Structural Concrete - Hassoun

CHAPTER11
MEMBERS IN
COMPRESSION AND
BENDING
Residential building, Minneapolis, Minnesota.
11.1 INTRODUCTION
Vertical members that are part of a building frame are subjected to combined axial loads and bending
moments. These forces develop due to external loads, such as dead, live, and wind loads.
The forces are determined by manual calculations or computer applications that are based on
the principles of statics and structural analysis. For example, Fig. 11.1 shows a two-hinged portal
frame that carries a uniform factored load on BC. The bending moment is drawn on the tension
side of the frame for clarification. Columns AB and CD are subjected to an axial compressive
force and a bending moment. The ratio of the moment to the axial force is usually defined as
the eccentricity e, wheree = M n /P n (Fig. 11.1). The eccentricity e represents the distance from
the plastic centroid of the section to the point of application of the load. The plastic centroid is
obtained by determining the location of the resultant force produced by the steel and the concrete,
assuming that both are stressed in compression to f y and 0.85 f ′ c, respectively. For symmetrical
sections, the plastic centroid coincides with the centroid of the section. For nonsymmetrical
sections, the plastic centroid is determined by taking moments about an arbitrary axis, as explained
in Example 11.1.
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