Ultimate shear capacity of bolt group.xls
The instantaneous centre of rotation method to determine the ultimate shear capacity of a bolt group, as described in the LRFD Code:
The basic idea behind this method is that when a bolt group is loaded in shear, it will rotate about an instantaneous center of rotation (IC). The displacement of each individual bolt in the group will be proportional to its distance from the IC.
By writing equilibrium equations for the forces on the bolts, we can solve for the location of the IC as well as the ultimate shear force the bolt group can resist before failing.
Specifically, we write three equilibrium equations:
- Sum of horizontal forces = 0
- Sum of vertical forces = 0
- Sum of moments about IC = 0
Solving these three equations allows us to find the coordinates of the IC (xIC, yIC) as well as the ultimate shear force Vu.
However, we have to be careful, because if the calculated IC is too far away from the bolt group, it likely indicates a mathematical error. In this case, we should recalculate Vu by taking moments about the center of the bolt group instead.
The key steps are:
- Write equilibrium equations
- Solve for IC location and Vu
- Check if IC is too far - if so, recalculate Vu about group center
This method provides a way to analytically determine the ultimate shear strength of a bolt group using principles of instantaneous centers of rotation.Yakov has many more calculations available from his own website - you'll find a link here.
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