Question

5. A beam 2 meters long is supported as shown below. An unknown distributed load with a uniform distribution is present on the beam as well as a concentrie reading at point B) will be extra credit. 8 TO SCALE 2-0m sEcToN Om STRAMN STAE 6STRAIN READING AT Pr. B lo

Answer 1

Gicen strain at C=-250 $\mu$

since C is at the neutral axis pof the section, the strain at C is only due to axial load P

sress at C=-250*10^-6*50*10⁹ =-12.5MPa= -12.5 N/mm²

cross sectional area of beam=20*40=800 mm²

axial load = -12.5*800/1000=-10 kN

P=10 kN (compressive)

given strain at A=3500 $\mu$

the strain at A is due to axia load P as well as due to bending moment at that section

Strain at A due to P=-250 $\mu$

strain at A due to bending moment = 3500-(-250)=3750 $\mu$

stress at A due to bending moment = 3750*10^-6*50*10⁹=187.5 MPa=187.5 N/mm²

bending moment at the section = stress*section modulus of beam = 187.5*20*40²/6*10^-6= 1 kNm

the bending moment at the section in terms of w = w*1²/2=0.5w

0.5w=1

w=2 kN/m