Question

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:

The problems are 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.

Locate the centroid of the plane area shown:

A)

B)

READ THE PROBLEM DESCRIPTION!!!!!! IF YOU SOLVE THE PROBLEM INSTEAD OF PROVIDING APPROXIMATIONS AND EXPLANATIONS THEN I WILL NOT THUMBS UP!!!!! If it is correct I will rate it immediately.

Answer 1

A)

The area is made of 2 part, 45 mm square and 27 x 45 triangle

A rectangle of 72 x 45 mm

the centroid of this full rectangle is (36, 22.5)

now a traingle of 27 x 45 is removed, this will cause a shift of centroid to the right and to top

part of the area missing in the rectangle = (27*45/2) / 72*45 = 0.19

shift of centroid to the right = 36*0.19 = 6.84

shift to top = 22.5 *0.19 = 4.3

actual centroid = 42.84 , 26.8

B) The piece is made of 2 parts vertical piece of ht = 8 in and width 1 in

centroid of the vertical part = 0.5,4

horizontal part ht = 1in, width = 3in

centroid of the horizontal part = 1.5, 0.5

because of the horizontal part the centroid of the whole area will shift down ward.

it is 5 in down from top and 2 in above from bottom

The centroid will shift down in 5:2 ratio

= 4* 2/7 = 1.14

Horizontally it will shift to the right by 1:3

= 0.5 * 3/4 = 0.375

actual centroid = 0.5 + 0.375 , 4-1.14 = 0.875 + 2.86