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). This distance is called the deﬂection and it is the output variable. The applied force is the input. The following table gives the measured deﬂection x that was produced in a

Question

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). This distance is called the deﬂection and it is the output variable. The applied force is the input. 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.

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 = af to describe the relation. The value of the constant a can be determined from the slope of the line. Choosing the origin and the last data point to ﬁnd the slope, we obtain

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

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

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

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

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 1.3.1: The deﬂection of a cantilever beam is the distance its end m......

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