The First Kind of Exercise Problem 1 Check the Strength of Beam g=50 kN/m 200 B分 2000 1000 20 F4=37.5kN Fs=112.5kN 25 Solution Draw the diagram of bending moment 14.1 M(kN.m)
Determine the constraint forces Draw the diagram of bending moment Problem 1 F FRB =112.5kN RA=37.5kN M(kN.m) x O 25 Solution 14.1 The First Kind of Exercise: Check the Strength of Beam A B
The First Kind of Exercise Check the Strength of Beam Problem 1 Check the strength of section B 25 14.1 M(kN.m) M=- ×50x12=-25kN-m 25×103 max M2x0.050= 2.136×10-5 x0.05=58.5MPa>[o] Ma×0.130=152MPa[o
1 2 50 1 25 kN m 2 MB = − = − max 0 130 152 MPa> . B z M I − − = = Check the strength of section B Problem 1 The First Kind of Exercise: Check the Strength of Beam M(kN.m) x O 25 14.1 B . . MPa . . I M σ Z B 0 05 58 5 2136 10 25 10 0 050 5 3 max = = = − + + []
The First Kind of Exercise Check the Strength of Beam Problem 1 25 Check the strength of section C 14.1 M(kN.m) In order to determine the bending moment diagram of section C,the position of section C should be calculated firstly. F=fR4-qm=0x-35-075m 950 1 Me=F4x-29r2=14.1kN-m Mcx0.130 14.1×103 2136x10×0130=858MPa>[o Conclusion:the strength is not safe
In order to determine the bending moment diagram of section C, the position of section C should be calculated firstly. FS = FRA − qx = 0 0.75m 50 R 37.5 = = = q F x A 2 R 1 14 1kN m 2 . M F x qx C A = − = + [] Conclusion: the strength is not safe. Check the strength of section C Problem 1 The First Kind of Exercise: Check the Strength of Beam M(kN.m) x O 25 14.1 C . . MPa . . . I M σ Z C 0130 858 2136 10 141 10 0130 5 3 max = = = − +
12-2提高弯曲强度的措施 口1.减小最大弯矩 华十 q=p/1 副梁 M 午++ ⊕ (b) (e)
12-2 提高弯曲强度的措施 ◼ 1. 减小最大弯矩
12-2提高弯曲强度的措施 2)改变支座的位置 q 细 \023 2U卜 401 50
◼ 2) 改变支座的位置 12-2 提高弯曲强度的措施