A Cantilever Beam Deflection Model

The deflection of a cantilever beam is the distance its end moves in response to a force applied at the end (Figure 1.3.1). The following table gives the measured deflection x that was produced in a particular beam by the given applied force f . Plot the data to see whether a linear relation exists between f and x.

Force f (lb) 0 100 200 300 400 500 600 700 800

Deflection x (in.) 0 0.15 0.23 0.35 0.37 0.5 0.57 0.68 0.77

Question

A Cantilever Beam Deflection Model

The deflection of a cantilever beam is the distance its end moves in response to a force applied at the end (Figure 1.3.1). The following table gives the measured deflection x that was produced in a particular beam by the given applied force f . Plot the data to see whether a linear relation exists between f and x.

Force f (lb)	0	100	200	300	400	500	600	700	800
Deflection x (in.)	0	0.15	0.23	0.35	0.37	0.5	0.57	0.68	0.77

Accepted Answer

The plot is shown in Figure 1.3.2. Common sense tells us that there must be zero beam deflection if there is no applied force, so the curve describing the data must pass through the origin. The straight line shown was drawn by aligning a straightedge so that it passes through the origin and near most of the data points (note that this line is subjective; another person might draw a different line). The data lies close to a straight line, so we can use the linear function x = a f to describe the relation. The value of the constant a can be determined from the slope of the line, which is

[latex]a = \frac{0.78 − 0}{800 − 0} = 9.75 × 10^{−4} in./lb[/latex]

As we will see in Chapter 4, this relation is usually written as f = kx, where k is the beam stiffness. Thus, k = 1/a = 1025 lb/in.

Question 1.3.1: A Cantilever Beam Deflection Model The deflection of a canti...

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