Question

A uniform cubical block of side 2m and density 0.2 g/cc is fixed to the horizontal floor as shown in figure. A force 5 kN is applied on the top face of the cube, then

• A. Normal stress at section ABCD is $1.25\text{kN}/{\text{m}}^2$
• B. Shear stress at section ABCD is $1\text{kN}/{\text{m}}^2$
• C. Normal stress at section EFGH is $0.75\text{kN}/{\text{m}}^2$
• D. Shear stress at section EFGH is $1\text{kN}/{\text{m}}^2$

Answer 1

Answer: (A), (B), (D)

The correct options are
A

Normal stress at section ABCD is $1.25\text{kN}/{\text{m}}^2$

B

Shear stress at section ABCD is $1\text{kN}/{\text{m}}^2$

D

Shear stress at section EFGH is $1\text{kN}/{\text{m}}^2$

Weight of block above section ABCD

$\text{W}=(2\times 2\times 1)\times 2000=8000\text{N}$

${\sigma }_{\text{N}}\text{(at ABCD)}=\frac{F_1}{A}=\frac{8000-3000}{4}=1.25\text{kN}/{\text{m}}^2$

${\sigma }_{\text{N}}\text{at EFGH}=\frac{16000-3000}{4}=3.25\text{kN}/{\text{m}}^2$

${\sigma }_{\text{S}}\text{at ABCD}={\sigma }_{\text{S}}\text{at EFGH}=\frac{4\text{kN}}{4m^2}=1\text{kN}/{\text{m}}^2$