Cases with Axial and Bending Moment (Non-Linear Behavior)

170
f
y
f
y
Figure 11-
8: Sketch for computing plastic moment of steel H-section.
Figure 11-9 shows the reduction of the ultimate moment due to axial loading for H-sections (Horne 1971). The values in the horizontal axis in this graph are the applied axial load normalized by the (non-eccentric) compressive axial load capacity, P
u
. The values in the vertical axis in this graph are normalized values of the yield moment.
P
u
is obtained as follows
𝑃𝑃
𝑢𝑢
= 𝑓𝑓
𝑦𝑦
𝐴𝐴 Equation 11-50) Where A = cross-sectional area of pile. The relationship between the normalized load and normalized yield moment becomes slightly nonlinear for normalized yield moments greater than about 90 percent. Therefore, the effect of axial loads causes a reduction in plastic moment capacity (as compared to a linear relationship) that is small when the applied axial load is approximately 20 percent or smaller than P
u

171
Figure 11-
9: Effect of axial loading on plastic moment in steel H-section.
As a result, a constant, elastic value of the section bending stiffness, and therefore yield moment, fora steel section can be used for all ranges of normal loads without significant error. If desired, the equations maybe modified to reflect the nonlinear behavior. However, reduced values of the modulus of the steel section will affect the computed value of the yield moment only slightly.

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