Question

Two simply supported beams are made up of the same material and are of the same cross-section. Both beams carry uniformly distributed loads of equal intensities. One beam is 2 m long and the other is 4 m long. The 2 m long beam shows a central deflection of 1 mm. What is the central deflection of the 4 m long beam?

• A. 16mm
• B. 2mm
• C. 8mm
• D. 1 mm

Answer 1

The correct option is A 16mm

As we know that,

$\delta =\frac{5}{384}\frac{w{L}^4}{EI}$

Both the beams have same load intensity (w). material (E) and cross- section (I).

$Beam1:L=2m,{\delta }_1=1mm$

${\delta }_1=\frac{5}{384}\times \frac{w}{EI}\times (2{)}^4$

$\therefore 1=C\times (2{)}^4\Rightarrow C=\frac{1}{(2{)}^4}$

$Beam-2,L=4m$

${\delta }_2=\frac{5}{384}\times \frac{w}{EI}\times (4{)}^4$

$\Rightarrow {\delta }_2=C\times (4{)}^4$

$\therefore {\delta }_2=\frac{1}{2^4}\times 4^4=16mm$