15.5 STATICALLY INDETERMINATE

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There are a number of problems that cannot be solved with statics methods. In fact, all problems are inexact, but luckily we can solve some using statics.

These types of problems often occur when the number of forces known is equal to the number of useful governing equations. This is known as completely constrained.

When there are more equations than unknowns the problem may be overconstrained.

When there are fewer equations than unknown forces, the problem may be underconstrained.

The basic types of cases are,

be cautious with this class of problems. You may actually be able to calculate a solution, but the answer will not be correct realistically, and mathematically speaking.

Consider problem 2.4-1 from Hibbler

Example #2

Example #3, problem 2.4-19 from Gere and Timoshenko

15.5.1 Summary

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basic moments and calculations

- using normal components

- using perpendicular components

- using vectors and cross products

a review of cross products, and the positive direction for angles/moments

force couples and moments were shown to be able to freely move about a rigid body.

a force can be moved away from its axis if a moment is also added.

mechanical schematic symbols were discussed with applications to statics.

indeterminate problems

15.5.2 Practice Problems

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1. Determine the reactions at A and E.

15.5.3 References

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Hibbeler, R.C., Engineering Mechanics: Statics and Dynamics, 6th edition, MacMillan Publishing Co., New York, USA, 1992.

Soustas-Little, R.W. and Inman, D.J., Engineering Mechanics Statics, Prentice-Hall, 1997.