The ratio of the maximum deflections of a simply supported beam with a central load W and of a cantilever of same length and with a load W at its free end, is
A. $$\frac{1}{8}$$
B. $$\frac{1}{{10}}$$
C. $$\frac{1}{{12}}$$
D. $$\frac{1}{{16}}$$
Answer: Option D
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A. $$\frac{2}{3}$$
B. $$\frac{3}{2}$$
C. $$\frac{5}{8}$$
D. $$\frac{8}{5}$$
Principal planes are subjected to
A. Normal stresses only
B. Tangential stresses only
C. Normal stresses as well as tangential stresses
D. None of these
A. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{R}}}{{\text{E}}} = \frac{{\text{F}}}{{\text{Y}}}$$
B. $$\frac{{\text{I}}}{{\text{M}}} = \frac{{\text{R}}}{{\text{E}}} = \frac{{\text{F}}}{{\text{Y}}}$$
C. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{E}}}{{\text{R}}} = \frac{{\text{F}}}{{\text{Y}}}$$
D. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{E}}}{{\text{R}}} = \frac{{\text{Y}}}{{\text{F}}}$$
A. $$\frac{{\text{M}}}{{\text{T}}}$$
B. $$\frac{{\text{T}}}{{\text{M}}}$$
C. $$\frac{{2{\text{M}}}}{{\text{T}}}$$
D. $$\frac{{2{\text{T}}}}{{\text{M}}}$$
Maximum deflection at centre of span for simply supported beam = wl^3/48EI
And maximum deflection at the free end for cantilever beam of same span= wl^3/3EI
Ratio=(Wl^3/48EI)÷(wl^3/3EI)
=1/16 is the Correct Answer
For Simply Supported beam deflection= PL^3/48EI
For Cantilever beam deflection= PL^3/3EI
ratio=PL^3/48EI * 3EI/PL^3=3/48=1/16
WL^2/48EI *3EI/WL^3 = 1/16L
Maximum deflection at centre of span for simply supported beam = wl^3/48EI
And maximum deflection at the free end for cantilever beam of same span= wl^3/3EI
Ratio=(Wl^3/48EI)÷(wl^3/3EI)
=1/16