# How to represent a load supported at multiple points on multiple beams?

I have a frame, similar to a container frame, with two vessels inside. Each vessel is supported at four points on two beams, as shown in this mockup:

I am using ANSYS to simulate the loaded frame. How should I represent the impact of the weight of the vessels on the frame so that my structural analysis is correct? Should I divide the total weight of the vessels by four and place that force on each supporting plate or use remote force to represent the weight of each vessel?

I know only the mass and center of gravity of vessels. I don't have full models of the vessels, just a model of the frame.

If the vessels (and the load distribution of whatever they're containing) are truly symmetric (or close enough), then yes, you can simply replace them with four equal concentrated loads at the points where they are supported.

If the vessels aren't symmetric but can be reasonably considered to have a pretty uniform stiffness (they don't have two really strong legs and two weak ones, for example), then you can use the vessels' centers of gravity to calculate the load distribution via this equation: $$R = P\cdot\left(1-\dfrac{c_x}{L_x}\right)\cdot\left(1-\dfrac{c_y}{L_y}\right)$$ where $c_x$ and $c_y$ are the distance in the $x$ and $y$ axes, respectively, from the desired support to the center of gravity, and $L_x$ and $L_y$ are the spans between supports in the respective axes.

So, if the center of gravity is perfectly centered between all supports, then $\dfrac{c_x}{L_x}=\dfrac{c_y}{L_y}=\dfrac{1}{2}$ and $R = \dfrac{P}{4}$.

If, however, the center of gravity is at coordinate $\left(\frac{L}{3}, \frac{L}{3}\right)$ (so, close to the bottom-left support), then the load will be distributed $\frac{4}{9}$ at the bottom-left support, $\frac{2}{9}$ at the top-left and bottom-right supports, and only $\frac{1}{9}$ at the top-right support.

If the vessels are totally asymmetric, then you need to know the actual vessel geometry to calculate the load distributions.

This is a simple assumption which is perfectly correct for static analyses. If you need to deal with vibrations or other dynamic behaviors, then there may be fluctuations on how much load goes to each support.

• Thank you Mr. Wasabi. If vessels are asimetric, but I know center of gravitiy, can I use force in center of gravitiy (remote force in ANSYS) for static analysis of frame structure and distibution of stress ? – Sysrq147 May 27 '16 at 22:21
• @sysrq147 I've never used ANSYS, so I'm not entirely sure how those remote forces work. I assume you apply the force in space and tell it which beams are affected by it. This is only acceptable if you can also define where the forces must be transmitted, otherwise it will find the single closest point on each beam, which would be possibly incorrect, since the force needs to be transferred to two points on each beam. – Wasabi May 27 '16 at 22:33