Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

examples that demonstrate various support conditions and how they influence the behavior of

an object. Try to explain the behavior of each case in your own words. First, look at the examples

of a support given in the first column of Table 10.2, then look at the reaction forces. If you need

help, read the explanation column.

Boundary and Initial Conditions

The manner in which an object is held in place also influences its behavior. Figure 10.16 dem-

onstrates the effects of boundary conditions. How would you describe qualitatively in detail, by

how much, and the manner by which, each beam bends? It is very important for you to clearly

understand that boundary conditions refer to conditions at the boundaries of the object — as

the term implies boundary conditions represent what is happening at the boundaries of the

object. These conditions provide information about how the object is supported at its bound-

aries. You also need to understand that for some problems, support conditions, and loading

could change with time and as a result we need to specify the initial conditions before we could

predict the behavior of the object.

10.4 Work–Force Acting Over a Distance

When you push on a car that has run out of gas and move it through a distance, you perform

mechanical work. When you push on a lawn mower and move it in a certain direction, you are

doing work. Mechanical work is done when the applied force moves the object through a dis-

tance. Simply stated, mechanical workis defined as the component of the force that moves the

object times the distance the object moves. Consider the car shown in Figure 10.17. The work

done by the pushing force moving the car from position 1 to position 2 is given by

(10.11)

Note from examining Equation (10.11) that the normal component of the force does not

perform mechanical work. That is because the car is not moving in a direction normal to the

ground. So next time you are mowing the lawn, ask yourself if you should push on the lawn

mower horizontally or at an angle? Another point you should remember is that, if you were to

push hard against an object and were not able to move it, then by definition, you are not doing

any mechanical work, even though this action could make you tired. For example, if you were

W 1  2  1 F cos u 21 d 2

10.4 Work—Force Acting Over a Distance 267

d

F F

 

■Figure 10.17

The work done on the car

by the force Fis equal to

W 1  2 (Fcos u)(d).

■Figure 10.16

Simple examples to demonstrate

the effect of boundary conditions.

In your own words, explain the

behavior of each case.

F

F

F

F

F

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