Civil Engineering Reference
In-Depth Information
6
Deep beams under top and
bottom loading
A.R.CUSENS, University of Leeds
Notation
A
i
area of reinforcement at dis-
tance
y
i
y
i
distance from top of beam to
reinforcing bar
A
s
area of main tension reinforce-
ment
L
effective span
L
1
,
L
2
combinations of top and bo-
tetc tom load
A
v
area of vertical shear reinfor-
cement within a distance
s
L
o
clear span
A
vh
area of horizontal shear rein-
forcement within a distance s2
M
u
ultimate bending moment
V
ab
applied shear force from bot-
tom loads
b
width of deep beam
d
effective depth of deep beam
(to centre of main tensile steel)
V
at
applied shear force from top
loads
f
cb
modulus of rupture of concrete
V
cb
shear capacity of beam assum-
ing bottom loads only
f'
c
cylinder crushing strength of
concrete
V
ct
shear capacity of beam assum-
ing top loads only
f
cu
characteristic cube strength of
concrete
V
c
contribution of concrete to
shear strength of beam
f
y
characteristic yield strength of
reinforcement
V
n
nominal shear strength of
beam
h
a
effective height of deep beam
r
v
ratio
A
v
/bd
V
r
contribution of steel to shear
strength of beam
s
spacing of vertical shear rein-
forcement
V
u
ultimate shear strength of
beam
s
2
spacing of horizontal shear
reinforcement
W1, W2
wall types
v
u
maximum value of shear stress
in concrete
etc
θ
r
angle between reinforcement
and diagonal crack
w
b
uniform bottom loading on
beam
λ
1,2
constants (Eqn. 6.)
w
t
uniform top loading on beam
ρ
w
A
s
/
bd
x
e
clear shear span
6.1
Introduction
The nature of deep reinforced concrete beams has various implications in
structural situations. In other chapters, attention has been drawn to the
modifications needed to general flexural theory in order to predict the
