal theorem (d) Johnson's theorem.

3.37.

W hich of the fo llo w in g is not a compression member? t (a) Boom (b) Strut (c) Stanchion (d) None of the above.

3.41.

The ratio between 'angle of re and 'angle of friction' is (a) 0.3 (b) 0.5 (c) 1.3 (d ) 1. The Greenberg and Prager's th in plastic analysis of structur also known as (a) upper bound theorem (b) lower bound theorem (c) plastic hinge theorem (d) both (a) and (b). The cases of support sinking encountered w hen (a) soil conditions change at n distances (b) load geography is undula (c) both of the above (d) none of the above. A b ea m o f sp a n V of fie rigidity 'E l' stores strain energy to I •Ml d x dx ■ K dx {a) (b) 2 EI EI

(c) 3.42.

1Mx dx I f

(d)

: MIdx 2EI '

The te n sio n and com pr m em bers are stressed to 1500 cm2 and 1200 kgf/cm2 resf in the truss shown in Fig. 6. If 2 x 106 k g f/ c m 2 the ve deflection of joint F will be 6t

6t

Fig. 6.

Theory o f Structures □ □ 3.85 IS .75 mm nifr'j 21.3 mm * ~ 1 mm iu’i 14.2 mm.

(c) both of the above (d) none of the above. A 2-hinged sem i-circu lar arch of radius V carrying a concentrated load 'P ' at the cro w n d ev elo p s horizontal thrust equal to (a) Pr (b) Vfv (c) (P /r)2 (d) P/r. A continuous beam is shown in Fig. 8 support B sinks by 10 mm during loading. Value of I = 8000 cm4, and E = lx lO 6 kgf/cm 2. U se m om ent distribution method, and find fixed end m om ent M DC due to external load only

3.47.

tia p ey ro n 's theorem is also known as- die theorem of I |s| 3-moments 2-moments ‘ (£ A steel rod of sectional area 250 sq. mm connects two parallel walls 5 m apart. The nuts at the ends were lightened w hen the rod was heated to 100°C. If a steel = 0.000012/°C, Esteel = 0.2 M N /m m 2 the tensile force developed at a temperature of 50°C, is

A simply supported beam carries varying load from zero at one and W at the other end. If the len. of the beam is a, the shear force v* be zero at a distance x from le loaded point where x is a («) 2

h n

A sim p ly su p p o rte d u n ifo rm rectangular bar breadth b, depth d and length L, carries an isolated load W at its m id-span. The sam e bar experiences extension e under same te n sile lo ad . T he ra tio o f the m axim u m d e fle c tio n to the elongation is d (fl) 1

3.93.

(b) 2

(c) 120 N/m m 2 (d) 150 N/m m 2.

3.98.

(b)

f

(d)

The ratio of the stresses product by a suddenly applied load and 1 a gradually applied load on a : a is (a) 1/4 (b) 1/2

(c) 1 (d) 2 . A yield moment of a cross-secti defined as the moment that will produce the yield stress in (ia) the outermost fibre of the s^ (,b) the innermost fibre of the s (c) the neutral fibre of the Si (d) the fibre everywhere. The p oin t of contraflexu re is point where (a) B.M. changes sign (b) B.M. is maximum (c) B.M. is minimum (d) S.F. is zero. The S.F. diagram of a loaded shown in Fig. 15 is that of

Fig. 15.

Theory o f Structures □ □ 3.91 (a) a simply supported beam with isolated central load (b) a simply supported beam with uniformly distributed load (c) a can tilev er w ith an isolated load at the free end (d) a cantilever w ith a uniform ly distributed load.

(«)

1 :

1

- :2

(b)

2 :

1

\ :1

(c) (d)

1 : none

1 : 2 of the above.

3.103. In the truss (Fig. 16) the force in the member AC is

The ratio of the section modulus of a square section of side B and that of a circular section of diameter D, is i(fl)\ 2n

10 t

5t

(b) 3n 16 (d)

16' The m o m en t o f in e rtia of a rectangular section of width B and dep th D ab o u t an axis p a ssin g through C .G . and p arallel to its width is

(«)

BD

(b)

6

(d) 12 1. The maximum magnitude of shear stress due to sh ear force F on a rectangular section of area A at the neutral axis is F F (b) A 2A 3F

(c) 2A

{a) 6.25 t compressive (b) 8.75 t tensile (c)

8.75

t tensile

BD B2D

(0

Fig. 16.

