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# Beam Theory for larger cross section

hi,

i want the mid point deflection in case of "four point bend test" on a specimen of length 140mm, width of 40mm and thickness of 10mm.

Problem is that, beam theory is valid if the cross-sectional dimensions are less than axial dimensions. Here this condition is violated. i had modeled the specimen in Abaqus and the diffection at mid point is almost double that of the actual diffection calculated from beam theory.

how can i find the theoritical difflection at mid point in this case?

i had one option, using timoshenko beam theory and applying larger deflection theory. will it be a reasonable approximation in this case?

Ravitej

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## Comments

## Use KCPT

R. Chennamsetti, Scientist, R&D Engineers, India

Here length/width = 3.5. This is close to plate structure. You consider this as a plate, with two opposite edges are simply supported and remaining two are free.

You may get formula for deflection in book like Roark's Stress-Strain formula (You may just check the Title).

Here, length is 14 times the thickness . Kirchoffs Classical Plate Theory (KCPT) gives a good approximation. Mindlin (Timoshenko in case of Beams) plate theory may not be required.

## Ravitej Kommana IIT

Ravitej Kommana

IIT Kanpur

INDIA.

i think plate theory can be applied for flat specimens.

here is my specimen orientation with loading. can i apply plate theory for this?

## Assuming 140 X 40 mm in plane dimensions and 10 mm out of plane

R. Chennamsetti, Scientist, R&D Engineers, India

Please note that you mentioned

thickness as 10mm. In plate theory thicknee is out of plane dimension. Based on this (140 and 40 mm are in-plane dimensions and 10 mm out of plane) only I mentioned KCPT.## yes

yes..earlier i might have discribed the specimen in wrong way..b/c the meaning of width and thickness had changed in our opinions. thts y i had posted the picture of my model..

yes..in this case i cant apply plate theory..please check the other one i had posted in different tag..

Ravitej Kommana

IIT Kanpur

INDIA.

## Hi Ramdas

hi ramdas,

outcome of the suggested boundary condition(constarining the whole face) is good. but i had tried with different boundary condition( constraining only the line corresponding to neutral layer instead of total face). now the results are more close to the theoritical when compared to those of earlier boundary condition. can i use this kind of boundary condition??

Ravitej Kommana

IIT Kanpur

INDIA.