# Buckling load equation for buckling struts

• Nexus305
In summary, the conversation discusses the use of Euler's equation to find the buckling load of a wing strut in a plane experiencing a compressive load. The strut is pin-jointed at both ends with dimensions of 150 mm outside diameter, 100 mm bore, and 5 m length. The second part of the question involves finding the buckling load if the strut is prevented from moving laterally at its center, using the equation P = (4*Pi^2*EI)/L^2. This is because the effective length of the column is cut in half when secured at the center.
Nexus305
I was trying to solve a question where they told me to find the buckling load of a wing strut in a plane that experiences a compressive load along its axis. The strut can be considered to be a pin-jointed at both ends. Dimensions of the strut is as follows: outside diameter is 150 mm and bore is 100 mm and length of 5 m.

For finding the buckling load i used Euler's equation for struts P = (Pi^2*EI)/L^2 and I got the correct answer but i don't understand what exactly I have to do in the second part of the question. Here it is:
(b) Find the buckling load if the wing is re-designed so that the strut is prevented from moving laterally in all planes at its centre.

For this my lecturer had used this equation P = (4*Pi^2*EI)/L^2
So basically 4 times the previous equation. I want to know how he got that equation and when should I use it.

Thanks!

Think about what shape the strut would be when it buckled, if the mid point was restrained.

(Hint: it is similar to two struts joined end to end).

In that case isn't it supposed to be P=(2*Pi^2*EI)/L^2, instead of P=(4*Pi^2*EI)/L^2

Because if the beam is like 2 struts joined end to end, there will be 2 deflections. The top half and the bottom half would deflect right? How does the equation have a 4 in it?

I think it is because the effective length of the column is cut in half. By doing this and squaring it, it is like multiplying the equation by 4. You still need to use the actual length of the column in that equation. Someone please correct me if I am wrong.

thanks a lot guys!..makes sense now

The original length of the strut is: L
When it is secured at the center, each segment becomes: L/2
(L/2)^2 = L/4
which gives you your 4 in the numerator.

## What is the buckling load equation for buckling struts?

The buckling load equation for buckling struts is a mathematical formula used to calculate the critical load at which a strut will buckle or fail under compressive loads. It takes into account factors such as the material properties of the strut, the length of the strut, and the end conditions.

## Why is the buckling load equation important in structural engineering?

The buckling load equation is important in structural engineering because it helps engineers determine the maximum load a strut can withstand before buckling occurs. This information is crucial in designing safe and stable structures that can support the intended loads.

## What are the assumptions made in the buckling load equation for buckling struts?

The buckling load equation makes certain assumptions, such as the strut being perfectly straight and uniform, the material having a constant stiffness, and the load being applied in the direction of the strut's axis. These assumptions may not hold true in real-world scenarios, but the equation still provides a good estimate of the buckling load.

## Can the buckling load equation be applied to all types of struts?

No, the buckling load equation is specifically designed for calculating the critical load of slender struts under compressive loads. It may not be applicable to thicker or more complex struts, such as those with varying cross-sectional shape or subjected to other types of loads.

## How can the buckling load equation be used in practical applications?

The buckling load equation can be used to determine the maximum load a strut can withstand, which is crucial in designing structures such as columns, beams, and trusses. It can also be used to assess the stability of existing structures and make necessary modifications to prevent buckling failure.

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