A simply supported beam AB is subjected to a 35kN point load at mid-span as show

Question

A simply supported beam AB is subjected to a 35kN point load at mid-span as shown. The beam section is 310UB32.0 of Grade 300 steel. The two end supports at A and B, and the load point at C, all have full lateral and twisting restraints. a) Check if the beam AB subject to 35kN point load satisfies the deflection limit of Span/250 (Appendix B, AS4100) b) For the beam AB: i) Calculate the Nominal Section Capacity, M_s: ii) Calculate the Reference Buckling Moment, M_o: iii) Calculate the Nominal Member Moment Capacity, M"_b: iv) Calculate the Design Bending Moment, M*: v) Check if the beam AB has adequate strength to carry the 35 kN point load.

Explanation / Answer

a) Weight of beam = w=32 kg/m=313.6 N/m

Span of beam = L=12 m

Modulus of elasticity = E=200 GPa = 2*1011 N/m2

Concentrated load on beam = 35 kN

Moment of inertia of beam = I = 63.2*106 mm4 = 63.2*10-6 m4

deflection of beam at midspan due to self weight = 5wL4/384EI = (5*313.6*124)/(384*2*1011*63.2*10-6)

= 6.7*10-3 m = 6.7 mm

Deflection of beam at midspan cue to cocentrated load = PL3/48EI

= (35000*123)/(48*2*1011*63.2*10-6)

= 0.09968 m = 99.67mm

Total deflection of beam = 6.7+99.67 = 106.37 mm

Span of beam = 12000mm

Span/250 = 12000/250 = 48

106.37>48 (it does not satisfy deflection limit)

b)i) Yield strength of section = 300 MPa=300*N/mm2

Plastic section modulus = 424*103 mm3

Moment capacity = 300*424*103 = 127200000 Nmm = 127.2 kNm

  

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.