q a wooden beam of the rectangular cross

Question

Q.  A wooden beam of the rectangular cross section is subjected to bending moment of 5KNm. If the depth of section is to be double the breadth and stress in wood is not to exceed 60N/cm². Find out dimension of the cross section of the beam.

Sol.: As we know that σ/y = M/I;

Where

σ = 60 N/cm² = 60 × 10⁴ N/m2

d = 2b

y =  d/2

M = 5KNm = 5 × 10³ Nm

I =  bd³/12; for the rectangular cross section
By substituting all values we get

60 × 10⁴ / (d/2) = 5 × 10³/(bd³/12)d = 2b;

60 × 10⁴ / (2b/2) = 5 × 10³/(b.(2b)³/12)

b = 0.232 m = 23.2 cm

d = 2b = 46.4 cm

b = 23.2 cm,  d = 46.4 cm .......ANS