The torsion of solid or hollow shafts - Polar Moment of Inertia of Area. Stress and force when thermal expansion a pipe, beam or similar is restricted. Restricted Thermal Expansion - Force and Stress Shear Modulus (Modulus of Rigidity) is the elasticity coefficient for shearing or torsion force. mass of object, it's shape and relative point of rotation - the Radius of Gyration. Low-Frequency Vibrations Effects on Building ConstructionsĮffects of low-frequency vibrations on building constructions. Hooke's law - force, elongation and spring constant. Reduced load capacities in ropes, cables or lines - due to acting angle. mass and acceleration.įorces and Tensions in Ropes due to Angle Mechanical properties of fibers used to reinforce polymer composites. The force required to keep a system of forces in equilibrium. Some typical properties of engineering materials like steel, plastics, ceramics and composites. Specific Weight and Specific GravityĪn introduction to density, specific weight and specific gravity.Ĭalculate lateral earth pressure acting on basement walls. In instances where you have more unknowns than equations, the problem is known as a statically indeterminate problem and you will need additional information to solve for the given unknowns.Density vs. The number of unknowns that you will be able to solve for will be the number of equilibrium equations that you have. Once you have your equilibrium equations, you can solve them for unknowns using algebra. Collectively these are known as the equilibrium equations. Your first equation will be the sum of the magnitudes of the components in the x direction being equal to zero, the second equation will be the sum of the magnitudes of the components in the y direction being equal to zero, and the third (if you have a 3D problem) will be the sum of the magnitudes in the z direction being equal to zero. Once you have chosen axes, you need to break down all of the force vectors into components along the x, y and z directions (see the vectors page in Appendix 1 if you need more guidance on this). If you choose coordinate axes that line up with some of your force vectors you will simplify later analysis. These axes do need to be perpendicular to one another, but they do not necessarily have to be horizontal or vertical. Next you will need to choose the x, y, and z axes. It is also useful to label all forces, key dimensions, and angles. This is done by removing everything but the body and drawing in all forces acting on the body. The first step in equilibrium analysis is drawing a free body diagram. In the free body diagram, provide values for any of the know magnitudes or directions for the force vectors and provide variable names for any unknowns (either magnitudes or directions). This diagram should show all the known and unknown force vectors acting on the body. The first step in finding the equilibrium equations is to draw a free body diagram of the body being analyzed. Once we have written out the equilibrium equations, we can solve theĮquations for any unknown forces. We do this by summing up all the x components of the force vectors and setting them equal to zero in our first equation, and summing up all the y components of the force vectors and setting them equal to zero in our second equation. For two dimensional problems, we will split our one vector equation down into two scalar equations. In order to solve for any unknowns in our sum of forces equation, we actually need to turn the one vector equation into a set of scalar equations. This is the basis for equilibrium analysis for a particle. If we know that the body is not accelerating then we know that the sum of the forces acting on that body must be equal to zero. If a body is in static equilibrium, then by definition that body is not accelerating. Equilibrium Analysis for Concurrent Force Systems
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