NRCS TR-30 Structural Design of Standard Covered Risers (1965)

NRCS TR-30 Structural Design of Standard Covered Risers (1965)
U. S. Department of Agriculture
Soil Conservation
Service
Engineering
Division
Technical
Release
Design Unit
April 1, 1965
STRUCTURAL DESIGN OF STANDARDCOVEREDRISERS
No. 30
PFUXFACE
This Technical Release presents the criteria
and procedures
established
for the structursl
design and detailing
of Standard Covered Risers.
Various criteria
and proportions
of drop inlet spillways
were selected
at a meeting of the "Subcommittee on Standard Structural
Details"
held
in Spartanburg,
South Carolina,
during October 23-27, 1961. Additional
criteria,
together with procedures
for the structural
design of Standard Covered Risers, developed as a result of the Subcommittee's
meeting were reviewed at a meeting of Engineering
and Watershed Planning
Unit Design Engineers held in Washington, D. C., during May 20-24, 1963.
A revised edition
of "Criteria
end Procedures for the Structural
Design
dated April 1, 1964, was then sent to the
of Standard Covered Risers",
Engineering
and Watershed Planning Unit Design Engineers for their use,
Release is an outgrowth of the prereview and comment. This Technical
ceding meetings and reviews.
Criteria
and procedures
used in the preparation
of standards should be
selected to insure applicability
to the widest practical
range of site
This philosophy
was used in preparing
this Technical
conditions.
Much of the material
contained herein either applies directly,
Release.
or may be adapted readily,
to risers of types other than the Standard
Covered Risers.
Mr. Edwin S. Ailing developed most of the procedures
for structural
This Technical
Release was prepared by
design presented herein.
Mr. Ailing and other personnel of the Design Unit, Design Branch,
Engineering
Division
at Hyattsville,
Maryland.
I
-
i
TECHNICAL RELEASE
NUMBER 30
STRUCTURAL DESIGN OF STANDARD COVEREDRISERS
Contents
Page
PREFACE
NOMENCLATURE
CHAFTERl.
CRITERIA
Standard Proportions,
Details,
and Data
Limitations
on the Use of the Standard Plans
Riser Heights
Pipe Velocities
Ice Conditions
Allowable
Stresses and Bearing Pressures
Concrete
Reinforcing
Steel
Earth Bearing Pressures
Loads
Loads on Riser Walls
Lateral
soil pressures
Water pressures during pipe flow
Composite wall pressure diagram for design
Loads on Cover Slab
Embankment Load on Riser
Wind
Flotation
Criteria
Location of Construction
Joints in Riser Walls
cm
2.
l-l
l-l
l-l
l-l
l-l
l-2
l-2
l-2
l-2
l-2
l-2
l-2
l-3
l-4
l-5
l-5
1-6
1-6
1-6
METHODSOF ANAIYSIS AND DESIGN PROCEDURES
Cover Slab Walls
Cover Slab
Riser Walls, Horizontal
Bending
Closed Sections
Equilibrium
relations
Analysis for corner moments, Q
Members are prismatic
Members are non-prismatic
Design approach
Considerations
Direct design by charts
Wall thickness and steel selection
Sections at Low Stage Inlet(s)
2-l
2-l
2-3
2-3
2-3
2-5
2-5
2-8
2-10
2-10
2-11
2-15
2-15
ii
Page
Contents
2-15
Sections at the Conduit Entrance
Riser Walls, Vertical
Bending
Wall-to-Footing
Connection
Verticti
flexure
in sidewalls
Vertical
flexure
in endwalls
Evaluation
of coefficients
Ky
Example of computation
of MvC and VVC
Wall thickness by shear due to vertical
bending
Vertical
steel
Division
of wall loading
Well Thickness Change Locations
Provision
for Moment from Embankment Loading
At closed sections
At conduit entrance
Stability
Analyses
Riser in the Reservoir
Area
Riser in the Embankment
Footing Strength Design
CHAPTER 3.
4
2-18
2-18
2-18
2-21
2-22
2-26
2-27
2-27
2-27
2-28
2-28
2-28
2-29
2-30
2-31
2-32
2-32
EXAMPLE DESIGN
3-l
3-l
Riser Data
Cover Slab and Cover Slab Walls
Riser Wall Loading
Design of Riser Walls
Wall Thickness at Wall-to-Footing
Connection
Design for Horizontal
Bending
Vertical
Steel at Wall-to-Footing
Connection
Vertical
Steel for Moment from Embankment Loading
Stability
Analyses
Preliminaries
Analyses
Footing Strength Design
Projection
Loadings
Design
Example Plans
;:;
4
;I;
z-87
318
3 -10
3-12
3 -12
3 -12
3-14
Figures
Figure
Figure
Figure
l-l
l-2
Figure
Figure
Figure
Figure
Figure
Figure
2-l
2-2
2-3
2-4
2-5
l-3
2-6
Water pressures on riser walls during pipe
Representation
of heads during pipe flow.
Composite wall pressure diagram for design
standard X%SerS
(vb(-.)
= 30
fPS).
flow.
of
Definition
sketch of cover slab,
Cover slab and cover slab wall steel layout.
Definition
sketch for horizontal
bending.
Shear distribution
assumed by usual theory.
Assumed variation
in moment of inertia.
Typical direct design chart for co in horizontal
bending I)
l-3
l-4
l-5
2-l
2-3
e-4
2-7
2-8
2-12
4
iii
Figures
c
Figure
2-7
Figure
2-8
Figure
2-9
Figure
2-10
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
2-11
2-12
2-13
2-14
2-15
Figure
3-l
Figure
3-2
2-16
2-17
2-18
2-19
Page
Typical direct design chart for As in
horizontal
bending.
Steel layouts at closed horizontal
sections
of riser.
Suggested tabular
form for design of closed
sections for horizontal
bending.
Layout of horizontal
steel in sections at the
conduit entrance.
Vertical
section through sidewall.
Vertical
section through endwall.
Sketches for analysis of pinned frame.
Pinned frame deflections.
Vertical
steel at wall-to-footing
connection.
Typical load division
curve.
Assumed embankment loading.
Analysis of bearing pressures.
Moment in footing
due to vertical
bending.
Direct design
D = 30 in.
Plan of trial
chart
for
horizontal
2-12
2-15
2-16
2-17
2-18
2-22
2-23
2-25
2-27
2-28
2-29
2-30
2-32
bending,
footing.
3-4
3-9
Tables
Table
Table
Table
Table
Table
Table
Table
Table
Table
2-l
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
Table
3-l
Table
3-2
Cover slab design summary.
Cover slab and cover slab wall steel.
Force coefficients
for horizontal
bending,
n.
Moment coefficients
assuming prismatic
members,
and using the PCA moment
concentrated
reactions,
corrections
- not to be used for design.
Data for analyses with non-prismatic
members.
Moment coefficients
for horizontal
bending,, m.
Data for preparation
of direct design charts for
horizontal
bending.
Values of functions.
Pinned frame corner moments and deflection
coefficients.
Summary of riser wall design for horizontal
bending.
Vertical
steel for moment from embankment
loading at usual closed sections.
