A 6 meter long supported wooden beam of rectangular section

A 6 meter long supported wooden beam of rectangular section 10 cm × 20 cm deep is strengthened by mild steel plates 0.5 cm x 10 cm wide at the top and bottom fibre over the entire length. Find the minimum supportable uniformly distributed load considering failures in steel and wood due to flexure. Weakening of wood due to screws and weakening of the steel plates due to drilled holes may be ignored
Permissible tensile stress for steel = 156.8 N/mm²
Permissible tensile stress for wood = 14.89 N/mm²
Young's modulus of mild steel = 1.96 × 105 N/mm²
Young's modulus of wood = 0.117 × 105 N/mm²

Modular ratio , M =	E_s	=	1.96 × 105	= 16.75
	E_t		0.117 × 105

Equivalent Steel area & width of timber

=	200 × 100	= 5.97 mm
	16.75 × 200

I =	100 × 210³	= 14.5 × 10⁶ mm⁴
	12

Stress in timber =	156.8	× 100 ×	1	= 8.915 N/mm²
	105		16.75

(If permissible stress in steal = 156.8 MPa)

Stress in steel =	14.89	× 105 × 16.75 = 261.88 N / mm²
	100

(If permissible stress in wood = 14.8 MPa) I_max = 156.8 MPa

	M	=	σ
	I		y

M =	156.8 × 14.5 × 10⁶	= 21.65 Nm
	105

	wl²	= M = 2165 × 10⁶
	8

⇒ w = 4.81 kN/m.