Question

The cross-section of a beam is shown below. The top rectanular piece of the cross-section is a steel section 6 inches wide by 8 inches deep. The dimensions of the member are shown below in the table. The cross-section is loaded in bending by a moment about the zz-axis. The allowable bending stress of the cross-section is 42 (ksi).

Determine:

a) the elastic centroid of the cross-section.

b) the yield moment.

c) the plastic centroid of the cross-section

d) the plastic moment.

a) The elastic centroid of the cross-section is ______(in) from the base of the cross-section.

b) The yield moment of the cross-section is ______ (k-in).

c) the plastic centroid of the cross-section is ______ (in) from the base of the cross-section.

d) the plastic moment of the cross-section is _____ (k-in.).

Moment Area of Wall Thickness Section (in2 Inertia Kin4 t (in) HSS8X6X1/2 11.6 98.2 0.5

can someone help me with this civil engineering problem?

Answer 1

1. 
   Elastic Centroid: bin Areas: A, - (846) -(5x7) 8in 13 in Az 10x1.5 15 in 0. Sun joun o 1.5in Az = 1x8 sin Cenksoid distances from yu X-X: I'ya to Tin _x X & in You (*)+10+1 15 in Y2 = (1 + 1 - Gin 13(15)+ isd 1/2 0.5 in Agi + A2Y₃7A₂y3 Elastic comboid 5 A+ AzzAz 1576)+ 8(0.5) 13+ 15 + 8 8.0a8 in foom base Tua Yield Moment yield Moment My = fy. Z |(at) = 42x I Isac y 42 x 98.8 8:028 513.77k-in JO My CS Scanned with CamScanner
   
   IN 51 po .8m y = 13(1-33) + (4.995)(1665) lorimo 13+4.995 yo 5.757 in ITUI 6-610n Y (6-67 X1.5)(6.61)+(\*B)(6-61+) C6-67x115) + (1x8) As soon -AAS Y 2 - 5.039 in A volte A = A + Azt A3 ind jour 13+15+ 8 (1)(-) + 36 in? C) -N-PO) ka)-(28) Zpo A lyntya) (1) + El = call + 36 ( 5-751+5-039) Ols 31+ 2a 2 194.398 Mp - 194.328 x42 8161.776 k-on CS Scanned with CamScanner