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aerobod · 12-31-2010, 12:37 PM

I just did some calculations to determine the maximum distortion of the OEM braces (Pull Rods, to give it the BMW name), to determine whether any upgrade is going to have any effect other than a placebo.

The maximum force able to be transmitted by the pull rod without significant movement is determined by the securing bolts in this case. The M10x1.25 10.9 bolt can be torqued to a maximum value of 80Nm, leading to a clamping force of approximately 40,000N. Assuming a friction coefficient of 0.2, a maximum of 8000N of shear force can be resisted by the clamping bolts. Assuming a 2x safety factor before failure, 4000N can be transmitted in shear by the clamping bolts.

So, what does this 4000N of force along the strut do?

The pull rod has a width of approximately 40mm and thickness of 11mm, giving a cross-section of 0.00044m^2 (it seems as though the Strong Strut brace is 1.5" x 0.25" angle, leading to a very similar cross section of 0.000444m^2). The length between clamping bolts is approximately 1.1m.

The Young's Modulus of aluminium is generally 70GPa, varying little from alloy to alloy (compared with steel that varys from about 60 to 240, depending on alloy, but is about 200 for cold rolled A36, for example).

So, in tension, elongation will be (force x length) / (cross_section x Young's_Modulus) = (4,000 x 1.1) / (0.00044 x 70,000,000,000) = 0.00014m or 0.14mm. For the Strong Strut this would be approximately 0.05mm, assuming steel with a Young's Modulus of 200GPa.

In compression, the forces are unlikely to be anything other than axial on the OEM pull rod. Due to the brace in the middle, the maximum un-supported length is 0.6m, think of 400kg pushing down on a 40x11x600mm rod on end, it won't bend out-of-plane to any noticeable degree (if 10% of the force was mis-aligned, then that 400N force would deflect the rod only 1mm vertically, causing no appreciable difference in length change, compared with in tension).

So, in summary, is it worth the approximately 8kg / 18 lbs weight penalty of the Strong Strut braces to alleviate up to a maximum of 0.1mm of body flex between the two mounting points 1.1m apart?

12-31-2010, 12:37 PM	#29
aerobod Car Geek 3626 Rep 3,593 Posts Drives: Caterham R500, M2-G87, Macan S Join Date: Mar 2008 Location: Calgary iTrader: (0)	I just did some calculations to determine the maximum distortion of the OEM braces (Pull Rods, to give it the BMW name), to determine whether any upgrade is going to have any effect other than a placebo. The maximum force able to be transmitted by the pull rod without significant movement is determined by the securing bolts in this case. The M10x1.25 10.9 bolt can be torqued to a maximum value of 80Nm, leading to a clamping force of approximately 40,000N. Assuming a friction coefficient of 0.2, a maximum of 8000N of shear force can be resisted by the clamping bolts. Assuming a 2x safety factor before failure, 4000N can be transmitted in shear by the clamping bolts. So, what does this 4000N of force along the strut do? The pull rod has a width of approximately 40mm and thickness of 11mm, giving a cross-section of 0.00044m^2 (it seems as though the Strong Strut brace is 1.5" x 0.25" angle, leading to a very similar cross section of 0.000444m^2). The length between clamping bolts is approximately 1.1m. The Young's Modulus of aluminium is generally 70GPa, varying little from alloy to alloy (compared with steel that varys from about 60 to 240, depending on alloy, but is about 200 for cold rolled A36, for example). So, in tension, elongation will be (force x length) / (cross_section x Young's_Modulus) = (4,000 x 1.1) / (0.00044 x 70,000,000,000) = 0.00014m or 0.14mm. For the Strong Strut this would be approximately 0.05mm, assuming steel with a Young's Modulus of 200GPa. In compression, the forces are unlikely to be anything other than axial on the OEM pull rod. Due to the brace in the middle, the maximum un-supported length is 0.6m, think of 400kg pushing down on a 40x11x600mm rod on end, it won't bend out-of-plane to any noticeable degree (if 10% of the force was mis-aligned, then that 400N force would deflect the rod only 1mm vertically, causing no appreciable difference in length change, compared with in tension). So, in summary, is it worth the approximately 8kg / 18 lbs weight penalty of the Strong Strut braces to alleviate up to a maximum of 0.1mm of body flex between the two mounting points 1.1m apart?
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