2-2
2-3
2-5
2-8
2-9
2-10
2-13
2-21
2-24
3-5
3-7
V
A
i:
A,
a
3
*
ab
a,
B
b
C
C
D
d
d"
E
e
F
fc
fps
f,
H
equivalent
area of reinforcing
= area of footing;
steel
= area of reinforcing
= ratio used to obtain properties
of non-prismatic
of flow
= area of the conduit
=
=
=
=
=
=
area of the riser
"weighted"
width of riser endwall
width of reinforced
concrete member
carry-over
factor
distance from center of gravity
axis to extreme
pipe
conduit
= effective
force
compressive
members; area
fiber
diameter
depth of reinforced
=d -t/2
= modulus of elasticity
= base of Naperisn logarithms
=
=
=
=
=
steel
stress
concrete
= 2.7183
member
-
-
-
in concrete
foot per second
tensile
stress in reinforcing
steel
Hh
hs
head
= head over crest of the cove-ed inlet of the riser
= depth of embanlunent or sediment at the riser at the section
below the crest of the covered inlet
hvr
hw
h,
I
j
=
=
=
=
=
hx
velocity
head in the riser
inward pressure on riser wsll in feet of water
distance from crest of covered inlet to point under consideration
second moment of area, moment of inertia
ratio used in reinforced
concrete relations
soil pressure to vertical
soil pressure
K = ratio of lateral
deflection
coefficient
KY = horizontal
k
= kip, thousand pounds; stiffness
coefficient
klf = kips per lineal
foot
Revised
8-l-68
vi
c:
ksf
ksi
L
M
MF
= kips per square foot
= kips per square inch
= length;
span length,
C.C. of supports
= moment
= fixed end moment
moment
MS = equivalent
moment in the riser wall at the wall-to-footing
connection
Mvo = vertical
moment in the riser wall at section under consideration
Mvx= vertical
In = moment coefficient
NE = direct compressive force in the riser endwall
forces, but not including
uplift
NGR = sum of vertical
distance from pipe invert
at the riser to crest of the covered
Nib = vertical
inlet of the riser
distance from pipe invert
at the riser to soil surface.
N\T~~= vertical
The soil surface may be either the sediment or the embankment
(berm) surface.
No = direct vertical
compressive force at the wall-to-footing
connection
Ns = direct compressive force in the riser sidewall
distance from the soil surface to the crest of the covered
Nsh = vertical
inlet of the riser
n = modular ratio;
force coefficient
pressure per unit area
P = soil bearing pressure;
pcf = pounds per cubic foot
psf = pounds per square foot
psi = pounds per square inch
and shrinkage
steel ratio in reinforced
concrete
pt = temperature
= unit load; uniformly
distributed
load
q
qKx = the unit load resisted
by horizontal
bending at the section under
consideration
qvx = the unit load resisted
by vertical
bending at the section under
consideration
qX = the total unit load at the section under consideration
R = redundant force
spacing of reinforcing
steel
S = stiffness;
T&S = temperature
and shrinkage
riser wall thickness
t
= thickness;
= footing
thickness
tf
= bond stress in concrete
U
v
= total
shear;
volume
4
vii
VVQ = shear in the riser wall at the wall-to-footing
connection due
to vertical
bending
V, = shear in the riser wall at the section under consideration
due
to vertical
bending
= shear stress
V
in concrete;
velocity
of flow
of flow in the conduit
vb = mean velocity
of flow in the riser
vr = mean velocity
in the direction
of M; weight
W = width of footing
= unit weight, unit weight of water
W
wb = buoyant unit weight of soil
wm = moist unit weight of soil
unit weight of soil
WS = saturated
X = distance from the wall-to-footing
connection to the section
under consideration
deflection
of the riser wall at the section under
Y = horizontal
consideration
B = (j+jw4
h = distribution
Co
= perimeter
factor
of reinforcing
steel
l-1
TECRRX!ALRELEASE
NUMBER 30
STRUCTURAL DESIGN OF STANDARDCOVEREDRISERS
h
CHAPTER 1.
CRITERIA
Proportions,
Details,
,
Standard
and Data
Refer to Engineering
Standard Drawing ES-150, "Drop Inlet Spillways,
Standard for Covered Top Riser",
and to Technical Release No. 29
"Hydraulics
of Two-way Covered Risers".
Structural
detail
drawings
shall conform with practice
as shown in the latest
edition
of "Manual
of Standard Practice for Detailing
Reinforced
Concrete Structures"
by
AC1 Committee 315.
Limitations
on the Use of the Standard
Plans
Riser Heights
For the purpose of developing
and presenting
the standard risers,
the
following
vertical
distances are defined:
N-zh = vertical
distance from pipe invert
at the riser to
crest of the covered inlet of the riser
distance from pipe invert
at the riser to
Nis = vertical
soil surface.
The soil surface may be either the
sediment or the embankment (berm) surface.
Nsh = vertical
distance from the soil surface to the crest
of the covered inlet of the riser.
The standard risers
shall be designed using 5 ft increments and combinations of Nib and Nis.
N,h shall not exceed 20 ft, Nis shall not exceed 35 ft, and Nib shall not exceed 40 ft nor be less than 3D.
Pipe Velocities
The maximum allowable
mean velocity
in the pipe conduit of standard
risers is vb( -)
must exceed 30 fps at an
= 30 fPs= If the velocity
actual site, the riser to be used, particularly
the elbow section,
should be treated as a special design.
Ice Conditions
Ice pressures are highly indeterminate,
therefore
the standard risers
shall not be designed for ice loads.
Where ice of considerable
thickness can occur, the riser should be located in the embankment at a berm,
thus eliminating
ice pressures.
1-2
Allowable
Stresses
and Bearing
Pressures
Concrete
Class 4000 concrete shall be assumed in the design of the standard risers.
Allowable
concrete stresses and other criteria
shall be in accordance
with National
Engineering
Handbook, Section 6, sub-section
4., Reinforced
Concrete (g-64 revision)
except as modified
in the following
notes:
constant allowable
bond stresses
(1) As a design convenience,
shall be used for all bar sizes 5 #7, these are:
tension top bars,
u = 245 psi
all other tension bars, u = 350 psi
(2) Shear stress, as a measure of diagonal tension,
shall be
limited
so that web steel is not required.
(3) Minimum thickness
of cover slab is 8 in.
(4) Minimum thickness
of riser walls is 10 in.
(5) Wall thickness
increments shall not exceed 3 in.
Reinforcing
Steel
Intermediate
grade steel sh&Ll be assumed in the design of the standard
risers.
Allowable
steel stresses and other criteria
shall be in accordConcrete (g-64 revision)
exance with JTEH-6, sub-section
4., Reinforced
cept that the minimum steel ratio for principal
steel and for temperature
and shrinkage steel shall be pt = 0.002 in each face in each direction,
thicknesses
greater than 16 inches shall be considered
as 16 inches.
Earth Rearing Pressures
The allowable
bearing values given are the allowable
excess pressures
over the pressure whfch would exist at the elevation
of the bottom of
the footing
if the riser were not present.
(1) Saturated foundation:
Allowable
average excess pressure =l,OOO psf
Allowable
maximum excess pressure = 2,000 psf
(2)
Moist foundation
Twice the above values.
In no case shall the line of action of the reaction
lie without the middle
The loading conditions
to be investigated
are listed
third of the base.
under "Stability
Analyses".
Loads
Loads on Riser Walls
The design of horizontal
sider both lateral
soil
and vertical
sections of riser walls
pressure and water pressure loadings.
must con-
Lateral
soil pressures.
- For the design of the riser walls, lateral
soil pressures shall be assumed uniformly
distributed
around the riser
and Kq = 45 pcf where K = the ratio of lateral
to vertical
soil pressures and wb = buoyant unit weight of soil.
l-3
Water pressures during pipe flow. - The loading on the riser wall
during pipe flow is equal to the difference
between the pressures
on the exterior
and interior
sides of the wall as illustrated
in
Figure l-l.
Hh
.
.
Figure
l-l.
