Youre supposed to design a wshape steel beam Please thurough

You\'re supposed to design a w-shape steel beam

Please thuroughly explain the process of choosing the w-shape beam, particularly what tables were used.

4) A 28-ft long wide-flange steel beam is supported vertically 4 ft from each end. The top flange is unbraced its entire length. The bottom flange is laterally supported at the vertical support locations. The beam supports a uniform live load of 3 k/ft and a uniform dead load of 6 k/ft. Assume the beam is 50-ksi. Only check for moment and shear - do not check for deflection Wou W?L 4\'-0\" 20\'-0\" 4\'-0\"

Solution

As per LRDF=1.2W_d+1.6W_l=12

As per ASD=6+3=9

moment As per LRDF =wl²/8+2*wl²/2=792

moment As per ASD=wl²/8+2*wl²/2=594

?t = 0.90 (LRFD) ?t = 1.67 (ASD) (as per AISC Specification Section F1)

hence maximum moment =1.67*792=1332.64k-ft or 15991.68k-in

M=f_y*Z

15992=50*Z_x

Z_x=320in³

hence now search for W-section in AISC Steel Construction Manual

hence for given moment W12X16 with Z_x=329>320 hence o.k

area of section 4.71in²

shear capacity =4.71*50=235.5k

actual shear =198k hence ok