This is the first post in the Laser category. I wrote “Structural Beam Bending” because I am not referring to a laser beam, but an aluminum beam in my laser.

It took me a while to get back on the engineering concepts train. The last time I did any unit conversions at all was at least 5 years ago.

The first major hiccup I experienced while attempting to do beam bending calculations with a program called BeamBoy was that I wanted to determine my beam lengths in inches. All of my material data is in metric, so converting mm4 to in4 took me a moment to realize you simply divide by (mm/inch)^4, which is 25.4^4, or 416,231.4256

Unlike programming, physics information is not as readily available in easily digestible formats. I will outline my experiences to help anybody else who stumbles across this blog.

**To calculate beam deflection: **

Find your material’s Moment of Inertia, Modulus of Elasticity, and the Distance to Farthest Fiber.

My parts come from Misumi, so their data sheet looks like this:

The Moment of Inertia for the two axes are clearly shown. The Modulus of Elasticity is a property of the material, and I couldn’t actually find the exact grade of aluminum Misumi is using, so I looked online for average values and it ranged from 9,000,000 PSI to 11,000,000 PSI.

Distance to farthest fiber is the farthest distance from the beam’s neutral axis, so I interpret that to be 1/2 the width. This may be wrong.

First, start up BeamBoy and type in the length of your beam.

Enter in the properties of your beam as discussed above: moment of inertia, modulus of elasticity, and distance to farthest fiber.

Next, add two supports to your structure, I simply added a support at the start and end of my beam.

Add a distributed load over the length of your beam equal to the weight per distance (in my case, lb/ft) to simulate the weight of the beam itself.

Optionally, add a distributed or point load to the beam. I wanted maximum deflection for a given weight so I used a point load in the “worst” possible spot: the center, away from my 2 support structures.

Click calculate and see your results!

PS: I tried doing this in Solidworks beam modeler but the results don’t seem to be accurate.. Perhaps it’s because I was using a distributed load?

The Solidworks beam simulation is potentially a huge time saver as you the length, material properties and thickness is auto calculated.

Just can’t trust it yet.

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Hi. How do you read the deflection on a particular place on the beam in Solidworks?

I only get some unintelligible URES(mm) values.

Is there a tool in Solidworks that lets you plot a point on the beam and measure maximum deflection?

I’m sorry but I’m not sure — I used the manual BeamBoy calculations since I was clearly not able to get it working correctly.

The furthest fiber distance is half the height (for a cross-section that is symmetric along the x-axis).

For pure bending, you have to solve the differential equation y”=-M/(E·I),

where M is the bending moment, E is the Young’s modulus of the material and I is the second area moment. How easy it is to solve this equation depends on which if the constituents are functions of x (which runs along the length of the beam). In the basic case, only M is a function of x, and EI is constant along the length of the beam. You can find the analytical solution for simple cases like these in reference books. For a simply supported beam with a point-load in the middle, the solution for the maximum deflection is: F·L³/(48·E·I), where F is the load, L is the length of the beam.

The maximum bending stress is: M·e/I, where M is the bending moment and e is the furthest fiber distance.

If you want to know about solid mechanics, read “Mechanics of Materials” (http://www.amazon.com/Mechanics-Materials-James-M-Gere/dp/0534934293) by Timoshenko and Gere. It also shows you how to calculate the second area moment.

Depending on the materials used and their geometry, you might also want to take shear deflection into account. This is usually not done in standard engineering texts, because in metals shear doesn’t contribute much to the total deflection. Shear is governed by the differential equation y’ = α·V/(G·A), where α is a factor that depends on the shape of the cross-section (1.5 for rectangular ones), V is the shear force in the cross-section, G is the shear modulus, and A is the surface area of the cross section.

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to calculate beam deflection

Structural Calculations

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