Chapter-5 IES-15.
Deflection of Beam
S K Mondal’s
The bending moment equation, as a function of distance x measured from the left end, for a simply supported beam of span L m carrying a uniformly distributed load of intensity w N/m will be given by [IES-1999]
wL w 3 L-x L-x Nm 2 2 wL 2 w 3 c M= L-x L-x Nm 2 2
wL w 2 x x Nm 2 2 wL 2 wLx d M= x Nm 2 2
a M=
b M=
IES-15. Ans. (b) IES-16.
A simply supported beam with width 'b' and depth ’d’ carries a central load W and undergoes deflection Dž at the centre. If the width and depth are interchanged, the deflection at the centre of the beam would attain the value [IES-1997] 2
d a G b
3
§d · b ¨ ¸ G ©b¹
IES-16. Ans. (b) Deflection at center G
§d · c ¨ ¸ G ©b¹ Wl3 48EI
In second case, deflection G c
§d· d ¨ ¸ ©b¹
3/2
G
Wl3 § bd3 · 48E ¨ ¸ © 12 ¹
Wl 3 48EI c
Wl 3 § db3 · 48 E ¨ ¸ © 12 ¹
Wl 3 d2 § bd 3 · b 2 48 E ¨ ¸ © 12 ¹
d2 G b2
IES-17.
A simply supported beam of rectangular section 4 cm by 6 cm carries a midspan concentrated load such that the 6 cm side lies parallel to line of action of loading; deflection under the load is Dž. If the beam is now supported with the 4 cm side parallel to line of action of loading, the deflection under the load will be: [IES-1993] (a) 0.44 Dž (b) 0.67 Dž (c) 1.5 Dž (d) 2.25 Dž IES-17. Ans. (d) Use above explanation IES-18.
A simply supported beam carrying a concentrated load W at mid-span deflects by Dž1 under the load. If the same beam carries the load W such that it is distributed uniformly over entire length and undergoes a deflection Dž2 at the [IES-1995; GATE-1994] mid span. The ratio Dž1: Dž2 is: (a) 2: 1
IES-18. Ans. (d) G1
(b)
Wl3 48EI
2:1
and G 2
(c) 1: 1
§W· 5 ¨ ¸ l4 © l ¹ 384EI
(d) 1: 2
5Wl3 Therefore Dž1: Dž2 = 5: 8 384EI
Moment Area Method IES-19.
Match List-I with List-II and select the correct answer using the codes given below the Lists: [IES-1997] List-I List-II 1. Moment area method A. Toughness B. Endurance strength 2. Hardness C. Resistance to abrasion 3. Energy absorbed before fracture in a tension test D. Deflection in a beam 4. Fatigue loading Code: A B C D A B C D (a) 4 3 1 2 (b) 4 3 2 1 (c) 3 4 2 1 (d) 3 4 1 2 IES-19. Ans. (c) Page 229 of 429