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Statics: Loading Types and Constraints

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Loading Types & Constraints

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When analyzing a statics problem it is important that you have an understanding of different loading situation and constraints that a part can be placed under. The object must have one of each for it to be a statics problem.

Types of Loading

There are different types of forces that can be placed on an object. An object could have a point load placed on it, a distributed load, or a moment.

Point Load

A point load is a load that is placed on an infinitely small point on a object. Point loads are typically represented in the x, y, or z direction on a part. To view what a point load looks like refer to the figure below.

point load representation for a statics or strength of materials problem

Distributed Load

A distributed load is a force/(unit length). When dealing with distributed load it is best to transform it into a point load. To do this you would have to calculate the area under the curve of the distributed load and you would also need to determine where the point load would occur on the object. Two common types of distributed loads are rectangular distributed loads and triangular distributed loads. Refer to the figures below.

Distributed load (rectangular and trianglular) representation for a statics or strength of materials problem

Moments

Moments represent rotational forces. A three dimensional problem can have up to three summed moments on it. You would calculate a moment the same way that a torque would be calculated, which would be the force times the perpendicular length. The difference between a moment and a torque is that a torque represents twisting while a moment represents bending. To view what a moment would look like refer to the figure below.

Moment representation for a statics or strength of materials problem

Also, when dealing with torques or moment you need to know if the torque is positive or negative. A positive moment or torque has a counter-clockwise rotation, while a clockwise rotation means it is negative. The way you can tell if you are not sure is to follow the right hand rule, which is sticking your them out on you right hand and following the direction of the curl of your fingers. This will represent a positive torque or moment.

The right hand rule is used to determine whether a torque or moment is positive or negative

Types of Constraints

All Statics problems also have constraints. There are three different types of constraints, fixed, pinned, and rolling. From these constrains it is possible that there could be a total of six resultant forces and moments for a 3d problem, which means the maximum number of statics equations that can be used to describe a problem would be six.

Fixed Constraint

A fixed constraint constrains an object from rotating and translating. Due to those constraints there will be reaction forces and moments in a all directions on that constraint. Refer to the figure below.

Representation of a fixed constraint for a statics / strength of materials problem

Pinned Constraint

Pinned constrains are constraints that prevent translation in all direction, but allow a rotation about the pin. This in turn will cause resultant forces but there will be no resultant moment for a two dimensional problem. Refer to the figure below.

Representation of a pinned constraint for a statics / strength of materials problem

Rolling Constraint

A rolling constraint prevents translation in one direction. All other directions and rotations are not constrained, which means there will be only one resultant force due to that constraint. Refer to the figure below.

Representation of a rolling constraint for a statics / strength of materials problem



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