Tests on risers
difference
inlet
l . Ap/w = (Hh + h,) - (p/w)
Water pressures
of the standard
may be taken as
of the riser
*
h-r
to a distance
on riser
walls
proportions
show that
= 6.0 from the crest
difference
For vb(mm)
vr
= 30 fPs:
= (ab/+)y,
= 3013.82
hvr = (vr>2/2g
= ($/3D2hb
= q/3-82
= 7.85 fps
= (7.85)2/2g
= 0.96 ft
Thus,
4/w
= 6.0 x 0.96 = 5.76 ft
and
4/w = 3.0 x 0.96 = 2.88 ft
where vr = mean velocity
of flow
ar = area of the riser
ab = area of the conduit
pipe
in the riser
flow.
the pressure
of the covered
equal to 1.5D below the crest
is !?iiihL
h
- 3.0 below distance
v-r
where hvr is the velocity
head in the riser.
pressure
during
and the
1.5D below the crest,
l-4
For design,
use &/w
= 6.0 ft
and 3.0 ft
respectively.
Figure 1-2 illustrates
a method of representing
the various
heads involNote that negative
pressures
(below atmospheric)
ved during pipe flow.
The maximum possible
are possible
at and near the crest of the riser.
magnitude of these negative
pressures is about:
= 300 psf for D = 24 in.
(6 hvr - 0.5~)62.4
negative
head
hx
I;
Ap/w lp/w=inside
I("
+ hx) = outside
Figure
l-2.
D/2 -
heat
heat
Representation
of heads during
pipe
flow.
Composite wall pressure diagram for design. - For design purposes, two
loading conditions
are defined:
(1) pipe flow - pressures as described above,
no flow - water surface at the crest of the covered
(2)
inlet of the riser,
lower inlets,
if any, assumed
plugged.
These two conditions
may be combined and a composite diagram drawn as
The resulting
diagram will contain,
when
illustrated
in Figure l-3.
N,h > 6, three straight
lines given by:
for 0 5 h, I 6.0
(1) h, = 6.0
for 6.0 5 h, S Nsh
(2)
$,, = hx
for N,h 5 hx s Nib
(3) h, = hx + 0.72 h,
l-5
6'
w,
/
/
/
t
1
\
hX
Nsh
7
A
hS
0
.
.A
Kwbhs
9
Figure
”A
hx
l-3.
embanlanent
or
' sediment
level
v
Composite wall pressure diagram for
risers
(vb(ma)
= 30 fps).
design
of standard
where
h, = inward pressure on riser wall .n feet of water
h, = distance from crest of covered inlet to point under
consideration
h, = depth of embankment or sediment at the riser to the
section h, below the crest of the covered inlet
N,h and Nib as previously
defined.
Note that
the crest
KWb/W
=
4/w
= 6.0 ft has been used to a distance of 6.0 ft below
of the covered inlet,
and that 0.72 is obtained from
45/62.4
= 0.72.
Loads on Cover Slab
The cover slab live load shall be 100 psf.
The weight of any equipment to be installed
on the cover slab shall be incorporated
in a
special design.
Bnbankment Load on Riser
For stability
analyses and to check the vertical
steel required
in
the downstream endwall,
it shall be assumed, for risers located in the
embankment, that the difference
between the downstream and the upstream
lateral
earth pressures is Kwm = 50 pcf on the downstream endwall for
1-6
moist
conditions
and is Kn = 30 pcf for
saturated
conditions.
A triangular
pressure distribution
shall be used, but the resultant
force shall be assumed to act at mid-height
instead of at third-height
of h, to account for possible
"arching
effect".
Take the unit soil
140 PCf.
Wm = Ws =
weights for moist or saturated
conditions
as
Neglect friction
which may act on the side-walls.
Wind
Risers located in the reservoir
area shall be designed for wind acting over the entire sidewall
using 50 pounds per square foot pressure.
Risers located in the embankment shsll not be designed for wind.
However, the catalog of available
standard risers,
when prepared,
will
specify a maximum allowable
wind projection.
This wind projection
is
the vertical
distance between the surface of the backfill
and the top
of the riser at any stage of construction.
Flotation
(1)
(2)
Criteria
When the riser is located in the reservoir
area, the
ratio of the weight of the riser to the weight of the
volume of water displaced by the riser shall not be
less than 1.5.
Low stage inlet(s),
if any, shall be
assumed plugged for this computation.
When the riser is located in the embankment - same as
(l), but add to the weight of the riser,
the buoyant
weight of the submerged fill
over the riser footing
projections.
Take the buoyant unit weight as w-b = 50 pcf.
Location
of Construction
Joints
in the Riser
Walls
The first
construction
joint above the top of the footing
shall be D + 12
inches above the pipe invert
at the conduit entrance0
The distance between the first
and second, and all other pairs of construction
joints below
the topmost joint in the riser walls shall be 5 ft except that the distance
between the topmost and the next to the topmost joint shall be 4 ft for
risers having D = 36 in.
The topmost construction
joint in the riser walls
shall be 7.0, 6.5, 7.0, 10.5, and lo,0 ft below the crest of the covered
inlet of the riser for risers having D = 24, 30, 36, 42, and 48 in. respectively.
The distance between the first
and second construction
joints above the
The blank
top of the footing
shall be left blank on the standard plans.
distance makes it possible to adapt the plans for a specific
standard
This adaptability
of the standard plans
riser to a range of heights.
imposes that there can not be a change in wall thickness at the second
construction
joint.
2-1
cHAFTER2.
METHODSOF ANALYSIS AND DESIGN PF0XDUFU3S
Cover Slab Walls
b
i
.
The cover slab wslls support the cover slab,
of the
cantilever
beams. In the top portion
will be 10 in. thick (the minimum thickness).
the cover slab walls
placement difficulties,
With 10 in. walls, #5 @ 15" C.C. are
thick.
give
0.25
Pt = 120 = 0.0021 2 0.002.
With this
show that
wall thickness and amount of steel,
further
analysis is unnecessary.
acting as variable
depth
riser,
the riser walls
Thus, to avoid steel
will also be made 10 in.
required
in each face to
rough
computations
will
Cover Slab
The minimum thiclmess of the cover slab is 8 in., this is an adequate
The total loading is 200 psf (100 psf live
thickness for all D values.
Cover
slab
span is 3D + 10 in. C.C. of supports with
+ 100 psf dead).
Thus,
the
cover
slab need be designed only once for each
10 in. walls.
(The
only
exception
to this might occur in the case of
conduit size D.
short risers which require
additional
wall thickness to satisfy
the floin
which
event
the
procedures
given
below
can
be
suittation
criteria
ably modified.)
Moments in the cover slab are highly indeterminate.
Therefore,
the positive center moments shall be conservatively
taken as l/8 qL2. Negative
steel in the amounts required
moments shall not be computed, but negative
for T & S (temperature
and shrinkage)
shall be provided
and shall be
lapped with the outside T & S cover slab wall steel.
A construction
joint shall be provided
in the cover slab walls at the elevation
of the
high stage crest.
q = 200 psf
Figure
2-l.
Definition
(live
+ dead)
sketch
of cover
slab.
2-2
The cover
slab design
follows
from a consideration
of Figure
d
= 8 - 2.5 = 5.5 in.
As(min)
= 0.002 x 8 x 12 = 0.192 sq in./ft
#4 @ 12 = 0.20 sq in./ft
#5 @ 15 = 0.25 sq in./ft
v max
= 1.50 qD = 1.50
vmsx
=
CO
Tnax
25D
= - ujd = 350 x 718 x 5.5 = D/67.3 in./ft
Vmm
=
-
qd
bd
l/8
=
X
200 X D/l2
As may be determined
Table
= 25D ibS/ft
25~ - 200(5.5/u)=
12 x 5.5
x 0.200( 3D ,'F)'
directly
2-l.
Cover
o
.
37gD
- 1.4 psi
= O.O001735(3D
from ~~-164,
slab design
30
36
vmax, Psi
7
10
0.36
42
48
12
14
17
0.45
0.54
0.62
0.71
1.2
l-7
2.4
3.2
4.1
0.19
0.20
0.29
0.39
0.50
#[email protected]
#[email protected]
#[email protected]
#4z
# %7 l/2-
---
M, ft
kips/ft
-A, req'd.,
sq in./ft
Steel
selected
kips/ft
summary,
24
in./ft
+ 1O)2 ft
sheet 1 of 3.
