Physics 9: 5-7 Uneven forces on Rigid Bodies
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 9: Sections 4-7
- 9.5: Hooke's Law states that when something is stretched, the force acting on the body is proportional to the distance stretched, multiplied by some constant which depends on the material and its condition by an elastic modulus. At some point L becomes great enough that the material will snap. F = k * ΔL = (EAΔL]/Lo.
- We identify stress as the pressure on an object, force/area
- We identify strain as the change in length contrasted to the original length, ΔL/Lo.
- If we rewrite our force equation above as F/A = E ΔL/Lo, we discover that stress = elastic modulus * strain. The elastic modulus is also known as Young's Modulus.
- Shear stress deforms an object according to ΔL = FLo /GA, where G is the shear modulus.
- Bulk changes if pressure is exerted from all sides, according to B = -ΔP/ΔV/vo.
- 9.6: Fracture occurs when stress, strain, or shear forces break an object. In creating buildings, architects try to balance forces so that the greatest stress or strain on a materia is significantly less than the material's ability to withstand the forces acting in a given situation. It may make sense to use materials with high compressive strength as weight-bearing components, while other materials should be used if tensile forces or shear forces are at work.
- 9.7: Arches require that both downward and outward forces be balanced. Pillars must not only support the weight of the arch or dome, they must also push inward to compensate for the outward component working along the curve of the arch.
|Each of the buildings below solves the problem of supporting a dome or high vault differently. [For more information, see Great Buildings Online.|
||Flying buttresses support the tower above the crossing at Chartres Cathedral (thirteenth century)
||The dome of St. Paul's, London (seventeenth century) rises 366 feet above its foundation; the interior and exterior domes hide a brick cone that provides the necessary support.
||Romanesque arches and extensions from the main building support the dome of the Pantheon, Paris (18th century)
- Hooke's Law
- Young's Modulus
- Shear Stress
- Bulk Modulus
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