Question

The beam of building structure (Fig. 3a) is made of mild steel I-section beam with 80mm deep and 60mm wide as shown in Fig. 36. The beam is bolted (simply supported) onto the girder on both side over a span of 1.0 m. The loading from deck is expected to transfer onto the beam as the form of uniform distributed load, w. The material is to be treated as elastic-perfectly plastic, with yield strength of 240 MPa, and elasticity modulus of 200 GPa. Girder 60 T IO the other 80 Beam (a) (b) Fig. 3: (a) The building structure and (b) cross-sectional dimension of I-section beam a) Find out the shape factor of the beam. b) Find out the magnitude of uniform distributed load, w the beam could sustain for it to have at least 60mm of elastic core depth.

Answer 1

10 flange fy yeild strength - 240 mpa = 240 o/mm2 NA - Nutral Anis - Klo 80 Plastic moment NA Safe facton web flange Yeild moment + I Ymar ① Yeeld moment (My) = fy 7 lehet a b] [body] cox 104 (600) x103"} 3 [10 x 60 → 1-2 12 7 I 965,000 mm Iman = 8/2 = 40 - 5790000 mm My 940 x 1965.000) {Aby. V ② Plastic moment (MP) = fy (A. 8. + A2. 72.743 %; +4444 here (A = A4) 4 (Az = ₃) 30 480 Al A2 7 Mp=240 x [ (60x10 x 36) + (30x10x15) (30310 315372 A3 Ay 5. 7 Mp=12240000 mm Me 12740000 15) Safe farfon my 5790000 2.11 7 safe facfon = 2.11

6) Area of the I section beam . 2 2 A1 = (60x10) mm = 600 mm A2 = (10 x 60) mn Az =(60 x 10) mm = 600 mm? - 600mm Area = Alt A₂ t Az = 1800 mm² The uniform distributed load aw. The magnitude of the uniform distributed load - We Area = (1800 mm2) xw [Find Lec] here critical depth (Ne) = 60 mm 1st step ů to to calculate bending moment w1% BM and step is to calculate the total load. (W) MR = BM - Then calculate the self weight of the beam (dead load) 5.W= b.Dxr here & density of concrete (25 kN/m3) Load cannoyting capacity total load - Self weight - w-self net