Building Design and Construction Handbook - Merritt - Ventech!

9.56 SECTION NINE
where A oh � area enclosed by centerline of the outermost closed transverse torsion
reinforcement, in 2
p h � perimeter of the centerline of the outermost closed transverse torsion
reinforcement, in
The reinforcement for torsion requires that
� T � T (9.47)
n u
where T n � nominal torsional moment strength which � T s, the nominal torsional
moment strength provided by torsion reinforcement
Stirrups. The transverse reinforcement required for torsion is calculated from
T � (2A Aƒ cot �)/s (9.48)
n o t yv
where s � spacing of torsion reinforcement in direction parallel to longitudinal
reinforcement, in
A o � 0.85 A oh
A t � area of one leg of a closed stirrup within a distance s, in 2
ƒ yv � yield strength of closed transverse torsion reinforcement, psi
� � angle of concrete compression diagonals in truss analogy for torsion,
which must not be taken smaller than 30� nor larger than 60� for nonprestressed
members but may be taken as 45� for non-prestressed members
and as 37.5� for prestressed members with an effective prestress
force not less than 40% of the tensile strength of the longitudinal reinforcement
For design, Eq. (9.48) can be re-arranged to calculate
where � � strength-reduction factor, � 0.85
A /s � T /(� 2 A ƒ cot �) (9.48a)
t n o yv
Since A t is defined as the area of one leg of a closed stirrup, it must be taken into
account when the stirrup requirements for shear and torsion are added to provide
the total amount of transverse reinforcement required. Stirrup area for shear, A v,is
based on all the legs of a stirrup. If the required stirrup area for shear is A v/s, and
that for torsion is A t/s, the total amount of transverse reinforcement required to
resist shear and torsion is calculated
� �
A A 2A
v�t v t
Total � � (9.49)
s s s
Longitudinal Reinforcement. The additional longitudinal reinforcement, A �, required
for torsion is calculated from
2
Al � (A t/s)p h(ƒ yv/ƒ y�)cot
� (9.50)
where A t/s � amount calculated from Eq. (9.48a)
ƒ y� � yield strength of longitudinal torsion reinforcement
The amount of longitudinal torsion reinforcement in the flexural compression
zone may be reduced by an amount equal to M u/(0.9 d ƒ y�), where M u is the factored
moment acting at the section in combination with T u.