A steel plate d x b is sandwiched rigidly between two timber joists each D x B/2 in section. The moment of resistance of the beam for the same maximum permissible stress σ in timber and steel will be: Where Young’s modulus of steel is m times that of the timber

A

$$\frac{\sigma(BD^{2}+mbd^{2})}{6D}$$

B

$$\frac{\sigma(BD^{3}+mbd^{3})}{6D}$$

C

$$\frac{\sigma(BD^{3}+mbd^{3})}{4D}$$

D

$$\frac{\sigma(BD^{2}+mbd^{2})}{4D}$$