How to calculate what size steel RHS to use?

Question

I am welding up a rack to support a distributed load of up to 1000kg, what is the process to work out what steel section size I should use? Many Thanks.

Answer 1

Because the weight is quite high, and the use is for supports, I will assume that you will use the same cross-section for the shelve columns (if there are any). In you use the same cross-section, you probably will not have a problem with buckling

I am assuming RHS refers to Rectangular Hollow Cross-section.

Regarding the process that you need to follow IMHO for the shelves is:

1. Define the allowable deflection $\delta_{all}$ (usually its about $\frac{1}{200}L_{\text{shelves span}}$ and the allowable stress (usually its safety factor times the yield stress $N\cdot \sigma_y$)

2. Determine the support type. Are the shelves simply supported or are they welded on the frame. In any case I'll be using the formulas for simply supported beams.

• max deflection: $\delta_{max} = \frac{5 wl^4}{384EI}$
• max operating stress: $\sigma = \frac{wl^2}{8I}\cdot \frac{y_{max}}{2}$

where:

• $E$ is the young's Modulus
• $I$ is the second moment of area which you can find in tables or calculate
• $y_{max}$ is the height of the RHS.

3. you can solve for I (which is depended on the geometric properties of the cross-section), for both constraints (Deflection and stress) and you will obtain two parameters:

$$I_{Deflection} = \frac{5 wl^4}{384E\delta_{max}}, \qquad \frac{2 I}{y_{max}}= \frac{wl^2}{8\sigma_{Allowed}} $$

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UPDATE:

The equations for the fixed ends (see welded shelves on the frame) are:

• max deflection: $\delta_{max} = \frac{wl^4}{384EI}$
• max operating stress: $\sigma = \frac{wl^2}{12 I}\cdot \frac{y_{max}}{2}$

As you can see they are less stringent (that is why I opted for the simple beam), because that would built in a safety factor.