Agree with methodology - great explanation! One small gripe though - confused by equation F = EAx/L. Shouldn't "L" be the original length, not the extended length? - A level physics was 30 years ago for me so apologies if Hooke's law has changed since lol
Hi, thanks for the excellent videos. In one of your other videos (Beam supported at mid-span by a spring) you mention the importance of the signs of the deflections (ie: positive for deflections acting upwards, negative for deflections acting downwards). Does this apply here? I initially though the unrestrained expansion of the column would be positive (acting upwards), the reduced expansion due to the beam would be negative (acting downwards) and the final 'real' expansion would be positive (acting upwards). Using that approach would result in: "2.16mm - (-2.47x) = x", with "x = - 1.47mm". Any advice you could offer to help get my head around that aspect would be appreciated!
Hi Stuart! Honestly, it doesn't matter which direction you take as positive or negative. It's more to help you keep a track of summing multiple deflections -- thermal expansion, virtual work force, restraint force etc., not too dissimilar to initially guessing direction of reaction forces on a structure. If you have the direction wrong, then you will just get a negative number so the actual result should not change.
Without taking the time to do hand calculations, my guess is: 1) There would be an induced compressive axial load in the beam and horizontal reactions due to the thermal expansion 2) Due to the additional axial load there is likely to be a magnified deflection due to P-Delta effect, or the Perry-Robertson magnification 3) Thus the column would probably be allowed to expand further upwards and hence experience smaller compressive force as the additional deflection = less vertical restraint. Refer to 10:35 for the effect of deflection vs. restraint.
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Really useful content. Keep them coming. I appreciate the hard work put into these 👍🏻
Agree with methodology - great explanation! One small gripe though - confused by equation F = EAx/L. Shouldn't "L" be the original length, not the extended length? - A level physics was 30 years ago for me so apologies if Hooke's law has changed since lol
Keep the videos coming, they are really good :D
Great video!
Thank you once again..✌
Hi, thanks for the excellent videos.
In one of your other videos (Beam supported at mid-span by a spring) you mention the importance of the signs of the deflections (ie: positive for deflections acting upwards, negative for deflections acting downwards).
Does this apply here? I initially though the unrestrained expansion of the column would be positive (acting upwards), the reduced expansion due to the beam would be negative (acting downwards) and the final 'real' expansion would be positive (acting upwards). Using that approach would result in: "2.16mm - (-2.47x) = x", with "x = - 1.47mm".
Any advice you could offer to help get my head around that aspect would be appreciated!
Hi Stuart! Honestly, it doesn't matter which direction you take as positive or negative. It's more to help you keep a track of summing multiple deflections -- thermal expansion, virtual work force, restraint force etc., not too dissimilar to initially guessing direction of reaction forces on a structure. If you have the direction wrong, then you will just get a negative number so the actual result should not change.
Hi, ty for the excellent explanation! Could you please explain what happens if C was a pinned restraint instead of a roller?
Without taking the time to do hand calculations, my guess is: 1) There would be an induced compressive axial load in the beam and horizontal reactions due to the thermal expansion 2) Due to the additional axial load there is likely to be a magnified deflection due to P-Delta effect, or the Perry-Robertson magnification 3) Thus the column would probably be allowed to expand further upwards and hence experience smaller compressive force as the additional deflection = less vertical restraint. Refer to 10:35 for the effect of deflection vs. restraint.
@@TheStructuralExam thank you so much !