## Composite loop connection

engidesk toolbox for the calculation of the stress distribution of a loop connection built from uni-directional rovings

Free

• ### Short description

For almost every load-bearing structure, forces have to be induced or diverted in a way, that the transmission of force is to be configured. The engidesk toolbox at hand allows for the pre-dimensioning of those loop connections in which UD-layers wind around a bolt in form of a parallel loop.

### Details

Release

Last Update

Current version

Price

Licence

Language

01.10.2015

07.03.2016

1.1

Free

MIT-Licence

English, German

### Screenshots

Example Dashboard

• ### Assumptions of the model:

Forces remain constant over the loop's width

There is no friction effect between bolt and loop

No consideration of residual stress caused by thermical and swell effects

The calculation is carried out according to the method of elasto-statics, whereat utilizing a single infinitesimal element, 3 equation systems (balance, equation of elasticity & geometrical relations) can be derived and solved. Calculating the tangential stress works according to the following formula:

$\sigma_{ t }(r)=-p_{ i }*E_{ v }*\left( \frac{ r_{ i }^{ 1+E_{ v } } }{ r_{ i }^{ 2*E_{ v } }-r_{ a }^{ 2*E_{ v } }} *r^{ E_{ v }-1 }*-\frac{ r_{ i }^{ 1-E_{ v } } }{r_{ i }^{ -2*E_{ v } }-r_{ a }^{-2*E_{ v }} }*r^{ -E_{ v }-1 }\right)$

The average tangential stress results from:

$\bar{\sigma}_{ t } =\frac{ \frac{ F }{2 } }{b*\left( r_{ a }-r_{ i } \right) }$

The calculation of the radial stress takes place via the following formula:

$\sigma_{ r }(r)=\frac{ -p_{ i }*r_{ i }^{ 1+E_{ v } } }{ r_{ i }^{ 2*E_{ v } }-r_{ a }^{ 2*E_{ v } }}+\frac{ -p_{ i }*r_{ i }^{ 1-E_{ v } } }{ r_{ i }^{ -2*E_{ v } }-r_{ a }^{ -2*E_{ v } } }*r^{ -E_{ v }-1 }$

In case the loop is supported sideways, a triaxial state of stress prevails. The calculation of the axial stress in longitudinal direction of the sideways supported bolt is carried out according to the following formula:

$\sigma_{ z }(r_{ i })=\left( \nu_{ \perp\perp }*\frac{ \sigma_{ r }(r_{ i }) }{E_{ \perp } } + \nu_{ \perp\parallel }*\frac{ \sigma_{ t }(r_{ i }) }{ E_{ \parallel } }\right)*E_{ \perp }$

Annotation: The experimental proof of prototyping is mandatory, due to the fact that details in the design might heavily influence the load-bearing capacity of the connection. Most importantly, since the structural durability cannot be predicted reliably with the help of FE-methods as well.

• ### Name

engidesk GmbH

Since the company’s formation as RWTH Aachen university spin-off in 2012, engidesk GmbH represents a modern and dynamic software house based in Aachen, Germany. The highly committed team of young professionals around the founders Dr. Lars Lambrecht and Marc Branscheid constantly enhances its uniquely innovative development environment for research and development engineers. The engidesk software enables companies & research facilities to make better use of their technical know-how by harmonising and standardising complex calculations across work groups and entire companies. Unique and easy-to-use interfaces allow for the seamless combination and merger of any calculation know-how to single, directly applicable modules – regardless of the original developing system. Above that, the engidesk market place provides knowledge holders with the possibility to commercialise valuable know-how by putting up problem oriented – all compatible – calculation sequences for sale.