Handbook of Civil Engineering Calculations

Cu = OXSaW T 11 = AJy (1)

f.H/£Si (2)

Jc

\.\8qd

a=l.l8qd c= (3)

K 1

M 11 = ^AjJd-^] (4)

Mn = <K/^(1-0.59?) (5)

Mu = <t>bd

2

ftq(l-0.59q) (6)

bdfc-\$df$-2bfcMul<No*

A* = 7 <7)

/v

= 0.85^/J 87,000

P

*~ .£ 87,000+./;

( )

^=°-

85

Mwz)

(9)

In accordance with the Code,

,max = 0.75, 6 = 0.6375^(^^) (10)

Figure 3 shows the relationship between Mn and As for a beam of given size. As A 8 in-
creases, he internal forces C 14 and Tu increase proportionately, but M 11 increases by a
smaller proportion because the action line of C 11 is depressed. The M 11 -A 8 , diagram is para-
bolic, but its curvature is small. By comparing the coordinates of two points Pa and Pb,
the following result is obtained, in which the subscripts correspond to that of the given
point:

T^f" <

n

Asa Asb >

where Asa<Asb

CAPACITYOFA

RECTANGULAR BEAM

A rectangular beam having a width of 12 in
(304.8 mm) and an effective depth of 19.5 in
(495.3 mm) is reinforced with steel bars hav-

Areo of reinforcement A 5

FIGURE 3

Ultimate

moment

M

u