Knowing that sigma 220 MPa and tauall 100 MPa select the m

Knowing that sigma = 220 MPa and tau_all = 100 MPa, select the most economical metric wide-flange shape that should be used to support the loading shown. W360 times 216 W690 times 125 W760 times 147

Solution

solution:

1) as we konw that point B and C are support and they are subjected to equal bending moment,hence design has to be withstand only bending stresses and shear stresses are negligible

2)from static equillibrium taking moment about B and C we get

Rby=629.14 kN

Rcy=-629.14 kN

3)where bending moment inside the bar is at point B and point C,as we have to design for maximum but both of them are equal in strength

Mb=Mc=385*10^3*1.3*1000=500.5*10^6 Nmm

4)hence maximum bending stresses in bar at maximu distance is given by

Sd=Mb*y/I

I=b*d^3/12

y=maximum distance from neutral line

hence

3) for first choice of W360*216

Sb1=500.5*10^6*108/360*216^3/12=178.78 N/mm2

4) for W690*125

Sb2=500.5*10^6*62.5/690*125^3/12=278.53 N/mm2

5)for W760*147

Sb3=500.5*10^6*73.5/760*147^3/12=182.85 N/mm2

6)as Sb1<Sb3<Sb2

hence Sb1 eans first choice W360*216 is most economic and Sb1<200,hence design will besafe

7)maximum shear force is 385 KN,shear force in first choice is

t1=385*10^3/360*670=1.596 N/mm2<100 MPa

8)as design W360*216 is safe and most economic hence it is siutable for given loading