Calculating Bending Moment of a Steel Tube

[fcukniles]

Hi,
I need to work out the bending moment of a steel tube, 25mm diameter (3mm thick) 410mm long.

im assuming i have to use youngs modulus in some way? what's the correct formula for working out when it will bend?
thanks
chris

 

[brewnog]

Well firstly you need to decide how the load is applied, and how the tube is constrained.

Then get drawing some free body diagrams.

 

[tacman]

Hi Chris,

To calculate the bending moment of a steel tube, you will need to use the formula:

M = (E*I)/R

Where:
M = Bending moment
E = Young's modulus of elasticity
I = Area moment of inertia
R = Radius of curvature

First, we need to calculate the area moment of inertia (I) for the steel tube. This can be found using the following formula:

I = π*(D^4 – d^4)/64

Where:
D = Outside diameter of the tube
d = Inside diameter of the tube

In this case, D = 25mm and d = 19mm (since the tube is 3mm thick, the inside diameter is 6mm smaller than the outside diameter). Plugging these values into the formula, we get:

I = π*(25^4 – 19^4)/64 = 0.0001165 m^4

Next, we need to determine the radius of curvature (R). This can be calculated using the following formula:

R = (E*I)/M

Where:
E = Young's modulus of elasticity (200 GPa for steel)
I = Area moment of inertia calculated above
M = Maximum stress (which is the bending moment divided by the section modulus)

Assuming the maximum stress is within the elastic limit of the steel, we can use the section modulus as the radius of curvature. The section modulus is given by:

S = π*(D^3 – d^3)/32

Plugging in the values for D and d, we get:

S = π*(25^3 – 19^3)/32 = 0.000403 m^3

Now, we can calculate the bending moment (M) using the formula:

M = (E*I)/R = (200 GPa * 0.0001165 m^4)/0.000403 m^3 = 57.5 Nm

Therefore, the bending moment of the steel tube is 57.5 Nm.

I hope this helps! Just remember to always double check your units and make sure they are consistent. Good luck with your calculations!