Question 1.3.1: A Cantilever Beam Deflection Model The deflection of a canti...
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 |
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
a = \frac{0.78 − 0}{800 − 0} = 9.75 × 10^{−4} in./lbAs 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.