D, inches
co req'd.,
2-1:
--II-
--
The cover slab layout is shown in Figure 2-2 and the cover steel selected
is tabulated
in Table 2-2.
The layout must be modified
locally
near the
30 in. diameter manhole in the cover slab.
2-3
Table
2-2.
Cover
slab and cover
slab wall
steel.
1
CWl, cw2, cw3, cw4 = #pa5
rD
cs5
24
30
#[email protected]
#[email protected]
42
36
-#[email protected]
cs6
=
48
#[email protected]
#%7 l/2
#me5
cs7, cs8 = #[email protected]
-
cs6
cw4
Cw2--\
\
e---cw1
AeH -construction
2" Clear
Figure
2-2.
I
joint
cw3/
Cover
Cover slab and cover
Riser
Walls,
Horizontal
slab wall
steel
lavout.
Bending
Sections
For overall
economy the sidewalls
and endwalls shall have the same
thickness at any horizontal
section.
Since equal thicknesses
are
used, moments and direct compressive forces can be expressed conveniently as functions
of t/D.
Figure 2-3 shows the various moments and
forces of interest.
Closed
Equilibrium ---- relations.
- The relations
be written
directly
from a consideration
NE = l/2 q(3D + 2t)
NE/qD
Ns = l/2 q(D + 2t)
Ns;~~
NK = O.~O~(NE + MS)
NK/~D
= 1.414 q(D I- t)
for
the compressive
of statics
as:
= l/2 (3 + 2t/D)
= l/2 (1 + 2t/D)
= 1.414 (1 + t/D)
forces
can
2-4
3D + t
I:
I I:
I
31,
I
I
tttttt
9
SF
NE
L
I
NK = resultant
of components of NE and
NS which are perpendicular
to the
cut section.
Figure
2-3.
Definition
sketch for
horizontal
bending.
‘/
2-5
These relations
of the endwall
Table
2-3.
together with the shear in the sidewall
are swnmar ized in Table 2-3.
Force coefficients
for
horizontal
bending,
t/D
0.00
0.25
0.50
0.75
1.00
Ns
0.50
1.50
1.41
1.50
0.75
1.75
1.77
1.50
1.00
2.00
2.12
1.25
2.25
2.48
1.50
1.50
NE
NK
VSF
1.50
at the face
n.
2.50
2.83
1.50
Ni or Vi = niqD
The relations
for the various moments can also be written
from a consideration
of statics,
however MK must be known before the relations
can be evaluated.
The relations
are:
Msc = i s(3D + ‘d2 - MK
MSF= 6
q(3Jd2
- %c
MEC =EpC-$q(D+tj2
Mm = Mx + i q(Dj2
Msc
3 = !j (3 + t/Dj2
-s
qD
MSF
= 1.125 - %C
-
sD2
sD2
%C
-=-- MK i( 1 +
qD2
qD2
MEF
= [email protected]+ 0.125
qD2
t/Dj2
qD2
Note that the expressions
for MsC and MEC assume, in common with most
structural
analyses, the support reactions
for any member are concentrated at the support centerlines.
Analysis for corner moments, MK. - Thought should be given to the effects
of the assumptions used in analyzing for moments. Any reasonable method
of analysis may be employed (as Moment Distribution,
Slope Deflection,
etc.)
but
the
results
may
vary
widely
depending on
Conjugate Structure,
the assumptions followed.
The effects
of using two basically
different
assumptions are presented below.
Moment Distribution
is used as the method of analysis because of its
simplicity
due to symmetry of both loading and shape.
Members are prismatic.
- - The basic assumption is:
the members of the
closed frame are prismatic.
Under this assumption,
one cycle of Moment
Distribution
results
in final values for MK, since together with symmetry of loading and shape, the sidewall
and endwall carry-over
factors
2-6
are equal.
where
Thus MK is given
by:
MF = fixed end moment, and
h = distribution
factor.
In the above equations,
justed.
The distribution
S = stiffness
substitute
factors
= YU
magnitudes only, signs
are determined from:
or
ad-
t
so
ss a 3D1+ t
are already
and
SE a: -D+t1
and
kE =
thus
xs
The fixed
=
SS
$3 + SE
end moments may be written
SE
sS + sE
as:
q(3D + t>2 and &$ = $
q(D + t)2
Note that these expressions,
along with those for
support reactions
are concentrated
at the support
XSC and MEC, assume the
centerlines.
Observe that even if the assumption of prismatic
members was correct,
values for moments obtained from the above analysis would be incorrect.
The moment values would be incorrect
because beam reactions
are not concentrated
at support centerlines.
The reactions
are in reality
distributed in some unknown way over the thickness of the member providing
the
support.
If the reaction
(and hence shear) distribution
were known, it
would be possible to compute correct values for MF from which correct
values of MK could be obtained.
Similarly
with the shear distribution
known, correct expressions
for MsC and Mx could be written.
Since the
approximate procedure
is
shear distribution
is not known, the following
sometimes advocated to obtain better values of moments.
Figure 2-4 shows the shear distribution
assumed by usual theory.
moment at the face of the support using usual theory would be:
MF = MK - k&l where &4 = VA(t/2).
The Portland Cement Association
in its "Continuity
in Concrete
Frames" (page 28), would give the moment at the face as:
where NPCA = VA(t/T).
MF = N - &=A
The
Building
2-7
The difference
6&d
in AM values
= V&/2)
is:
- v&/3)
Thus, the FCA moment correction
= VA(+)
is VA(t/6).
c
Figure
Or, for
2-4.
Shear distribution
theory.
the sidewalls:
S(EM)g/qD2
And, for
assumed by usual
= &(s
+ &)
- &($
+ &)
endwalls:
6(nM)&D2
The procedure using these moment corrections
would then be: (1) compute
using
the
assumptions
of
prismatic
members
and concentrated
53, etc.
(2) add these moment corrections
to negative
moments and subreactions,
tract them from positive
moments. Many engineers,
however, would not
reduce the positive
moments. Table 2-4 gives the moment coefficients
obtained by use of the above procedure.
These values are given for purposes of comparison only, they shall not be used in the design of standard covered risers.
2-a
Table 2-4.
Moment coefficients
assuming prismatic
members, concentrated
reactions,
and using the FCA
moment corrections
- not to be used for design.
0
0.00
0.25
0.50
0.75
1.00
MK
0.58
0.58
0.54
0.58
0.46
0.67
0.54
0.77
0.50
0.62
0.66
0.88
1.00
0.45
0.67
0.41
0.71
0.71
0.54
0.59
0.75
0.63
are for
M/qD2
MSF
NYC
M?3F
ME
0.58
0.62
0.50
Moment coefficients
How well the PCA moment correction
takes
assumption of concentrated
reactions
is
error due to the assumption of prismatic
ratio of t/D.
Since high ratios of t/D
is desirable
that a more nearly correct
care of the error due to the
not known. In any case, the
members increases with the
will occur in some risers,
it
analysis be employed.
Members are non-prismatic.
- - The basic assumption is:
the members of
the closed frame are non-prismatic
and have moments of inertia
which
approach infinity
outside of the clear span limits.
Figure 2-5 shows
this variation
in moment of inertia.
The assumption of large values of
moments of inertia
outside of the clear span limits
not only avoids the
error due to the previous
assumption of prismatic
members, but it also
reduces the error due to the assumption of concentrated
reactions.
The
error due to the assumption of concentrated
reactions
is reduced because moments in regions of large moments of inertia
have little
influence on final moments in indeterminate
structures,
that is, M/I values
Therefore
the FCA moment corrections
in such regions approach zero.
should not be applied to the moments resulting
from this analysis.
Figure
2-5.
Assumed variation
in moment of inertia.
