Civil Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 2 (Q.No. 12)
12.
A cantilever beam rectangular in cross-section is subjected to an isolated load at its free end. If the width of the beam is doubled, the deflection of the free end will be changed in the ratio of
Discussion:
14 comments Page 1 of 2.
Alex said:
8 years ago
Y1= WL^3/3EIx.
Ix = bd^3/12.
Now for b = 2b.
Iy = 2bd^3/12.
Iy = 2 Ix.
Now Y2 = WL^3/3EIy or WL^3/3E(2Ix)
Y2 = 1/2( WL^3/3EIx)
Y2 = 1/2 Y1.
So, option C correct.
Ix = bd^3/12.
Now for b = 2b.
Iy = 2bd^3/12.
Iy = 2 Ix.
Now Y2 = WL^3/3EIy or WL^3/3E(2Ix)
Y2 = 1/2( WL^3/3EIx)
Y2 = 1/2 Y1.
So, option C correct.
Anamika said:
6 years ago
Deflection of the cantilever is PL^3/3EI.
So, i=bd^3/12 according to the quetions ratio ( bd^3/12 )/(2b(2d)^3/12) =1/16,
ia/ib=0.0625.
ia/ib= 6.25% is the answer.
So, i=bd^3/12 according to the quetions ratio ( bd^3/12 )/(2b(2d)^3/12) =1/16,
ia/ib=0.0625.
ia/ib= 6.25% is the answer.
Ravi said:
7 years ago
Deflection of the cantilever is PL^3/3EI.
So, i=bd^3/12 according to the quetions ratio ( bd^3/12 )/(2bd^3/12) =1/2 is the answer.
So, i=bd^3/12 according to the quetions ratio ( bd^3/12 )/(2bd^3/12) =1/2 is the answer.
Paul said:
8 years ago
Pl3/3EI.
I = bd3/12 in 1st case ( d3 = cube of d).
I = 2bd3/12 in 2nd case,
The ratio will come as 2.
So, option D is correct.
I = bd3/12 in 1st case ( d3 = cube of d).
I = 2bd3/12 in 2nd case,
The ratio will come as 2.
So, option D is correct.
SUMIT said:
6 years ago
Deflection.
For point load, deflection (proportional) -> l^3/bd^3.
For udl deflection (proportional) -> l^4/bd^3.
For point load, deflection (proportional) -> l^3/bd^3.
For udl deflection (proportional) -> l^4/bd^3.
Jaz said:
6 years ago
1/2.
Definition=wl^3/3EI.
I=bd^3/12 for rectangular section according to question b=2b.
So, the deflection =1/2.
Definition=wl^3/3EI.
I=bd^3/12 for rectangular section according to question b=2b.
So, the deflection =1/2.
(1)
Mounika reddy said:
1 decade ago
y1 = MX^2/2EI For b.
I = bh^3/12 if b = 2b.
I = 2bh^3/12.
y2 = MX^2/4EI FOR 2b.
y2 = 1/2(y1).
I = bh^3/12 if b = 2b.
I = 2bh^3/12.
y2 = MX^2/4EI FOR 2b.
y2 = 1/2(y1).
Shubham verma said:
8 years ago
D diflection.
D1=PL^3/3EI
IF L=2L
THEN
D2=P(2L)^3/3EI
D2=8PL^3/3EI
D2=8D1
SO
D1/D2=1/8.
D1=PL^3/3EI
IF L=2L
THEN
D2=P(2L)^3/3EI
D2=8PL^3/3EI
D2=8D1
SO
D1/D2=1/8.
Kaushik Nandan Baruah said:
3 years ago
Deflection will increase on increasing width and decrease on increasing depth.
Amol said:
7 years ago
Option D correct.
{4wl^3÷Ebd ^3}÷{2wl ^3÷E bd ^3}= 2.
{4wl^3÷Ebd ^3}÷{2wl ^3÷E bd ^3}= 2.
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