BridgeDude1487
Structural
- Mar 10, 2016
- 7
I'm trying to calculate the relative stiffnesses of pile bents for longitudinal load distribution on a railroad bridge.
I know of two ways to do it: [ol 1]
[li]Modeling in an FEA program. (tedious and time consuming to do this for every bent on every bridge)[/li][li]Using n*3EI/L3 or n*12EI/L3 for each bent (depending on boundary condition assumptions at the free end), where n = the number of columns, E = the modulus of elasticity, I = the moment of inertia of a pile, and L = the effective pile length (I'm using exposed pile length + 5 * pile diameter).[/li]
[/ol]
My question is this: Doesn't this method ignore the effects of pile configuration, spacing, and the fact that the piles are all connected to the cap and restrained against relative rotation? For example, obviously a 4x2 pile bent and a 2x4 pile bent would deflect differently under the same load (and therefore have different stiffnesses). Same goes for pile bents with piles spaced further apart.
Am I correct in this thinking? If so, how would I take this into account? I've tried using different combinations of I, A and Σd2, but nothing I've tried seems quite right. It seems to make the configuration/spacing affect the stiffness too much. Different ways I've tried calculating the group moment of inertia include: n*I + ΣAd2, ΣAd2, Σd2. When I do this the stiffness goes up by a factor of about 30, which seems way too high. An FEA model of a single pile I put together has a stiffness of approximately 3EI/L3, and connecting 6 piles into configurations of 2x3 and 3x2 pile bents cause the stiffness to become about 3x this (so not quite 12EI/L3). The 2x3 and 3x2 stiffnesses were slightly different in my model (about 8% different), confirming my hypothesis that orientation/configuration does affect the stiffness.
Any help on this would be appreciated! Thanks
EDIT: Figured out a better way to describe this--I'm thinking of it as "parallel cantilever beams". The free beam ends would be connected to the pile cap. If this pile cap is not free to rotate, it turns into a guided cantilever system and the deflection of the beams would be 12EI/L3. This is the best case scenario, and represents an upper bound for stiffness. But the pile cap is free to rotateI've been modeling different layouts this morning and the more parallel beams you add in the direction of bending, the closer the stiffness gets to 12EI/L3. The biggest jump comes between 1 & 2 rows--1 row of piles still has a stiffness of about 3EI/L3. Adding a second row at a spacing of 3*dia increases this stiffness by approximately 2.6. 3 total rows increases it about 2.8. At 6 rows the total stiffness increase is over 3x the original 3EI/L3. There is also obviously a tension/compression couple in the corresponding beam rows. I'm sure this factors in somehow. I'm messing around with the numbers to see if anything pops out.
I know of two ways to do it: [ol 1]
[li]Modeling in an FEA program. (tedious and time consuming to do this for every bent on every bridge)[/li][li]Using n*3EI/L3 or n*12EI/L3 for each bent (depending on boundary condition assumptions at the free end), where n = the number of columns, E = the modulus of elasticity, I = the moment of inertia of a pile, and L = the effective pile length (I'm using exposed pile length + 5 * pile diameter).[/li]
[/ol]
My question is this: Doesn't this method ignore the effects of pile configuration, spacing, and the fact that the piles are all connected to the cap and restrained against relative rotation? For example, obviously a 4x2 pile bent and a 2x4 pile bent would deflect differently under the same load (and therefore have different stiffnesses). Same goes for pile bents with piles spaced further apart.
Am I correct in this thinking? If so, how would I take this into account? I've tried using different combinations of I, A and Σd2, but nothing I've tried seems quite right. It seems to make the configuration/spacing affect the stiffness too much. Different ways I've tried calculating the group moment of inertia include: n*I + ΣAd2, ΣAd2, Σd2. When I do this the stiffness goes up by a factor of about 30, which seems way too high. An FEA model of a single pile I put together has a stiffness of approximately 3EI/L3, and connecting 6 piles into configurations of 2x3 and 3x2 pile bents cause the stiffness to become about 3x this (so not quite 12EI/L3). The 2x3 and 3x2 stiffnesses were slightly different in my model (about 8% different), confirming my hypothesis that orientation/configuration does affect the stiffness.
Any help on this would be appreciated! Thanks
EDIT: Figured out a better way to describe this--I'm thinking of it as "parallel cantilever beams". The free beam ends would be connected to the pile cap. If this pile cap is not free to rotate, it turns into a guided cantilever system and the deflection of the beams would be 12EI/L3. This is the best case scenario, and represents an upper bound for stiffness. But the pile cap is free to rotateI've been modeling different layouts this morning and the more parallel beams you add in the direction of bending, the closer the stiffness gets to 12EI/L3. The biggest jump comes between 1 & 2 rows--1 row of piles still has a stiffness of about 3EI/L3. Adding a second row at a spacing of 3*dia increases this stiffness by approximately 2.6. 3 total rows increases it about 2.8. At 6 rows the total stiffness increase is over 3x the original 3EI/L3. There is also obviously a tension/compression couple in the corresponding beam rows. I'm sure this factors in somehow. I'm messing around with the numbers to see if anything pops out.
