N5 A wooden E10 GPa rectangular beam loading and cross secti

N5: A wooden (E-10 GPa) rectangular beam, loading and cross- section are as shown in Fig. P6.46. The normal strain at point A in Fig. P6.46 was measured as,x-600 ?. Determine the distributed force w that is acting on the beam. kNim 100 mm 25mm 0 5 m 0.5 m

Solution

the bending moment at section A= w*0.5²/2 = 0.125*w = 0.125*w*10⁶ N-mm

section modulus of beam = 25*100²/6 = 41666.67 mm³

stress at A=0.125*w*10⁶ / 41666.67 = 3*w N/mm²

Modulus of elasticity = 10 GPa = 1*10⁴ N/mm²

strain at A=600 *10^-6

Therefpore, 3*w = 1*10⁴ * 600 *10^-6 = 6

w=6/3=2 kN/m