/j \ 2F O 3A '

There are two hinged semicircular arches A, B and C of radii 5 m, 7.5 m and 10 m respectively and each carries a cencentrated load W at their crowns. The horizontal thrust at their supports w ill be in the ratio of

(d)

8.75

t compressive.

3.104. A bar of square section of area a2 is held such that one of its diameter is vertical. The maximum shear stress w ill develop at a depth h where h is (a)

2V3 4

(b) ' '

3V2 4

W 733.105. M axim um shear stress theory for the failure of a material at the elastic limit is known (a) Guest's or Trecas theory (b) St. Venant's theory (c) Rankine's theory (d) Haigs theory.

(

3.92

Civil Engineering (Objective Type)

□□

3.106. The total strain energy of a beam of length L, having moment of inertia of its section I, w hen subjected to a bending moment M, is

Mf2 8x (b) 2 EI

M; 8x («) EI

w

L M2 [o 2 EI 8x

EI

dx.

3.107. A sim ply supported beam w hich carries a uniformly distributed load has two equal overhangs. To have m axim um B.M . prod uced in the beam least possible, the ratio of the length of the overhang to the total length of the beam, is (a) 0.207 (b) 0.307 (c) 0.407 (d) 0.508. 3.108. If M, I, R, E, F, and Y are the bending moment, moment of inertia, radius of curvature, modulus of elasticity, stress and the depth of the neutral axis at section, then

(.b) E = 2 K 1 +

(c) —K ( l - 2 / m) = n[" 1 + —

(b)

M _ R I _ E

m

3.111. Pick up the indeterminate struct from those shown in Fig. 17.

(if)

Y

J _ _ R _ F_ M~ E ~ Y M

(c)

\

2

(d) all of the above. 3.110. A com pound bar consists of bars of equal length. Steel bar crc section is 35 mm 2 and that of bra bar is 3000 m m 2. These are subjec to a compressive load 100,000 Eb - 0.2 M N / m m 2 and E fc = M N/m m 2, the stresses develop are (a) a b= 10 N/m m 2;o = 20 N/i (.b) o fc= 8N/mm2; a = 16 N/i (c) ob= 6 N/mm2; 12 N/i (d) o b= 5 N/mm2; o = 10 N/r

(0 (fl)

m

_ Hinge _ c y b

E _F

R“Y

, M E (d) j - R

Y (Hi)

F

3.109. If E, N, K and 1/m are modulus of elasticity, modulus of rigidity, bulk m o d u lu s and P o isso n ra tio of materials, the following relationship holds good (a) E = 3K

m

(iv)

Fig. 17. (a) Figure (i) (b) Figure (ii) (c) Figure (iii) (d) Figure (iv).

Theory o f Structures □ □ 3.93 L112. A bar 2 metre long and having its area of cross-section A, is subjected to a gradually applied tensile load W. The strain energy stored in the bar is (a) (c)

WL 2AE

(b)

W2L AE

(d)

WL AE W 2L 2AE

13. A load of 1960 N is raised at the end of a s te e l w ire . T he m in im u m diameter of the wire so that stress in the wire does not exceed 100 N/ mm2 is : (a) 4.0 m m (b) 4.5 mm (c) 5.0 m m (d) 5.5 mm. Pick up the incorrect statement from the following : The torsional resistance of a shaft is directly proportional to (a) modulus of rigidity (b) angle of twist (c) reciprocal of the length of the shaft (d) m om ent of inertia of the shaft section. A re ctan g u lar colu m n show n in Fig. 18, carries a load P havin g eccentricities ex an ey along X and Y axis. The stress at any point (x, y) is D

A

C

X

-*IB

Fig. 18. P_ 12gr y («) bd 1 +

12er.x

(b) P P ' 6e y 6ex.x (C) bd 1 + —-— + — i—

(d)

