Determine the nominal section moment capacity of the beam segment in Figure 1(a)

Question

Determine the nominal section moment capacity of the beam segment in Figure 1(a) having a symmetrical cross-section as shown in Figure 1(b) considering bending about x-x. Note that the segment has no transverse load but it is subject end moments as shown in Figure 1(a). Consider full restraints at one of the ends of the segment and partial restraints at the other end. Assume the section to be heavily welded. (a) Calculate the maximum value of the length of the segment so that it will not be affected by lateral torsional buckling (global buckling) phenomenon. (b) What will be the nominal member moment capacity of the beam segment if the length of the segment is equal to the value obtained in 1(a)?

Explanation / Answer

a) we basically need to determine Lp for the section

Lp= 1.76*ry*sqrt(E/fy)

E=200GPA=2*10^5 N/mm²

Fy=500N/mm²

Moment of inertia of section about y-y = Iy =2*(10*341³/12)+

2*(600*8³/12 + 600*8*66.5²)=1.086*10^8 mm

Area of cross section=A=2*(341*10)+2*(8*600)=16420mm²

ry=sqrt(Iy/A)=81.3 mm

Lp=1.76*81.3sqrt(200000/500)=2862.55mm=2.86 m

b)Plastic section modulus of the section about x-x =(2*8*600²/4)+(2*341*10*305) =3520100 mm³

Moment capacity = 500*3520100/10^6=1760kNm

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