CIVIL ENGINEERING FORMULAS

134 CHAPTER FIVE

kddistance from extreme compression surface to neutral axis, in (mm)

ddistance from extreme compression to centroid of reinforcement, in

(mm)

When the steel ratio As/bd, where Asarea of tension reinforcement,
in^2 (mm^2 ); and bbeam width, in (mm), is known, kcan be computed from

(5.57)

Wherever positive-moment steel is required, should be at least 200/fy, where
fyis the steel yield stress. The distance jdbetween the centroid of compression
and the centroid of tension, in (mm), can be obtained from

(5.58)

Allowable Bending Moment

The moment resistance of the concrete, inkip (kNm) is

(5.59)

whereKc fckj. The moment resistance of the steel is

(5.60)

whereKsfsj.

Allowable Shear

The nominal unit shear stress, vacting on a section with shear Vis

(5.61)

Allowable shear stresses are 55 percent of those for ultimate-strength design.
Otherwise, designs for shear by the working-stress and ultimate-strength
methods are the same. Except for brackets and other short cantilevers, the
section for maximum shear may be taken at a distance dfrom the face of the
support. In working-stress design, the shear stress vccarried by the concrete
alone should not exceed 1.1. (As an alternative, the maximum for vc

may be taken as , with a maximum of 1.9 is the

28-day compressive strength of the concrete, lb/in^2 (MPa); and Mis the bend-
ing moment at the section but should not be less than Vd.)
At cross sections where the torsional stress vtexceeds 0.825 , vcshould
not exceed

vc (5.62)

1.1 2 fc

21 (vt/1.2v)

2

fc

fc 1300 Vd/M fc;fc

fc

v

V

bd

MsfsAsjdfsjbd^2 Ksbd^2

(^1) 
2
Mc^1  2 fckjbd^2 Kcbd^2
j 1 
k
3
k 22 n(n)^2 n