# How to find the tension in wires before a column buckles

I already have the solution for this problem, I just need some explanation about a certain part. Can someone please explain the highlighted section, how do I obtain the tension formula used here?

Force F is compression in mast, T is tension in guy wire. The three tensions sum up to F upwards considering components along the mast direction. For vertical force equilibrium assuming symmetry of three slant edges of a regular tetrahedron vector F should be directed downwards.

$$3 T \cos \theta = F$$

Inclination of guy wire to vertical mast by Pythagoras thm is

$$\cos \theta =\frac{5}{\sqrt{5^2+3^2}}= \frac{5}{\sqrt{34}}$$

By Euler buckling Formula for pinned column height $$L=5$$ meters

$$F= 3 T \cos \theta = \frac {15 T_{max}}{\sqrt{34}}= \frac{\pi^2 EI}{L^2} ;\; I = \pi R^3 . t$$

etc., $$T_{max}$$ can be calculated.

• How did you get $3Tcos\theta=F$ Jun 15, 2022 at 14:49
• Edited, including the picture you gave. Jun 15, 2022 at 19:00

Equate the compressive force, due to the tension in the cables, with the Euler Buckling Force Formula as shown in the graph below. Note that you need to account for the effect of the boundary condition by selecting a proper effective length factor "$$K$$".