# RHS beam deflection with support on one end

A 1400 mm long galv steel beam, size 40x20x2. 80 mm of the beam on one end is welded in flat position to a platform. How much weight can I put safely on the other end? What if instead of being flat it will be on a short side/rib? The platform is meant to spin, will this effect the weight the beam can hold at the other end?

I am not an engineer and do not understand the formulas I found in other posts. This is for a home project.

• Welcome to Engineering! I have rolled back your most recent edit, since it fundamentally changed the question and made the existing answer invalid. If you have a subsequent question on this topic, feel free to ask it as a new question and to add a link to this question if you believe it will be a relevant reference. – Wasabi May 22 '20 at 0:18

Assuming your platform is solid enough to fully support the moment created by the beam. we can consider your mechanism as a cantilever beam with a free length of $$L=1400-80=1320\text{ mm}$$.

For this beam $$c = 40 / 2 = 20$$.

Assuming:

\begin{align} F_y &=250\text{ MPa} \\ I &= I_{ext}-I_{int}=\dfrac{20\cdot40^3}{12}- \dfrac{18\cdot36^3}{12} = 44,458.6\text{ mm}^4 \\ M &= PL \\ \sigma &= \frac{Mc}{ I } =\frac{20M}{44,458.6} = 250\text{ MPa} \\ 20M &= 250\cdot44,458 \\ \therefore M &= 555,733.3\text{ Nm} \\ P &= M/1320=421N=421/9.8=42.9\text{ kg} \\ \end{align}

This is an un-factored stationary load. if we allow a factor of safety of 60% $$P=25.8\text{ kg}$$ If you need to turn the plate then you need to know the angular acceleration and calculate the angular moment of inertia and the lateral strength of the beam for that.

• +1 Though I like being overly conservative, so I'd've used the full span ($L = 1400$), since we're dealing with DIY welding, we can't be sure the beam can be assumed fixed at the very start of the weld. – Wasabi May 21 '20 at 15:08
• "we can't be sure the beam can be assumed fixed at the very start of the weld" what if I weld it to the platform + add a plate on top, thus joining everything together on the bottom and top. Is the danger that the weld joint will break off or the beam will bent? – anm767 May 21 '20 at 20:48
• Weld material is designed to be stronger than the sections they weld. My answer is meant to give a way of starting estimate of strength. Otherwise one can test the weld and the base to come up with a rigorous answer. – kamran May 21 '20 at 21:53
• Just looking this over - Is Fy a pressure, or a force? 250N, but MPa? If you are building playground equipment, you might look into some design guides: cpsc.gov/s3fs-public/325.pdf ; there's an official one ASTM F1487-17, that might talk about build details too. – asylumax May 22 '20 at 0:02