Figure 1.7(a) demonstrates three concepts of the stress-strain behavior of elasto- plastic materials. The lowest point shown on the diagram is the proportional limit, defined as the transition point between linear and nonlinear behavior. The second point is the elastic limit, which is the transition between elastic and plastic behavior. However, most materials do not display an abrupt change in behavior from elas- tic to plastic. Rather, there is a gradual, almost imperceptible transition between the behaviors, making it difficult to locate an exact transition point (Polowski and Ripling, 2005). For this reason, arbitrary methods such as the offset and the exten- sion methods, are used to identify the elastic limit, thereby defining the yield stress (yield strength). In the offset method, a specified offset is measured on the abscissa, and a line with a slope equal to the initial tangent modulus is drawn through this Elastic limit 0.2% offset 0.5% extension yield strength yield strength Proportional limit Strain, % Strain, % 0.2% 0.5% (a) (b) FIGURE 1.7 Methods for estimating yield stress: (a) offset method and (b) extension method. point. The point where this line intersects the stress-strain curve is the offset yield stress of the material, as seen in Figure 1.7(a). Different offsets are used for different materials (Table 1.2). The extension yield stress is located where a vertical projec- tion, at a specified strain level, intersects the stress-strain curve. Figure 1.7(b) shows the yield stress corresponding to 0.5% extension. Stress Stress
Figure 1.7(a) demonstrates three concepts of the stress-strain behavior of elasto- plastic materials. The lowest point shown on the diagram is the proportional limit, defined as the transition point between linear and nonlinear behavior. The second point is the elastic limit, which is the transition between elastic and plastic behavior. However, most materials do not display an abrupt change in behavior from elas- tic to plastic. Rather, there is a gradual, almost imperceptible transition between the behaviors, making it difficult to locate an exact transition point (Polowski and Ripling, 2005). For this reason, arbitrary methods such as the offset and the exten- sion methods, are used to identify the elastic limit, thereby defining the yield stress (yield strength). In the offset method, a specified offset is measured on the abscissa, and a line with a slope equal to the initial tangent modulus is drawn through this Elastic limit 0.2% offset 0.5% extension yield strength yield strength Proportional limit Strain, % Strain, % 0.2% 0.5% (a) (b) FIGURE 1.7 Methods for estimating yield stress: (a) offset method and (b) extension method. point. The point where this line intersects the stress-strain curve is the offset yield stress of the material, as seen in Figure 1.7(a). Different offsets are used for different materials (Table 1.2). The extension yield stress is located where a vertical projec- tion, at a specified strain level, intersects the stress-strain curve. Figure 1.7(b) shows the yield stress corresponding to 0.5% extension. Stress Stress
Chapter2: Loads On Structures
Section: Chapter Questions
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Transcribed Image Text:Figure 1.7(a) demonstrates three concepts of the stress-strain behavior of elasto-
plastic materials. The lowest point shown on the diagram is the proportional limit,
defined as the transition point between linear and nonlinear behavior. The second
point is the elastic limit, which is the transition between elastic and plastic behavior.
However, most materials do not display an abrupt change in behavior from elas-
tic to plastic. Rather, there is a gradual, almost imperceptible transition between
the behaviors, making it difficult to locate an exact transition point (Polowski and
Ripling, 2005). For this reason, arbitrary methods such as the offset and the exten-
sion methods, are used to identify the elastic limit, thereby defining the yield stress
(yield strength). In the offset method, a specified offset is measured on the abscissa,
and a line with a slope equal to the initial tangent modulus is drawn through this
Elastic
limit
0.2% offset
0.5% extension
yield strength
yield strength
Proportional
limit
Strain, %
Strain, %
0.2%
0.5%
(a)
(b)
FIGURE 1.7 Methods for estimating yield stress: (a) offset method and
(b) extension method.
point. The point where this line intersects the stress-strain curve is the offset yield
stress of the material, as seen in Figure 1.7(a). Different offsets are used for different
materials (Table 1.2). The extension yield stress is located where a vertical projec-
tion, at a specified strain level, intersects the stress-strain curve. Figure 1.7(b) shows
the yield stress corresponding to 0.5% extension.
Stress
Stress
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