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 Fun Trivia: G : General Technology

### Special Sub-Topic: What Do You Know About Statics?

 What is one of the primary assumptions made in the study of statics?

Objects analyzed are rigid bodies, meaning they do not deform. When studying statics, it is assumed that the objects being analyzed are rigid bodies. The deformation of the object while under the action of forces is not considered in statics, and is instead studied in a later course that builds on statics, typically called "strength of materials".

 One type of support for a beam is a pin connection. If a pin connection is able to turn and is viewed in two dimensions only, what type of movement can it NOT resist?
Rotational (moment). A pin connection that is free to turn can resist forces in any direction in plane of the pin, but it cannot support a moment, which is why the pin can rotate about its axis.

 A uniform steel beam is supported with a pin at its left end (point A) and a roller at its right end (point B). The beam is 5 meters long and a vertical (downward) point load of 6 kilonewtons (kN) is applied at the center of the beam (2.5 meters away from points A and B). Neglect the weight of the beam. What are the VERTICAL reactions at the supports A and B?
A = 3 kN (up), B = 3 kN (up). You could solve this problem by summing moments at one point, and then sum the forces in the y-direction. But there's a short cut. Since the beam and loading is symmetrical, just take the applied 6 kN force and divide it by 2, and that's the value of each reaction force. The reactions must point up to counteract the downward applied force. Since the loading is vertical, the horizontal reaction at A is zero.

 What is the mathematical definition, or magnitude, of a moment about a point?
Force x Distance. Moment is the rotational tendency of a force about an object, and is typically denoted by the letter M. The magnitude of a moment about a point is found by multiplying the force by the distance of the force application to the point.

 A truss is "a framework composed of members joined at their ends to form a rigid structure" (Meriam and Kraige, 2002). Examples include bridges and roof supports. What are the members in a truss typically assumed to be?
Two-force members. Truss members are two-force members, where two forces are applied at the ends of the member and are equal, opposite, and collinear (Meriam and Kraige, 2002).

 A uniform wooden beam is supported with a pin at its left end (point A) and a roller at its right end (point B). The beam is 3 meters long. A rectangular distributed load of 8 kN/m is placed on the beam. This load covers the entire span of the beam and is vertically pointing downward. Neglect the weight of the beam. What is the vertical reaction at the roller support at point B?
12 kN (up). The distributed load is resolved into a point load by finding the area of the load. Since the loading is rectangular, the area is simply the height (8 kN/m) multiplied by the length (3 meters), giving a point load of 24 kN. Since the force acts through the centroid of the loading, for a rectangle this would be the center of the beam, or 1.5 meters away from B. This problem is symmetrical, so the reaction at B is just half of 24 kN, giving a value of 12 kN. The vertical reaction at A is also 12 kN, and the horizontal reaction at A is zero due to the vertical loading.

 If the gravitational attraction, or weight, of an object is resolved into a single point load, where does this load typically act on the object?
Through the center of mass. When resolving the force of gravity of an object into a single point load, this load acts through the object's center of mass and points down toward the earth.

 A cantilever beam is a beam that is fixed at one end and free at the other. The fixed end can resist both force and moment. If a cantilever beam 2 meters long is loaded with a 10 kN point load applied vertically downward at the free end, what is the resisting moment at the fixed end? Neglect the weight of the beam.
20 kN-m. This is a perfect example of the definition of moment where M = force x distance. Since there is only one applied force present, this problem is solved simply by multiplying 10 kN by 2 meters, yielding an answer of 20 kN-m.

 How are the reactions at pin and roller connections determined for a truss?
The same way as for a beam. Finding the reactions for a truss is done exactly the same way as for a beam. You simply "collapse" the truss, or look at it the same as a beam, and go from there. There is no such thing as a truss method of reactions!

 A course that is taken after statics and that is closely related to statics is called dynamics. What is the primary (and most logical) difference between statics and dynamics?
Statics deals with equilibrium of bodies, while dynamics covers motion of bodies. Statics is the study of the equilibrium of bodies while being acted on by forces, and dynamics concerns the motion of these bodies. Some information for this quiz was taken from my own statics book: "Engineering Mechanics--Statics, 5th Edition" by J.L. Meriam and L.G. Kraige; published by John Wiley & Sons, Inc., in 2002.

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