• Wesley
In summary, the conversation is about designing a torsional testing rig for a Formula Sae car. The rig will have a beam with a pivot point in the front, and the goal is to determine the most cost-effective material and profile for the beam. However, the deflection equations for the beam are statically indeterminate, with two integration constants and only one initial condition. The person asks if there is a way to solve this or if there is a conservative approximation that can yield satisfactory results. The other person suggests making the slope at the pivot point zero and explains that a beam on one support is not indeterminate, but kinematically unstable. The original person then asks if knowing this, there is any way to find the constants.
Wesley
Hello

I am creating a torsional testing rig for a Formula Sae car, the front of the car will be pivoted about the center on a beam with the loading off to one side. In the design I need to calculate the deflection of the beam in order to determine which material and what profile of metal will be most cost effective however my deflection equations appear to be statically indeterminate. Below is a free body diagram

My problem is when I arrive at the equation for deflection I have two integration constants but only one initial condition saying that the deflection is 0 at the pivot. Is there a way to solve this or is there a conservative approximate that will yield satisfactory results?

image url: http://imgur.com/n45Wyhw

You could also make the slope at the pivot = 0. It's not entirely clear how this rig tests the torsional rigidity of your car, though.

So the back of the car will be held rigidly by 2 supports clamped down and the front will be held by this beam on supports that raise off of it to the hubs or the frame (universal design). In the middle of the beam where I have the pivot will be a piece of angle iron and on the far left weight will be applied to add a torsional force to the frame.

When doing the analysis I was unsure if I could say the slope is zero at the pivot I thought that was only for a cantiliver end. I know I can say the bending momment is zero however that doesn't help me.

A beam on one support is not indeterminate. It is kinematically unstable.

knowing that this beam is kinematically unstable is there any way to find the constants?

Indeterminate static beam loading is a type of structural analysis that involves determining the internal forces and reactions of a beam under various loading conditions. It takes into account the effects of both external loads and internal forces, such as bending moments and shear forces, on the beam.

Indeterminate static beam loading is important because it allows engineers to accurately predict the behavior and strength of a beam under different loading scenarios. This information is crucial in the design and construction of safe and efficient structures.

There are several methods used for indeterminate static beam loading, including the moment distribution method, the slope-deflection method, and the matrix stiffness method. Each method has its own advantages and is used in different situations depending on the complexity of the beam structure.

Indeterminate static beam loading makes a few key assumptions, including that the beam is composed of a single material, that the material is homogenous and isotropic, and that the beam is loaded in a linearly elastic manner. These assumptions allow for simplified calculations and analysis.

## What factors can affect the accuracy of indeterminate static beam loading?

The accuracy of indeterminate static beam loading can be affected by several factors, such as material properties, boundary conditions, and the complexity of the beam's geometry. It is important for engineers to carefully consider and account for these factors when using this type of analysis.

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