2-9
Because the members are non-prismatic,
the sidewall
and endwall
carry-over
factors
are not equal.
Hence, the distribution
of moments has to be performed.
The required
data is obtained as follows:
aSLS = t/2
a&
= t/2
&E
1
= 2
qE+2
or
+-
as
and
qE+2
thus
C!i = carry-over
factor
Si = stiffness
MT = fixed
= k$
i
Ccki
Li
end moment = m;qLT
where C!i = a function
of ai
where ki = a function
of ai
where ml?
2 = a function
of ai
Table 2-5 gives values of C, k, andm?
It is obtained
page 23 of "Handbook of Frame Constants",
by the FCA.
Table
2-Y.
Data for
Carry-over
Factors
a
0.00
0.05
0.10
0.15
0.20
0.25
Again
analysis with
members.
SS
As = SS i SE
Stiffness
Coefficient
C
k
0.500
0.575
0.648
0.719
0.786
0.846
4.00
5.23
7.11
10.17
15.56
26.00
and
hE=
in part
from
non-prismatic
Fixed end
Co~f~~~~ent
mF
0.0833
0.0913
0.0983
0.1046
0.1100
0.~46
SFI
SS + SE
Table 2-6 gives the moment coefficients
obtained by use of the above
procedure.
These values shall be used in the design of standard
covered risers.
2-10
Table
2-6.
Moment coefficients
bending, m.
for
horizontal
t/D
0.00
o.-25
0.50
MK
MSF
Msc
&a?
MEC
0.58
0.58
0.75
0.55
0.94
1.15
0.51
0.54
0.58
0.46
0.57
0.68
0.56
o-53
0.59
0.78
0.66
0.61
0.89
0.77
1.38
0.50
0.62
1.00
0.88
Mi = mtqD2
Design approach. - The process of design of closed sections of riser
walls for horizontal
bending can be reduced to a procedure which may
be both quickly and accurately
performed.
Considerations.
- - Using equal thicknesses
for sidewalls
and endwalls,
the minimum thickness
is governed by shear stress (as a measure of diagonal tension)
in the sidewalls
[d] distance from the face of the endSince thickness
is governed by shear, sections will be underwalls.
stressed in compression.
Hence, T & S steel in the compression side of
a section will not be counted upon as compressive steel, that is, the
presence or absence of compressive steel has a negligible
effect
on the
amount of tensile
steel required
in such a section.
The critical
section for bond is in the sidewalls
at the face of the
endwall.
Computations,
using the coefficients
for MsC to locate the
show that the ratio of required
point of inflection
in the sidewalls,
perimeter
of the f+> kside steel to the required
perimeter
of the
(-1 outside steel is:
JET*
VSF
-
1.50 1.50
- 0.38 = 0.745 for
t/D 5 1.00
where VP1 is the shear at the point of inflection.
Comparisons of the coefficients
for MsF and MsC for a given
show (since NS is the same for both moments):
t/D value
AsSF ' AsSC for t/D 2 0.17 (min. t/D = j$ = 0.208)
Computations for AsEF using Mm and NE, and computations
for
ing MsC and NS will show, for given values of hw, t, and D:
h,
2 ksc for all t/D values, however
do not differ
significantly.
The corner, with MK and NK., is not critical
given the usual standard bend.
the required
if
the negative
Assc us-
steel
areas
steel
is
2-11
consideraDirect design by charts. - - In the light of the preceding
it is possible to construct
charts which will permit the dirtions,
ect selection
of wall thicluless,
steel areas, and steel perimeters
for given wall loadings and conduit diameter.
t and Co vs. hw for
f
given
, x_
D:
Determine (hw),,,
for
VSF - qt d/12)
v=
bd
given
t, which makes v = 70 psi
= s+1.5D - &,
= 62.4(hw)vo
(9
- +12b
.
I
rearranging
.
(b)-m
and substituting
values,
=
L5D1314;
0833 ft
t - 2.5
Determine (Co),, required
(@SF) when v = 70 psi
ujd = vbd + q(d/12)
VSF = b’),
l
or
(co)~o
=
substituting
vb + (q/12)
uj
values,
(co)vo = 3.918 + 0.02426(hw)70
in./ft,
for
where
D is in ft, t is in inches, h, is in ft
bar sizes 5 #7
Thus curves similar
to Figure 2-6 can be drawn for each conduit diato hw for a given t and D.
meter, since CO and v are proportional
t and As vs. hw for given D:
The relation
of As vs. hw for a given t and D is nearly linear
since sections are under-reinforced.
Hence, only the As required (@EF) for the corresponding
values of t and b making v = 70 psi
need be computed.
These A, values may be computed from MEF and
NE using ~~-164, sheet 1 of 3.
Thus curves
similar
to Figure
2-7 can be drawn for
Table 2-7 provides
all the data necessary to
charts for each of the standard pipe conduit
shows the steel layout at closed horizontal
Using the direct
design charts the steel is
RHL
less
HH2
for
All
each conduit
prepare the
diameters.
sections of
selected as
by As but not less than 75 percent Co, and not
than that required
for T & S.
by A, and co, and not less than that required
T 8~ S.
other by As for T & S.
diameter.
direct design
Figure 2-8
the risers.
follows:
2-12
Figure
Typical
2-6.
direct
design
For a given
/-A,/
0
u\rurrr,
min\ for
chart
for
CO
in horizontal
bending.
D
Pt(min)
= 0*002
*.
\\
.
\'\
\'
\
L
'\
\
\
\
\
\
\
\
t,
>
t,
>
t,
I
0
Figure
2-7.
Allowable
shear
is exceeded to
right of this
line
1
Ty-pical
direct
design
chart
for
As in horizontal
bending.
2-15
Typical
Layout
(not to scale)
Detail
at Cover Slab Walls
CW2
Figure
2-8.
Steel
layouts
at closed
horizontal
sections
Wall thickness and steel selection.
- Use of a tabular
that shown in Figure 2-9 will facilitate
design.
of riser.
form similar
to
Observe that for a given value of loading on the riser
(hw) at the
four items must be determined:
wall thicksection under consideration,
The last three items
ness (t), (+> steel,
(-> steel, and T & S steel.
Hence, trial
solutions
using
depend on the wall thickness
selected.
different
thicknesses
should be investigated.
The combination
finally
chosen should reflect
consideration
of the requirements
of adjacent sections to insure that the whole will fit together.
Sections at Low Stage Inlets
No low stage inlet will be shown on the standards.
The location
and
size of this opening (if any) and the necessary steel changes are to
be handled by the field
as a modification
of the standard plans.
It
should be recognized that such openings, if sufficiently
large, will
cause a significant
change in structural
behavior
from that of the
usual closed section.
Sections at the Conduit Entrance
An exact analysis of horizontal
steel requirements
in this region
the riser walls is complicated
by two main factors:
(1) horizontal
structural
behavior
varies between the
limits
of usual closed section behavior
and pinned
ended frame behavior,
and
the connection
of the riser walls to the footing
(2)
causes vertical
bending and tends to restrain
horizontal
bending (this effect
is presented
under "wall-to-footing
connection"),
hence the
load on the walls at any distance above the
footing
is divided
between that producing horizontal bending and that producing vertical
bending.
of
hX
Range
value for
h, range)
(+)%eel
t
h,
CM=-
!4in.
r
Trial
A,
ft
1
(of Zter)
2
r:selected
Required
t
75fJo
in.
in.
in.2/ft
in./ft
3
4
5
6
V
Colon 3 obtained from riser design
Columns 5 and 8, 9, and 11 obtained
column 6 I- 75% of column 9.
Figure
2-g.
. ..m . ., ,,. . .
