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# Displacement calculation on static beam with uniform force and overhanging ends

## Question

I've been wracking my brain with this. I would like to calculate the displacement caused by the force on beam. I've simulated this on Solidworks and then started to calculate it by hand. The problem in this is the overhanging parts that do not give the right answer when calculating by hands while compared on simulation answer. Have I typed wrong value at some point or have I used wrong values? Material is S235J2G3 and beam is HE 300B.

Recommendations and suggestions are welcome.

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assume theta is the angle at right pin support.

M = w (0.9) (0.45) = 121500

theta = (w L^3 / 24 EI) - (ML / 3 EI) - (ML / 3 EI)

theta = [(300000 x 1.2^3) / ( 24 EI )] - 2 [(121500 x 1.2) / ( 3 EI )]

theta = (21600 / EI) - (97200 / EI) = - 75600 / EI

Your (right) end displacement should be

delta = 0.9 theta = - 0.9 x 75600 / EI = - 68040 / EI

E is based on material properties (for steel, E = 200 GPa = 200 x 10^9 Pa)

I is the second moment area of the beam (for HE300B, I = 2.517 x 10^-4 m4)

delta = - 1.3516 x 10^-3 m = - 1.3156 mm

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Thank you for the answer. Solidworks shows that the displacement along y-axel is -3.137, but I haven't calculated if it takes the beam weight into account or if the program itself calculates it using different method. I used simplified sketch with structural members in Solidworks.

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the result some different between hand solve and computer solve.

why the results are ddifferent. I couldn't understand.

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Amazing work, Murat!!!

it often happens like this because the hand calculation consider 1-D effect (only the moment area not 1-D) while the FEA consider 3-D effect.

if you make the FEA becomes line/ 1-D (Ansys and SW could do this), the answer would be much closer to hand calc.