Building Design and Construction Handbook - Merritt - Ventech!

CONCRETE CONSTRUCTION 9.51
that A sƒ y does not exceed 0.75 times the total compressive force at balanced conditions.
The total compressive force may be taken as the area of a rectangular stress
block of a rectangular member; the strength of overhanging flanges or compression
reinforcement, or both, may be included. For members with compression reinforcement,
the portion of tensile reinforcement equalized by compression reinforcement
need not be reduced by the 0.75 factor.
Flexural Design Strength: Tension Steel Only. For underreinforced rectangular
beams with tension reinforcement only (Fig. 9.12) and a rectangular stress block
with depth a (� � 0.75� b), the flexural design strength may be determined from:
0.59�ƒ
2
y
n y�
ƒ� � c
where a � Asƒ y/0.85ƒ�b c and jd � d � a/2.
�M � 0.90bd �ƒ 1 � (9.28a)
� �
9.46.2 Doubly-Reinforced Rectangular Beams
a
� 0.90Asƒy d � (9.28b)
2
� 0.90A ƒ jd (9.28c)
s y
For a rectangular beam with compression-steel area and tension-steel area A s,
A� s
the compression-reinforcement ratio is
A�s �� � (9.29)
bd
and the tension-reinforcement ratio is
A s
� � (9.30)
bd
where b � width of beam and d � effective depth of beam. For design, � should
not exceed
for
� �
ƒ�s ƒ� s
0.75 �b � �� � �� (9.31a)
ƒ ƒ
y y
0.85ƒ�� c 1 87,000 ƒ�s
�b � � �� (9.31b)
ƒ 87,000 � ƒ ƒ
y y y
where � stress in the compression steel, psi, and other symbols are the same as
ƒ� s
those defined for singly-reinforced beams (Art. 9.46.1). The compression force on
the concrete alone in a cross-section (Fig. 9.14) is
C � 0.85ƒ�ba (9.32)
1b c
where a � � 1c is the depth of the stress block and the compression reinforcement