Page 163 - Civil Engineering Formulas

100 CHAPTER THREE

where e b is the eccentricity, in (mm), of the axial load with respect to the plastic
centroid and d is the distance, in (mm), from plastic centroid to centroid of ten-
sion reinforcement.
When P u is less than P b or the eccentricity, e, is greater than e b , tension gov-
erns. In that case, for unequal tension and compression reinforcement, the ulti-
mate strength is

e
P u 0.85 f c bd m m 1 d

1 e 2 2 ( m m ) e m 1 d (3.38)
B d d d

where m f y /0.85f c
m m 1
A s /bd
A s /bd

Special Cases of Reinforcement
For symmetrical reinforcement in two faces, the preceding P u equation becomes

e
P u 0.85 f c bd 1 d

1 e 2 2 m 1 d e (3.39)
B d d d

Column Strength When Compression Governs
For no compression reinforcement, the P u equation becomes

e
P u 0.85 f bd m 1 d
c

1 e 2 2 e m (3.40)
B d d