I am trying to compare FEM analysis to hand calculations for I-beam bending. I am using "Roark's Formulas for Stress and Strain", seventh edition, for hand calculation formulas. And Patran 03 (nastran 01) for the FEM.
The cross sections are height=4.5 in, flange width = 3 in, flange thickness = .25 in, and web thickness = .125 in. The only value I have varied is length.
Looking at the mid point of the beam and using span/depth ratios greater than 15 I have found a difference in deflection of at most 20% (span/depth~30) and only about a 1% difference in extreme fiber stress. The difference in deflection decreases as the span/depth ratio increases. Down to < 5% when span/depth ~ 55. And the extreme fiber stress stays within 2% no matter the span/depth.
I assumed that the difference is due Roark's formula neglects shear deflection so I then added shear deflection using Roark's equation 8.10-1. The added shear deflection only marginally changed the deflections and hence the percent differences.
Now for the questions. Can anyone explain why FEM and roark deflections do not match? Also how do the extreme fiber stresses match when the deflections do not?
The cross sections are height=4.5 in, flange width = 3 in, flange thickness = .25 in, and web thickness = .125 in. The only value I have varied is length.
Looking at the mid point of the beam and using span/depth ratios greater than 15 I have found a difference in deflection of at most 20% (span/depth~30) and only about a 1% difference in extreme fiber stress. The difference in deflection decreases as the span/depth ratio increases. Down to < 5% when span/depth ~ 55. And the extreme fiber stress stays within 2% no matter the span/depth.
I assumed that the difference is due Roark's formula neglects shear deflection so I then added shear deflection using Roark's equation 8.10-1. The added shear deflection only marginally changed the deflections and hence the percent differences.
Now for the questions. Can anyone explain why FEM and roark deflections do not match? Also how do the extreme fiber stresses match when the deflections do not?
