E240509
Mechanical
- Jun 21, 2017
- 4
Hi all, a quick question for you guys to help as a refresher.
Say for instance a round bar is seated in a VEE BLOCK with included angle in the VEE of 90 degrees. Assuming vertically downward force of 500N from the weight of the bar, then the Normal force onto each planer face of the VEE would be 353N (500 x cos(45)).
If this same set-up was placed on a support block that made contact in 4 positions rather than 2 - lets say P1@30degrees, P2@60degrees with P3 and P4 symmetrical to these about the vertical axis. Assuming geometry, pad stiffness etc ensured the load was equally shared between all four, then how do I resolve those same normal forces at each pad. I would end up with 2 equations and 4 unknowns - I assumed there is some symmetry I can take advantage of in that P1 = P4 and P2 = P3.
With that in mind I get sum of forces in
X=0, 0.86P1 + 0.50P2 - 0.50P3 - 0.86P4 = 0
Y=0, 0.50P1 + 0.86P2 + 0.86P3 + 0.50P4 = 500
Using symmetry to remove P3 and P4 from the equations, and simplifying I get P1=P3 = 216.5N and P2=P4 = 125N. Putting these back into the original equations seems to be correct, but just can't help feeling I've slipped up somewhere so would love to hear thoughts.
Thanks.
Say for instance a round bar is seated in a VEE BLOCK with included angle in the VEE of 90 degrees. Assuming vertically downward force of 500N from the weight of the bar, then the Normal force onto each planer face of the VEE would be 353N (500 x cos(45)).
If this same set-up was placed on a support block that made contact in 4 positions rather than 2 - lets say P1@30degrees, P2@60degrees with P3 and P4 symmetrical to these about the vertical axis. Assuming geometry, pad stiffness etc ensured the load was equally shared between all four, then how do I resolve those same normal forces at each pad. I would end up with 2 equations and 4 unknowns - I assumed there is some symmetry I can take advantage of in that P1 = P4 and P2 = P3.
With that in mind I get sum of forces in
X=0, 0.86P1 + 0.50P2 - 0.50P3 - 0.86P4 = 0
Y=0, 0.50P1 + 0.86P2 + 0.86P3 + 0.50P4 = 500
Using symmetry to remove P3 and P4 from the equations, and simplifying I get P1=P3 = 216.5N and P2=P4 = 125N. Putting these back into the original equations seems to be correct, but just can't help feeling I've slipped up somewhere so would love to hear thoughts.
Thanks.
