Jef124
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Hello
I was trying to calculate the horizontal deflection of the free end of vertical clamped beam. The beam would be loaded at the free end with a horizontal force H and a vertical force P. My idea was to calculate an initial deflection due to the force H. Then calculate the additional deflection due to the previous deflection and the force P. I'd expect that when the force P is bigger than the Euler buckling load that the deflection would diverge but that's not happening when I try to calculate this.
I tried it on a beam with a length L of 6 m, stiffness EI = 1476600 Nm^2 (E=69 GPa, I=2140 *10^4 mm^4, H=1 kN. I calculated that the Euler buckling load P_{cr}=(Pi)^2EI/(2L)^2=101,20 kN and used a way bigger P=5000 kN.
For the initial deflection I used v_0=(1/3EI)HL^3=4,87607 *10^{-5} m. For the next iteration steps I used v_i=v_0 + (1/3EI)L^2P*v_{i-1} which eventually converges to v=5,08259 * 10^{-5} m instead of diverging.
I know 5000 kN isn't a realistic value and that the beam would probably yield with such a high load but shouldn't this diverge?
Also for loads smaller than the Euler buckling load, is this the right way to calculate the deflection? If not what would be a good way then?
Thanks in advance
I was trying to calculate the horizontal deflection of the free end of vertical clamped beam. The beam would be loaded at the free end with a horizontal force H and a vertical force P. My idea was to calculate an initial deflection due to the force H. Then calculate the additional deflection due to the previous deflection and the force P. I'd expect that when the force P is bigger than the Euler buckling load that the deflection would diverge but that's not happening when I try to calculate this.
I tried it on a beam with a length L of 6 m, stiffness EI = 1476600 Nm^2 (E=69 GPa, I=2140 *10^4 mm^4, H=1 kN. I calculated that the Euler buckling load P_{cr}=(Pi)^2EI/(2L)^2=101,20 kN and used a way bigger P=5000 kN.
For the initial deflection I used v_0=(1/3EI)HL^3=4,87607 *10^{-5} m. For the next iteration steps I used v_i=v_0 + (1/3EI)L^2P*v_{i-1} which eventually converges to v=5,08259 * 10^{-5} m instead of diverging.
I know 5000 kN isn't a realistic value and that the beam would probably yield with such a high load but shouldn't this diverge?
Also for loads smaller than the Euler buckling load, is this the right way to calculate the deflection? If not what would be a good way then?
Thanks in advance