P_ 1 bd

3.116. In a simple bending theory, one of the assum ption is that the plane se ctio n s b efo re b en d in g rem ain p la n e a fte r b e n d in g . T his assum ption m eans that (a) stress is uniform throughout the beam (b) strain is uniform throughout the beam (c) stre ss is p ro p o rtio n a l to the distance from the neutral axis (rf) stra in is p ro p o rtio n a l to the distance from the neutral axis. 3.117. W hen the shear force diagram is a parabolic curve between two points, it indicates that there is a (a) point load at the two points (b) no lo ad in g b etw een the two points (c) u n ifo rm ly d is trib u te d load between the two points (d) uniformly varying load between the two points. 3.118. Which of the following statement is correct ? (a) Continuous beam has only two supports at the ends (b) A u.d.l. spreads uniformly over the whole length of a beam (c) The B.M. is maximum where S.F. is maximum (d) At the point of contraflexure, the b e n d in g m o m en t is m axim um .

3.94

□ □ Civil Engineering (Objective Type)

3.119. When there is a sudden increase or 3.124. The ratio of the maximum deflec' decrease in S.F. diagram betw een of a beam sim ply supported at any tw o p o in ts it in d icates that ends loaded w ith a u.d.l. W over there is a entire length and w hen loaded vc load W at centre, w ill be (fl) point load at the two points (b) no lo a d in g b e tw e e n the tw o (a) 1 (b) 9/16 points (c) 5/8 (d) 2/3. (c) u.d.l. between the two points 3.125. The B.M. diagram for a cantil (d) uniformly varying load between beam subjected to a couple at the two points. free end of the beam would be 3.120. The S.F. diagram for a cantilever (a) rectangle (b) triangle beam of length L and carrying a (c) parabola (d) cubic parab gradually varying load from zero at 3.126. A beam sim ply supported at free end and w per unit length at ends carries a load W at the cer the fixed end is a causing deflection 5r If the w; (a) horizontal straight line of beam doubled the deflection (b) vertical straight line the centre under the same load (c) inclined line be (d) parabolic curve. (a) 8 (b) 1/2 5, 3.121. T he B .M . d ia g ra m fo r a sim p ly (c) 1/4 Sx (d) 1/3 81. supported beam loaded in its centre 3.127. For a beam of length L, fixed at is end, su p ported at the other (a) a right angled triangle lo ad ed W at th e ce n tre C (.b) an isoscles triangle m aximum B.M. w ill occur at (c) an equilateral triangle (a) fixed end (d) a rectangle. (b) centre 3.122. The S.F. at the centre of a simply (c) simply supported end supported beam of length 7' with a (d) betw een fixed end and ce gradually varying load from zero at 3.128. In the above problem the value both ends to ‘w ’ per m etre at the maximum B.M. w ill be centre is WL (a) w L /A (b) ivL/2 (a) ~ WL (b) 24 (c) zero (d) w\?/2. WL 3WL 3.123. Two long beam connected together (d) (c) 16 v” 7 16 by a h in g e H, and u n d er u .d .l. throughout on its length, is simply 3.129. In the Problem 127, the B.M. at supported. The B.M. on the hinge centre w ill be H will be 3WL ... WL (a) zero (b) (a) 16 16 (b) equal to reactions 5WL _5 (c) m axim um WL (d) (c) 16 32 (d) negative.

Theory of Structures □ □ 3.95 A self su p p ortin g steel chim ney transm its the lateral forces to the foundation by (a) fixed beam action (b) propped beam action (c) cantilever action (d) simply supported beam action. A beam carrying a u.d.l. rests on two supports 'b' apart w ith equal overhang is 'a' at each end, the ratio 't/a' for zero B.M. at mid span is («) 1/2 (b) 1 ’fr) 2 (d) 2/3. In the above problem, the ratio 'b/a' so that the maximum B.M. is small a s possible w ill be (i) 1 (b) 2

3.136. The ratio of the area under the B.M. diagram betw een any two points along a beam to the flexural rigidity El gives the change to the following param eter betw een the two points (a) deflection (b) shear force (c) slope (d) bending moment. 3.137. A simple beam AB of span L pinned at A and resting on rollers at B is subjected to a clockwise couple M at centre. The m axim um shear is (a) ML (b) M/L

same deflection