Deflection of beam with multiple cross sectional areas
Deflection of beam with multiple cross sectional areas
(OP)
Hi,
How would one go about calculating the deflection of a beam with multiple I-values.
The beam is simply supported, and symmetrical. It is made up of 3 sections, with the two ends near the supports being I1 and the middle section being I2. There are two equal point loads being applied to the beam at the points where the beams cross-section changes from I1 to I2, and I am trying to calculate the deflection at the points where the load is applied.
I have tried calculating the deflection of equivalent beams with cross sections I1 and I2 at these points and summing the deflection together but FEA analysis has given completely different results, meaning this method is completly wrong and I need to somehow calculate the beam as one.
Any help would be much apprciated.
Cheers
How would one go about calculating the deflection of a beam with multiple I-values.
The beam is simply supported, and symmetrical. It is made up of 3 sections, with the two ends near the supports being I1 and the middle section being I2. There are two equal point loads being applied to the beam at the points where the beams cross-section changes from I1 to I2, and I am trying to calculate the deflection at the points where the load is applied.
I have tried calculating the deflection of equivalent beams with cross sections I1 and I2 at these points and summing the deflection together but FEA analysis has given completely different results, meaning this method is completly wrong and I need to somehow calculate the beam as one.
Any help would be much apprciated.
Cheers






RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
Since this is a simple problem you can check the behavior of this non-prismatic beam by inputing the same value for I1 and I2 and checking against well known formulas for deflection or moment or shear. Then you can change I2 incrementally noting how it changes the results until you have I2 at the value you want.
Regards,

Qshake
Eng-Tips Forums:Real Solutions for Real Problems Really Quick.
RE: Deflection of beam with multiple cross sectional areas
http://newtonexcelbach.wordpress.com/2013/11/22/un...
Will calculate shears, bending moments, rotations and deflections for simply supported spans or continuous beams with any number of changes of section.
Since this is a symmetrical problem you could also analyse it as a cantilever fixed at mid span with a fairly simple calculation.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Deflection of beam with multiple cross sectional areas
then you draw the bending moment diagram
then you use M/I=E/R to get the radius of curvature at each point
then you integrate the curvature once for gradient, and again for deflection.
This is what we used to call engineering.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
Dik
RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
Quando Omni Flunkus Moritati
RE: Deflection of beam with multiple cross sectional areas
RE: Deflection of beam with multiple cross sectional areas
Draw the bending moment from one end by adding the areas under the shear diagram from the point at hand and the support, work your way across (no big deal with this case). in this case, you go from the support to the first load point, then the second.
Now, you load up the beam with the bending moment diagram as though it were a load, now calculate a "Secondary shear" caused by this load. It is convenient to divide the answers by EI for this diagram. this diagram shows the slope of the beam. From this "Secondary shear" diagram, calculate a "secondary moment" diagram. This secondary moment diagram shows the deflection of the beam.
Understand that you keep track of units as you perform this method. It takes less time to do it than for me to write this.
It is strange to say, but this was a method of choice when I started work right up until reliable computer programs appeared on the scene.
Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin