Question

Bars of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-sector dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

• A. Torsional load specimen
• B. Tensile and compressive load specimens
• C. Bending load specimen
• D. None of the specimens

Answer 1

The correct option is B Tensile and compressive load specimens


$\sigma =\frac{80\times {10}^3}{{40}^2}=50N/m{m}^2$

${\tau }_{max}=\frac{\sigma }{2}=25N/m{m}^2>20MPa$


${\tau }_{max}=\frac{16T}{\pi d^3}=\frac{16\times 64\pi \times {10}^3}{\pi (40{)}^3}$

$=16N/m{m}^2<20MPa$


$\sigma =\frac{\mu }{a^3/6}=\frac{320\times {10}^3}{\frac{{40}^3}{6}}=30N/m{m}^2$

${\tau }_{max}=\frac{\sigma }{2}=15N/m{m}^2<20MPa$