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Question: often you need to make an estimate of the forces...

Question details

Often you need to make an estimate of the forces where you would not have time or tools to perform a detailed analysis. In this module, we will discuss methods for estimating loads or other statics results on rigid bodies.  The Free Body Diagram is a good tool for estimation as you can visually add forces and moments. You can round given force values to one or 2 places of precision. You can also approximate centroids and centers of gravity by visual integration of the largest areas. For 2nd Moment of area and moment of inertia adjust for things further from the axis having more weight.

An example is below:

For the beam loaded and supported as shown approximate the reactions at A and B.

50 N 100 N 150 N 45- 450 mm--+--450 mm-

The 50 N load is close to support A so add 50 the reaction at A.

The 100 N load is about the middle of the beam so add 50 to both reactions.

The 150 N load is above support B so all of it gets transferred to B.

Reaction at A is approximately 100 N and reaction at B is approximately 200 N.

The reaction at A will be slightly greater and the reaction at B will be slightly less than the estimates.

Note that estimation is more of an art than a science so there is not a set procedure. Just apply logic and what you know about statics.

Assignment:

There are four problems listed below.  Approximate, the solutions for TWO problems and describe how you approximated the solutions.  An approximation is usually only one or two digits in accuracy. YOU ARE NOT TO COMPLETELY SOLVE THE PROBLEM. THESE SHOULD BE EDUCATED APPROXIMATIONS.

A) 9.35 and 9.36 Determine the moments of inertia of the shaded area shown with respect to the x and y axes. Fig. P9.35 Fig. P9.36

B) 6.9 and 6.10 Determine the force in each member of the truss shown. State whether each member is in tension or compression 5 kN С 300 30° 4 kN 4 kN Fig. P6.9 Fig. P6.10

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