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 chose 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. Source: Engineering Mechanics, Jacob Moore, et al. Since it is a particle, there are no moments involved like there is when it comes to rigid bodies. The equations used when dealing with particles in equilibrium are: Individual forces acting on the object, represented by force vectors, may not have zero magnitude but the sum of all the force vectors will always be equal to zero for objects in equilibrium. Therefore, if we know that the acceleration of an object is equal to zero, then we can assume that the sum of all forces acting on the object is zero. Newton’s Second Law states that the force exerted on an object is equal to the mass of the object times the acceleration it experiences. These objects may be stationary, or they may have a constant velocity. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.Objects in static equilibrium are objects that are not accelerating (either linear acceleration or angular acceleration). Young's Modulus, Tensile Strength and Yield Strength Values for some Materials Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more. Uniformly and concentrated floor loads Vector Addition ![]() The torsion of solid or hollow shafts - Polar Moment of Inertia of Area. ![]() Three-Hinged Arches - Continuous and Point Loads Static equilibrium is achieved when the resultant force and resultant moment equals to zero. Stress is force per unit area - strain is the deformation of a solid due to stress. Hoop and longitudinal stress thin-walled tubes or cylinders. Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure. Stress in Thick-Walled Cylinders or Tubes Stress is force applied on cross-sectional area. Steels - Endurance Limits and Fatigue StressĮndurance limits and fatigue stress for steels. Soil - Bearing StrengthĪllowable loads on soil. 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. Forces 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. Earth Pressure Acting on Basement WallsĬalculate lateral earth pressure acting on basement walls. Specific Weight and Specific GravityĪn introduction to density, specific weight and specific gravity. Center of GravityĪ body and the center of gravity. Center MassĬalculate position of center mass. Cable Loadsįorce and tension in cables with uniform loads. Bollard Forcesįriction, load and effort forces acting in ropes turned around bollards. Supporting loads, stress and deflections. Beams - Supported at Both Ends - Continuous and Point Loads Supporting loads, moments and deflections. Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads Stress, deflections and supporting loads. Beams - Fixed at Both Ends - Continuous and Point Loads Beam Loads - Support Force CalculatorĬalculate beam load and supporting forces. Area Moment of Inertia ConverterĬonvert between Area Moment of Inertia units. Deflection and stress, moment of inertia, section modulus and technical information of beams and columns.
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