Civil Engineering Reference
In-Depth Information
8
Shear strength predictionÏ
plastic method
M.W.BRAESTRUP, Rambull and Hannemann, Denmark
Notation
A
c
cross-sectional area of concrete
perpendicular to steel area
A
s
y
depth of triangular region in bia-
xial compression
A
s
cross-sectional area of steel rein-
forcement
y
o
value of
y
corresponding to yield-
ing of reinforcement,
y
o
=
h
f
/
v
£
h
/2
a
clear span between load and sup-
port platens
a
inclination of relative displacem-
ent rate
b
width of beam
¦
inclination of yield line (or ch-
ord)
c
distance from bottom face of be-
am to centroid of reinforcement
g
inclination of reinforcement rela-
tive to yield line
d
effective depth of beam;
d
=
h
-
c
f
c
cylinder strength of concrete
D
thickness of deforming zone ide-
alised as yield line
f
c
*
effective compressive strength of
concrete
e
1
first principal strain rate
f
y
yield stress of reinforcement
e
2
second principal strain rate
h
total depth of beam
e
s
strain rate in reinforcement
l
shear span between point load and
support reaction
h
relative rotation rate of rigid parts
θ
inclination of compressive conc-
rete strut
r
geometrical ratio of smeared rein-
forcement,
r
=
A
s
/A
c
V
effectiveness factor, v=
f
c
*
/
f
c
s
length of support platen
r
geometrical ratio of long- itudinal
reinforcement,
r
=
T
y
/
bhf
y
s
l
minimum support platen length to
attain flexural capacity
s
compressive concrete stress
T
force in longitudinal reinforcem-
ent
s
1
first principal concrete stress
s
2
second principal concrete stress
T
y
yield force of longitudinal reinfo-
rcement;
T
y
=
A
s
f
y
s
s
tensile stress in reinforcement
s
v
vertical component of compress-
ive concrete stress,
s
v
=
s
sin
2
θ
t
length of load platen
tl
minimum length of load platen
t
shear stress in concrete
V
applied point load
f
mechanical degree of reinforcem-
ent
f
=
T
y
/bhf
c
v
relative displacement rate in yield
line
x
width of triangular region in bia-
xial compression
