Contact stress under flat woven web sling

[GeorgeDH]

Hi

Does anybody know of an equation/reference for the contact stress distribution found between a flat strap web lifting sling around a circular section, (contacting half the circumference). I need to calculate the contact stress for the material is very delicate and don't wish to crush when loading

Many thanks for any help

George

 

[Ron]

A rigorous statics problem that I would suggest you resolve at major circumferential points. At the bottom of the circular section, your contact stress will be highest; however, that is essentially a line with an unknown width, times the width of the sling to get the stress...the problem, obviously is to get the width of the line at that point.

My suggested approach would be to consider a 45 degree radial, centered on the bottom of the circular section. This will give you an average contact stress over the length of the sling from 22.5 degrees, either side of the bottom center, times the sling width.

Otherwise you could resolve each angle from 90 degrees either side and see how the contact stress transitions to shear-friction as you approach 45 degrees either side of the bottom center.

 

[BAretired]

The maximum stress is 2T/wD where T is the tension in the sling, w is the width of the sling and D is the diameter of the circular section. The minimum stress is 0 at the point where the sling leaves the circular section.

BA

 

[GeorgeDH]

Thanks for the pointers

BAretired - I think 2T/wD would be the projected stress as an average across the diameter? The peak stress would be in the center diminishing to 0, perhaps a circular function, or parabolic I would imagine?

Ron, yes this seems a good assumption, so essentially put an average stress across projected onto the middle third of the diameter?

I was hoping there was a tidy equation that described it, perhaps frictionless if that was more straightforward.

A belt on a pulley was another analogy, but there seems to be little description anywhere?

Thanks

George

 

[dhengr]

GeorgeDH:
2T/wD looks good to me as an average max bearing stress, assuming no geometric irregularities and the like. Consider some fairly soft padding (medium durometer) btwn. the sling and the vessel which will compress and distribute any high stresses at irregularities. While max. contact (bearing) stress is certainly of interest when lifting your product, and selecting the proper sling, etc.; the bigger question might be how does the total circumferential loading affect your product given its shape, delicacy, etc.? How has this product been supported during production, and how will it be supported in its final installed location; they may be more significant and concentrated loadings. And finally, how is it going to be supported in transit and under those rougher handling conditions.

 

[Compositepro]

As BA said the contact pressure is 2T/wD.If curvature is constant, then pressure is constant. If curvature is not constant, then D is the local diameter of curvature. This neglects the small effect of friction on the sling tension.

 

[BAretired]

GeorgeDH,

The peak stress would be in the center diminishing to 0, perhaps a circular function, or parabolic I would imagine?

Neglecting friction, tension is constant around the half circle. Consider any two radii separated by a small angle d[θ]. The length of arc is Rd[θ] where R is the radius of the circular section. Each side of the small triangle is a force acting at d[θ]/2 from the tangent of the middle of the arc. The radial force is 2Tsin d[θ]/2 but as d[θ] approaches zero, this is the same as Td[θ] which acts on an area of wRd[θ]. So the contact pressure is T/wR or 2T/wD. As noted by Compositepro, it is constant for one half of the circle.

BA

 

[GeorgeDH]

Thanks folks

That's a fantastic description. To dhengr, funnily enough the material was never in transit until its final installation, as its a tree supporting a temporary treehouse for an art exhibition and the rigging is a suspension point from a branch, at the union.

The predominant failure mechanism will be bearing stress via truss action to the support (stem) as within a distance of D to it. The shear capacity is inordinately high and no bending stress.

Does that seem a fair assumption? We have an arborist who checks health and we are load testing to check for latent defects.

Thanks