Question

The cross-section of a timber beam with a steel strip is shown in the given figure. It is subjected to a sagging bending moment of 1000 Nm, $I_{xx}=1250\times {10}^{4}m{m}^4$ and modular ratio m = 20. The stresses at the lower surfaces of timber $\left({\sigma }_t\right)$ and steel $\left({\sigma }_s\right)$ will be respectively.

• A. $+6.4MN/m^{2}and-6.4MN/m^2$
• B. $-6.4MN/m^{2}and-32MN/m^2$
• C. $+6.4MN/m^{2}and-32MN/m^2$
• D. $+32MN/m^{2}and-6.4MN/m^2$

Answer 1

The correct option is C $+6.4MN/m^{2}and-32MN/m^2$

The moment of inertia of timber beam equivalent is given
$I_{xx}=1250\times {10}^{4}m{m}^4$
Stress at y = 20 mm

$\sigma =\frac{1000\times {10}^3\times 20}{1250\times {10}^4}$

$=1.6N/m{m}^2\left(Compressive\right)$

Stress at lower level of steel,

${\sigma }_s=m{\sigma }_{20}=1.6\times 20=32N/m{m}^2$

Stress at lower level of timber at y = 80 mm

${\sigma }_t=\frac{1000\times {10}^3\times 80}{1250\times {10}^4}=6.4N/m{m}^2$

Stress in timber is tensile, So it is positive.