# Thread: Beam deflection calculation frustration

1. ## Beam deflection calculation frustration

So this should be simple. I know it should be simple. However, after getting WILDLY different answers on several online calculators, and doing the calculations "the old fashioned way" several times but feeling like the number is just too small, I turn to you for validation and 2nd, 3rd, 4th opinions. Here is my method and numbers, please let me know if anything jumps out at you as flawed. Thanks in advance for your help!

Length: 117"
2" square steel tube with .125" thick walls (a=2, b=2-(2*.125)=1.75)
Total Weight= 29.7375 lbs (per Ryerson.com stock list, also verified manually)
Deflection formula for simply supported beam with distributed load (machinery's handbook): (5/384)*((WL^3)/(EI))
W= 29.7375 (see above)
L=117 (see above)
E=Modulus of Elasticity=29*10^6
I=Moment of Inertia (machinery handbook)=(a^4-b^4)/12=(2^4-1.75^4)/12=.551757

Soooo... (5/384)((29.7375*117^3)/(29*10^6*.551757)= .038755, max rate of deflection in center.

Also got mixed results using online calculator on a round shaft of outer diameter 1.5, inner 1.25- same length.

2. I don't know what other equations or online calculations you used but I have reviewed all of the elements of the your above calculation using my Machinery's Handbook and don't find any errors in your solution.

At the same time, since the only loading you are applying is the weight of the tubing itself and that distributed weight is only 3.05 lb/ft (per Ryerson Product Listing) I am not really surprised by the resulting small deflection. I also calculated the bending Smax at the center of the beam using my Machinery's Handbook and that stress is only 788.23 psi; which would correlate with a low deflection for the beam.

I have also verified the above formulas in my copy of Mark's "Standard Handbook for Mechanical Engineers" so I believe you can be confident of your above solution

I also looked at an online calculator for a concentrated load and saw an excessive deflection result. In reviewing the formulas shown for their solution I found that they were using "3" rather than the correct "48" as a divisor in their formula (an error factor of 16 times excessive deflection result). My conclusion being: Be wary of online calculators.

3. Originally Posted by cassandra
Soooo... (5/384)((29.7375*117^3)/(29*10^6*.551757)= .038755, max rate of deflection in center.
Your math looks right and it matches the calculator and equation here:

Beam deflections Beam Evenly Loaded Simply Supported Calculator

Beam deflections Beam Evenly Loaded Simply Supported Equations

Be aware that many online calculators use line load as opposed to total load.