Building Design and Construction Handbook - Merritt - Ventech!

CONCRETE CONSTRUCTION 9.49
section; that is, conventional elastic theory for homogeneous beams may be applied
to the transformed section. Section properties, such as location of neutral axis,
moment of inertia, and section modulus S, may be computed in the usual way for
homogeneous beams, and stresses may be calculated from the flexure formula,
ƒ � M/S, where M is the bending moment at the section. This method is recommended
particularly for T-beams and doubly-reinforced beams.
From the assumptions the following formulas can be derived for a rectangular
section with tension reinforcement only.
nƒ k
c � (9.18)
ƒ 1 � k
s
2
k � �2n� � (n�) � n� (9.19)
k
j � 1 �
3
(9.20)
where � � A s/bd and b is the width and d the effective depth of the section (Fig.
9.13).
Compression capacity:
where K c � 1 ⁄2ƒ ckj.
Tension capacity:
1 2 2
Mc � ⁄2ƒckjbd � Kbd c
(9.21a)
2 2
Ms � ƒsAjd� s ƒs�jbd � Kbd s
(9.21b)
where k s � ƒ s�j.
Design of flexural members for shear, torsion, and bearing, and of other types
of members, follows the strength design provisions of the ACI 318 Building Code,
because allowable capacity by the alternative design method is an arbitrarily specified
percentage of the strength.
9.46 STRENGTH DESIGN FOR FLEXURE
Article 9.44 summarizes the basic assumptions for strength design of flexural members.
The following formulas are derived from those assumptions.
The area A s of tension reinforcement in a reinforced-concrete flexural member
can be expressed as the ratio
A s
� � (9.22)
bd
where b � beam width and d � effective beam depth � distance from the extreme
compression surface to centroid of tension reinforcement. At nominal (ultimate)
strength of a critical section, the stress in this steel will be equal to its yield strength
ƒ y, psi, if the concrete does not first fail in compression. (See also Arts. 9.47 to
9.50 for additional reinforcement requirements.)