I
yps
A,
7
CO
in. yft
in./ft
8
9
Selected
#@S
#@S
10
Use
in.2/ft
11
A
chart for given &.
from r .ser design chart
Suggested tabular
(-)?Eeel
Required
-
m,
m-l, m2
T and S Steel
Required
Selected
form for
design
for
given
of closed
hw and t.
sections
for
horizontal
bending.
.m . . . . . . . .. . . ,----,-,“-,-;-“_111
-x--_. ^ m
. . .
2-17
show that the following
procedure
Analyses, presented subsequently,
yields conservative
results
for required
amounts of horizontal
steel:
(1) At and above D distance above the pipe invert
at the conduit entrance - design for usual closed
section behavior
under the assumption that the
entire load is resisted
by horizontal
bending.
(2)
Between D distance above the pipe invert
and the
- hold the steel amounts contop of the footing
stant at the values determined for D distance
above the pipe invert.
The layout of horizontal
steel can therefore
be the same as for the
usual closed sections except for the omission of two RR2 bars and
the addition
of two RH4 bars as shown in Figure 2-10.
RH4
Figure
2-10.
Layout
of horizontal
steel
entrance.
in sections
at the conduit
2-18
Riser
Wall-to-Footing
Walls,
Vertical
Rending
Connection
Rending is produced in a vertical
direction
in the riser walls wherever
a discontinuity
of section occurs.
Ususlly the action is not serious
and is adequately resisted
by the usual vertical
steel provided
for
T & S. However, vertical
bending of the same order of magnitude as is
present in horizontal
bending is produced by the wall-to-footing
connection, since the riser walls cannot deflect
horizontally
at this location.
When considering
riser wall design, the wall-to-footing
connection is assumed to be located at the elevation
of the pipe invert
at
the conduit entrance and the variation
in wall section due to the round
bottom is neglected.
Vertical
flexure
in sidewalls.
- No vertical
bending would occur at the
w&L-to-footing
connection
if the riser walls were not connected to the
footing,
that is, if the walls merely rested on the footing
without
However, with rotation
and translation
prevented,
moments
friction.
and shears are produced to satisfy
the requirements
of geometry.
Figure 2-11 illustrates
the various deflected
shapes and the loading on
the wall.
sidewsJ-1
deflection
no-load position
of
sidewall
sidewall
deflection
if
I
wall not
connected to
I
footing
-v
/
Figure
2-11.
Vertical
section
elevation
of
wall-to-footing
connection
through sidewall
+Y
Let:
moment in the riser wall at the wall-to-footing
Mvo = vertical
connection
shear in the riser wall at the wall-to-footing
connection
due to vertical
bending
unit load at the section under consideration
sx
= the total
vvo=
sm
Y
the unit load resisted
under consideration
the unit load resisted
under consideration
deflection
= horizontal
under consideration.
=
by horizontal
by vertical
of the riser
bending
bending
wsll
at the section
at the section
at the section
2-19
l
Then at any section:
qX = sm + SlJx
But the horizontal
deflection
the minus sign
at any section
is used since
may be expressed
as:
(Y) is in the minus direction.
Here:
Es' = athehorizontal
location
deflection
coefficient
of the section under
sv-x = s, -qHx=qx+=-Y
The differential
equation
EI ax"
d4Y = zx
which depends on
consideration.
R-r
KyD4
of the elastic
curve
of a beam is:
where ZX is a load function.
Here:
zx = - qiy(
or
I+-qx--
;4
y
and letting
484 = -&$
Y
then
It is possible to solve this equation by writing
the
and evaluating
the four constants of integration
by
conditions.
However, the equation
d4Y + 48% = 0
dx4
has already been solved for a semi-infinite
beam on
Part II, page 12,
tion (see "Strength of Materials",
loaded with MVO and VVo at its ends acting with the
general solution
using the boundary
an elastic
foundaby yimoshenko),
senses shown.
2-20
Timoshenko's
complimentary
solution:
cm w - /3MVo(cosBX - [email protected])]
together
'=
lead
with
the particular
solution:
a- qx
@%I
to the following
expressions:
%o =
0.1074
Vvo =
$1 -
%x=
-- VVO e-BXsinBX
B
+ &JO e-Bx([email protected]
Vvx=
- Vvoe+x(eos13X
- sinBX)
2qB
>
and
+ sinBX)
[email protected]+xsingX
where
MVX = vertical
moment in the riser wall at section under consideration
vm = shear in the riser wall at the section under consideration
due to vertical
bending
=
the
total
unit load at the wall-to-footing
connection
9
(9x)X&
'
These equations
follow
the usual
M
The units
sign convention:
V
of the various
quantities
are:
MVO, MVX = ft kips/ft
vvo9 Q-X = kips/ft
Q
B
q
1 Emensionless
= ft-l
= k!f/ft
Revised
8-l-6
2-21
The values
of various
functions
are given
for
convenience
in Table
2-8.
Moments "damp out" quickly with distance from the wall-to-footing
connection.
This may be seen by examination
of the expression
for R!vx"
Hence, the usual amounts of T & S steel soon become adequate to resist
the vertical
bending.
i
Table 2-8.
e+'sin
PX
0.0
SX e-SX(cosSX
0.000
0.291
0.5
1.000
0.242
0.014
-
0.011
- 0.013
1.5
2.0
- 0.011
- 0.006
-
- sinSX)
1.000
-
0.310
0.223
0.123
0.049
0.007
e+'([email protected]
+ sinSX)
0.823
0.508
0.238
0.067
- 0.017
- 0.042
- 0.039
- 0.026
1.0
2.5
3.0
3.5
4.0
4.5
5.0
Values of functions.
- 0.111
- 0.207
- 0.179
- 0.115
- 0.056
- 0.018
0.002
0.008
0.008
0.005
to that of the
Verticsl
flexure
in endwalls.
- This case is similar
sidewalls,
except that endwall deflections
oppose the direction
of
Also, intuitively,
loading a~&- hence, various
signs are reversed.
vertical
bending in the endwslls is small relative
to that in the
sidewaLLs.
Thus, T & S steel, properly
anchored, msy be adequate.
Figure 2-12 illustrates
the various deflected
shapes and the loading
on the wall.
The relations
again
are:
vvo =;
(1 -
L&L!$
h=+Be
"O
-BXsinSX
but
Vm = + Vvo e-BX(cospx
These quantities
- Mvo e*'(cosBX
+ [email protected])
- SinBX) + 24&3
are as defined
for
sidewalls.
e-f3XsinSX
2-22
Compare with
Figure 2-11
for sidewalls.
Figure
Evaluation
2-12.
Vertical
section
through
of coefficients
endwall.
Icy. - Before the vertical.
the horizontal
deflection
and shears can be evaluated,
Ky must be determined.
flexure moments
coefficients
structural
behavior
of the riser
As previously
noted, the horizontal
walls, at and near the conduit entrance,
is intermediate
between that
of the usual closed section and that of a pinned ended frame.
Vertical
flexure
increases with horizontal
deflections,
thus conservative design dictates
that KY be evaluated
on the basis of pinned frame
action since a pinned frame has larger
deflections
than a similar but
closed frame.
Also, the values obtained for corner moments
regarding
variations
ced by the assumptions,
Conservatism
is
in analyzing the structure.
tions giving small corner moments and hence,
(MK) are directly
influenin moments of inertia,
used
again served by using assumplarge sidewall
deflections.
Therefore,
KY, is evaluated
on the basis of pinned frame action and
prismatic
members. Figure 2-13 shows the moment diagrams resulting
from the statical
system selected.
Using (R) as the redundant force
2-23
and taking moments of moment areas abouti a line through
in accordance with the Conjugate Structure
concept:
z(3D + tj2
+ $3D
2
3
--X
=2x
x (3D +t>
+ tj2
x 2 x (3D +t>
x (D + t) x (3D + t)
3( D +t12
$X
the supports
x (D +t)
x (3D +t)
R(3D + t> x (3D +t>
+ R(3D + t> x (D +t)
x $ x (3D + t)
x (3D + t)
-
-
= original
II
structure
II
s(D+t)2
p+t
)2
v
)2R(3D+t,
r\
(
>
\
0
Figure
’
Z-13.
