3d static rigid body equilibrium problem

#3d static rigid body equilibrium problem free

However, if the supports are not properly constrained, the body may become unstable for some loading cases.ĮXAMPLE Given: The cable of the tower crane is subjected to 840 N force. In some cases, there may be as many unknown reactions as there are equations of equilibrium. IMPROPER CONSTRAINTS Here, we have 6 unknowns but there is nothing restricting rotation about the x axis. Are statically indeterminate structures used in practice? Why or why not? A problem that is statically indeterminate has more unknowns than equations of equilibrium. Thus, they do not appear in the equation.ĬONSTRAINTS FOR A RIGID BODY (Section 4.7) Redundant Constraints: When a body has more supports than necessary to hold it in equilibrium, it becomes statically indeterminate. Those forces do not appear in the moment equation since they pass through the point.

Usually, choosing the point where the maximum number of unknown forces are present simplifies the solution.

MX =  MY =  MZ = 0 The moment equations can be determined about any point.

These two vector equations can be written as six scalar equations of equilibrium (EofE).

Thus, in these cases, only force reactions are generated and there are no moment reactions created.ĮQULIBRIUM EQUATIONS IN 3-D (Section 5.6) As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e.,  F = 0 and  MO = 0. However, it is usually preferred to use two or more properly aligned bearings or hinges. IMPORTANT NOTE A single bearing or hinge can prevent rotation by providing a resistive couple moment. Similarly, if rotation is prevented, a couple moment is exerted on the body by the support. As a general rule, if a support prevents translation of a body in a given direction, then a reaction force acting in the opposite direction is developed on the body. Other support reactions are given in your text book (Table 5-2). SUPPORT REACTIONS IN 3-D (Table 5-2) A few examples are shown above.

How can we determine the reactions at these supports? How will we determine the reactions at the wheels D, E and F ? A 50 lb sign is kept in equilibrium using two cables and a smooth collar. How can we determine the support reactions at these joints for a given loading?ĪPPLICATIONS (continued) The weights of the fuselage and fuel act through A, B, and C. ĪPPLICATIONS Ball-and-socket joints and journal bearings are often used in mechanical systems. When doing a 3-D problem analysis, you have _ scalar equations of equilibrium. If a support prevents rotation of a body about an axis, then the support exerts a _ on the body about that axis.

#3d static rigid body equilibrium problem free

The entire equation of motion is F=Kx +Cv+Ma if velocity and acceleration has become zero than F=Kx, and the stress in the body obeys Hooke's Law.RIGID BODY EQUILIBRIUM IN 3-D (Sections 5.5 – 5.7) Today’s Objective: Students will be able to a) Identify support reactions in 3-D and draw a free body diagram, and, b) apply the equations of equilibrium. OR rigid means it is in static equilibrium which means its velocity and acceleration is zero.Īn object in static equilibrium is unable to move because all the forces acting on it compensate for one another, that doesn't mean the body isn't strained and deformed. It isn't clear from your post if rigid means in-compressible, zero strains. Once it is a rest on the moon, it is still deformed and has strains. It under goes velocities, rigid body translation, accelerations, etc.

Then I can take that stressed cube and put it on a rocket to the moon. For example I can compress a cube on earth and it is deformed, has strains and stresses. A body can have a rigid body motions, be in static equilibrium, have zero velocity, and acceleration, and still under strains a deformations within the body that produces stresses. You seem to be mixing the terms motion and deformation.