Simple FEA Question (Moment sum)...?

[justhumm]

To start to re-acquaint myself with finite element analysis, I am trying to model a very basic simply supported beam using solid elements in STAAD.

Span Length, L = 10 ft
Point Load at Midspan, P = 10 kip

Shear, V = P / 2 = 5 kip
Moment at Midspan, M = P * L / 4 = 25 kip-ft​

In STAAD, the beam is (4) x (4) x (20) solid blocks (with concrete material assigned). I applied the 10-kip point load as (5) 2-kip joint loads at midspan.

I calculated the shear at midspan by multiplying each (midspan) solid's resulting shear force (SXY) by the solid's cross sectional area. This resulted in V = 5 kips, as expected.

I calculated the moment at midspan by multiplying the normal force by the distance from the (mid-height) centroid by the Area (SXX * d * A). This resulted in only M = 14 k-ft.

Am I doing something incorrectly with the moment, or could I expect that much of a moment reduction when the "point" load is distributed over the width of the section? (resulting stresses attached in *.csv file)

Thanks in advance...

 

[Shu Jiang PEng SE]

I did the same analysis as you said and got a reasonable result.

20 feet long 16"x16" cross section beam is simulated with the element size 4x4x6, and one end is simply support and the other end is vertically support only at the bottom layer nodes. 10kips is applied to the five middle span nodes with 2kps each.

The stress at element center is approximately 0.64ksi, 0.21ksi, -0.2kis and -0.65ksi.
The force at top layer of element is 0.64x4x4x4=40.96kip, the force at bottom layer of element is 0.65x4x4x4=41.6kips, the force distance is 2+4+4+2=12", the moment is (40.96+41.6)/2x12=495.36kip-in=41.28kip-ft.

The force at second top layer of element is 0.21x4x4x4=13.44kip, the force at bottom layer of element is 0.2x4x4x4=12.8kips, the force distance is 2+2=4", the moment is (13.44+12.8)/2x4=52.48kip-in=4.37kip-ft.

the total moment is 41.28+4.37=45.65kip-ft, theoretical moment 50kip-ft. The error can be reduce once refine the beam mesh.


Sorry. I used the wrong span but that dose not influence the conclusion.

 

[justhumm]

Jiang:

Thank you very much for your response! It made me realize that I created my initial model with pin-pin end conditions for the beam. When I changed the end conditions to pin-roller, I got stress results much closer to the theoretical.

Cheers!

 

[jhardy1]

Also note that as far as matching theoretical beam results is concerned:

1. Your central load should apply 25% of the total load to each of the internal nodes, and 12.5% to the edge nodes, as they have only half the tributary width. Your load application effectively concentrates the line load towards the sides of your beam, and you can see this in your stress plots.

2. Your 3D stress results will be "disrupted" by the concentrated stresses around the point loads - think of this as being local bearing stresses superimposed on the global beam bending stresses, if you like. These local stresses are a "real" effect in the vicinity of a concentrated knife-edge load, but are not reported when you consider a classical 1D beam bending analysis.

http://julianh72.blogspot.com