Sketches
for
7I
c
>
+
R(3D+t >
analysis
= final
of pinned
frame.
moments
2-24
Thus:
R(3D + t)(36
+ 20%/D)
= qD2[3(3 + t/D)' + 6(3 + t/D)*(l
- (1 +t/D)3]
+ t/D)
and, by statics
MK = $3D
From Figure
I- t)2 - R(3D + t)
2-14,
the mid-span
For sidewall
Y = m'
For endwall
Y = i g
Solutions
of the equations
given in Table 2-9, where
dEI
- $ 'g
(3 + t/D)4
(1 + t/D)*
for
may be written
deflections
R, !I(,
- &
(3 + t/D)*
g
and Y yield
as:
(1 i- t/D)4
values
for
KY as
Ky==Y
qD4
Table
Pinned frame corner
coefficients.
2-9.
t/D
morhents and deflection
0.00
0.25
0.50
0.75
1.00
Sidewall
KY
0.616
0.872
1.188
1.573
2.043
Endwall
KY
0.085
0.140
0.215
0.314
o-437
0.78
0.88
1.00
1.14
1.29
MK
sr)'
Revised
u-65
2-25
l
I
PI
.
endwall
deflections
sidewall
Figure
2-14.
deflections
Finned frame deflections.
2-26
Example of computation of MvO and VVo. - The following
example is presented for two purposes; first,
to indicate
the ease with which the
computations
may be made and second, to indicate
the order of magnitude
of vertical
bending.
Assume: D = 4.0 ft
t =24in.
hw = 60 ft at the wall-to-footing
connection
. l . q = 3.74 klf/ft
At center
of sidewall:
t/D
.
= 0.50
l . KY = 1.188
B4
= 4 x 1.1;8
P2
B
=&
%O
vvo
At center
= 24148
x (4)4
= &
= 0.16g/ft
= 3.74
x 34.9
2
= 3.4
0.1
-Is 9 (I-
(1 _ 3.7~'~"~~16g)
2 x 3*74
0.1074x o.l6g)
= 54.1 ft
= 20.3
kips/ft
w?s/ft
of endwall:
= 0.50
t/D
. l . KY = 0.2l5
B
= 0.259
= 24.7 ft kips/ft
vvo
=&$'l-
2 x ~:~~7~ o.2~)=
13.6 kips/f't
Revised
u-65
2-27
l
Wall thickness by shear due to vertical
bending.
- The wall thickness
required
by shear at [a] distance above the wall-to-footing
connection
at the center of the sidewalls
due to vertical
action may be greater
than the thickness required
by shear at D distance above the connection
action.
This may be checked by:
due to horizontal
.
T
.
h&d
bd
v=
C
S 70 psi
where
d =t
- 3.5
at the center of
Vertical
steel. - Determine the outside steel required
The
force
system
consists
of
the
moment
MvC
and a direct
the sidewall.
If the amount of steel thus
force NC due to the weight of the riser.
required
exceeds that required
for T 8~ S, the height at which T & S steel
is adequate will have to be checked.
Thus, throughout
the length of the sidewall,
for the inside steel use
that required
by T & S, for the outside steel use the larger
of that
required
for T & S or that required
for vertical
bending at the center
of the sidewall.
In the endwall follow a procedure similar
to that for the sidewalls
except note that vertical
bending produces tension in the inside steel.
it will also be ade(Note, if T & S steel is adequate in the sidewalls
quate in the endwall.)
Figure
P-15 illustrates
the steel
concerned.
5" to Center
of Steel
Figure
Z-15.
Vertical
steel
at wall-to-footing
connection.
division
of wall loading
Division
of wsll loading.
- The theoretical
between horizontal
and vertical
bending along a vertical
line may be
obtained as follows.
From the sidewall
investigation
(the ssme end
result
is obtained from the endwall investigation):
2-28
substitution
gives
of the expressions
for
Y, VVO, and MvO and simplifying
:
¶.m
= sx
- q[e-BX(COSf3X
+ [email protected]) - y
e+'sinSX]
Thus qHX varies from qHx = 0 at the wall-to-footing
connection to
qm = qX at some distance above the connection
as shown by Figure 2-16.
This distance may be determined by setting the term in brackets in the
above equation to zero and solving
for X. The procedure for determining the required
horizontal
steel given under "Sections at the Conduit
Entrance" will be seen to be conservative.
Figure
2-16.
Typical
load division
curve.
Wall Thickness Change Locations
Since walls of different
thicknesses
have different
stiffnesses,
the
linear
increase in deflection
along any vertical
line in the riser will
be disrupted
at locations
where the thickness changes.
Hence, vertical
Analysis will show that this
bending is introduced
at such locations.
bending is not serious and is adequately
resisted
by the usual amounts
of T & S steel, when the changes in wall thickness are not large.
Provision
for Moment from Embankment Loading
At closed sections.
- Ordinarily
the vertical
steel provided
for T & S
As an approximate but
will be adequate to resist the moment produced.
quick check, the area of tensile
vertical
steel required
in the downstream
endwall may be determined
conservatively
as
As =ggTg
where
A,
f,
D
t
M
=
=
=
=
=
total steel required,
in.=
20 ksi
pipe diameter,
ft
wall thickness,
ft
moment at the elevation
being
checked.
2-29
If this check indicates
the T & S steel may be inadequate,
more exact
analyses can be employed before additional
steel is provided.
The moment may be computed as indicated
M = $Fhs = 0.0125 Bh;
where
ft
by Figure
I,
hS
I
I
I
I
I
I
1
-6
Z-17.
lbs
I
I
Figure
50 h&h,
I
I
U
use some
I
I
Y
Thus:
kips
B = width of endwall,
f-t (for convenience,
constant "weighted" width)
h, = as previously
defined,
ft
I
I
I
I
'Z-17.
wm = 5O)hs
Assumed embankment loading.
vertical
steel, in the ends of
At conduit entrance.
- Extra tensile
the sidewalls
adjacent to the conduit entrance,
may be required
since
the vertical
downstream endwall steel is interrupted
by the spigot wall
The amount may be determined
conservatively
from the above
fitting.
equations,
but the moment arm may need to be reduced slightly,
dependThis steel will also serve
ing on available
room to place the steel.
the additional
function
of providing
for the pinned frame action reaction.
2-30
Stability
Analyses
The plan dimensions and layout of the footing
must be such that the earth
bearing pressure and flotation
criteria,
previously
given, are satisfied.
Various load combinations
should be investigated,
depending on the location of the riser relative
to the embankment. As an estimate in these
analyses, the thickness
of the footing
may be taken equal to the thickness of the riser walls immediately
above the footing
plus about 3”.
Probably the difference,
if any, between the footing
thickness assumed
here and the footing
thickness
subsequently
determined by strength
design, will not cause these analyses to be significantly
in error.
Bearing pressures may be analyzed in several ways. Because of the manner
in which allowable
pressures are stated, the following
approach is suggested, see Figure 2-18.
Q
Figure
2-18.
Analyses
of bearing
pressures.
NGR
=A+7
..
where
MC
CL!?,&-6
* - &AW2 -Aw
but
..!
= moment about @ of bottom of footing
but not including
forces,
NGR = sum of vertical
in the direction
of M
w
= width of footing
A
= area of footing
M
thus
%lSX.
uplift
+q1+&,
and
Paver.
=- NGR
A
and
pmin.
when uplift
is present:
Pmin.(net)
To be adequate,
RIlSX.
Paver.
pmin.
