Question

Problem: A 7 m wide concrete bridge deck (with a span of 9.1 m) is supported by two identical simply supported lightly welded I-beams. The 350 mm thick concrete deck acts as a continuous lateral restraint along the whole length of the beams. The bridge is subjected to a uniformly distributed live load (Q) of 10 kPa. The dead load consists of the self- weight of the I-beams and the concrete deck. If the yield stress of the beams fy 320 MPa, and a 420 mm, h 519 mm, t- 12 mm, t2 -21 mm, determine the following 1. The design load (1.2G + 1.5Q) on a beam (2 marks) (Unit: kN/m) 2. The maximum design bending moment on a beam (1 mark) (Unit kNm) 3. The Beam section slenderness (1 mark) (Unit:) 4. The Beam section yield slenderness limit (1 marks) (Unit:) 5. The Beam section plastic slenderness limit (1 mark) (Unit:) 4 6. The effective section modulus (Ze) of the beam (2 mark) (Unit. x 10 mm2) 7. The Beam bending capacity (2 mark) (Unit: kNm) Q (kPa) Density of concrete: 25kNm Density of steel: 78.5kN/m

Answer 1

Design load: - LL (Q): - Shared equally log 2 beams = (10 times 7)/2 = 35 kN/m OL (G) Due to concrete dark = 25 times 0.35 times 7/2 = 30.625 kN/m Due to steel: - Area = 2 (420 times 21) + 12 times 378 = 22176 mm^2 Due to steel beam = 78.5 times 22176/10^6 = 1.74 kN/m Total DL = 30.625 + 1.74 = 32.365 kN/m Lead combination: - 1.2 G + 1.5 Q = 1.2 times 32.365 + 1.5 times 35 = 91.338 kN/m Max. Bending moment = Wl^2/8 = 91.330 times 9.1^2/8 = 945.46 kNm Z_e = I/y_max y_max = h/2 = 420/2 = 210 mm I = 2 times [450 times 21^3/12 + 450 times 2 times (210 - 21/2)^2] + 12 times 378^3/12 implies 126345177 mm^4 Z_e = I/y_max = 126345177/210 = 6,01,643.7 mm^3 = 60.16 times 10^4 mm^3 M implies 6_y middot Z_e = 320 times 60.14 times 10^4/10^6 192.5 kNm