= pmin. - Pup
the following
where
pup = 62.4~
must be satisfied:
5 allowable
maximum pressure
5 allowable
10
average
pressure
Pmin.(net)
t O
Direct design for required
bearing area is usually
impractical
because
the simplest procedure is to estiNGR is a function
of A. Therefore,
mate A, check adequacy and revise as necessary.
Riser in the Reservoir
Area
No endwall footing
projections
need to be used, required
bearing area
The following
may be provided
by using sidewall
footing
projections.
conditions
should be investigated:
(1) No sediment, wind on sidewall,
moist
soil condition.
(2) No sediment, no wind, water surface to design sediment
surface.
(3) No sediment, wind on sidewall,
water surface to design
sediment surface.
(4) No sediment, no wind, water surface to crest of covered
inlet.
(5) Sediment to design sediment surface,
no wind, water
surface to design sediment surface.
(6) Sediment to design sediment surface,
no wind, water
surface to crest of covered inlet.
(7) Sediment to design sediment surface,
no wind, water
surface to bottom of cover slab (riser
primed).
(8) The flotation
criteria.
Revised
8-I-68
.,
2-32
Riser in the Bnbankment
An upstream endwall footing
projection
will be used when ad'yantageous
even though its use msy introduce
some difficulty
regarding
the installation
of a reservoir
drain.---The
following
conditions
should be
investigated:
(1) Bnbankment present,
moist soil condition.
(2) l3nbankment present, water surface to embankment (berm) surface.
(3) Embankment present, water surface to crest of covered inlet.
(4) mbankment present
water surface to bottom of cover
slab (riser
primed j .
(3) No embankment placed, moist soil condition.
(6) The flotation
criteria.
Footing
Strength
Design
Design is similar
to that for the heel and toe of retaining
walls.
The footing
thickness may be controlled
by shear.
The critical
section for shear, as a measure of diagonal tension,
may be taken [d]
distance from the face of the riser wall, where [d] is the effective
Critical
footing
projection
loadings may be
depth of the footing.
determined from the various
stability
analyses previously
listed.
Note that the projection
may be subjected to positive
moment for some
loadings end to negative
moment for other loadings.
Particular
care should be exercised in detailing
the vertical
steel
connecting the riser walls to the footing.
When considering
footing
strength
design with the round bottom riser,
the footing
support for
the riser walls should probably be taken at D/4 above the pipe invert
at the conduit entrance,
rather than at the pipe invert
elevation,
to
account for the variation
in wall section and increased stiffness
of
this type of base.
Thus, the moment in the footing,
between the sidewalls, due to MvC and VVC is, as indicated
by Figure 2-19:
M = J$.ro + V&D/4
+ Q/2)
If desirable,
due to this moment, a greater thickness than tf can be
provided
in the footing
between the sidewalls.
That is, the footing
thickness between the sidewalls
may be greater than the footing
proThe moment expression
can be modified
accordingly.
jection
thickness.
No
Figure
2-19.
Moment in footing
NO
due to vertical
bending.
3-l
CMER
EXAMPLE DESIGN
3.
Riser
D
Data
= 30 in.
Nib = 40 ft
N-25 = 30 ft
N,h = 10 ft
Riser located in the embankment.
Location of riser wall construction
h, = 6.5, 11.5, 16.5, 21.5,
and 36.5 f-t
26.5,
31.5,
Cover
joints:
Slab and Cover
Slab Walls
Use standard design:
Cover slab thickness = 8 in.
Riser wall and cover slab wsll thickness
= 10 in.
Steel as given in Table 2-2.
Layout as shown in Figure 2-2.
Volume and weight - for subsequent computations:
Slab -
V = $(3
x 2.5 + g)
(5
x 2.5
= 86.5
+ f$)
w=
ft3
= 13.0 kips
Slab walls Above crest
= 29.5 ft3
w=
= 4.4 kips
Below crest
v=
4(3
4(+-j)
w=
(&)
($
x
(2x2.5)+
2
x
2.5
x
2
x
2.5)
= 50.0 ft3
=
7.5 kips
3-2
Riser
Wall Loading
As discussed in Chapter 1, the loads
h, = 6.0
h, = hx
h, = h, + 0.72(h, - 10)
Design
Wall Thickness
Try t = 15 in.,
t/D = 3
B
=(
of Riser
at Wall-to-Footing
hx = 40 ft
q = 62.4(40 + 0.72
x
on the riser walls are given
0
s h, s 6.0
6.0 5 h, 5 10.0
10.0 5 h, 5 40.0
by:
Walls
Connection
30)
=
3840 psf
d = 15 - 3.5 = 11.5 in.:
= 0.500
therefore
KY = 1.188
l/4
1
4 x 1.188 x
VITO = 3.840 x 3.70
c2.514
)
=&
(1 - Ow)
Mvo = 3.840 x2 (3.70)~
= 13.45
(1 - Ow)
kips/ft
= 23.5 ft kips/ft
Shear at d above the connection:
A( z)12 =0.259
gx= 3.70
e -px(cospX
- [email protected]) = 0.607
e+'(singX)
= 0.151
VVX = - 13.45(0.607)
V
- 2(23.5)(&)(0.151)
.
10100
b-x
= -bd = 12 x 11.5 -- 73 > 70 psi,
Try t = 18 in.,
t/D = g
=lO.l
therefore
kips/ft
no good
d = 18 - 3.5 = 14.5 in.:
= 0.600
B =&
vvo = 3* 840
x
therefore
3.81 (1 - w)
%.O = 3*840 z (30~~)~
(1 - w)
KY = 1.342
= 13.8 kips/ft
=
24.9
ft kips/ft
Revised
u-65
3-3
Shear at d above the connection:
px = gi
1 (14.5) = 0.318
12
e'Bx(cosf3X
- [email protected])
= 0.518
e+'(sinSX)
= 0.185
VVX = - 13.8(0.518)
- 2(24.9)(&)(0.185)
V
=
9600
= - 9.6 kips/ft
= 55 < 70 ps,i, therefore
12 x 14.5
and use t = 18 in.
thickness.
unless
horizontal
OK
bending
requires
Design for Horizontal
Bendin&
Table 3-l summarizes the wall thicknesses
and steel
Layouts will
which were selected using Figure 3-l.
ures 2-8 and 2-10.
a greater
sizes and spacings
be as shown in Fig-
Volume and weight - for subsequent computations:
Volume of riser above footing
= 86.5
Cover slab
=
Cover walls
79.5
Riser walls
17(38.24
lO(42.75
10(50.00
3(57*75
Weight of riser
-
18.75)
18.75)
18.75)
18.75)
=
=
=
=
above footing
331.3
240.0
312.5
117.0
1166.8 ft3
0.150(1166.8)
= 175.0 kips
Revised
11-65
II
R
Table
Swnmary of riser
3-l.
0
hW
- 10
13.5
min.
use
A,
10.0
16.0
10
10
-
13.5
- 17
22.0
17
- 22
30.6
10
22
-
27
39.2
12
27
- 32
47.8
15
32
- 37
56.5
15
37
- 40
57.3"
15**
design
for
horizontal
C-t-1 Steel
t
hX
wall
10
12
15
18
75fJo
f-1
Selected
A,
CO
bending.
T & S Steel
Steel
Selected
0.24
1.1
#%15
0.24
1.5
#?a5
0.26
1.7
#%12
0.26
2.3
#[email protected]
0.35
2.4
#%
9
0.35
3.2
#[email protected] 6
0.36
2.6
if!% 9
0.36
3.5
#[email protected] 6
0.46
3.4
#%
6
0.46
4.5
#[email protected] 6
0.38
3.1
j&2 9 0.30
4.2
#[email protected] 6
0.45
3.8
#&is 6
5.0
#[email protected] 6
0.38
3.1
#[email protected] g 0.38
4.1
#@ 6
0.45
9
As
Selected
0.24
#m5
0.29
#y&2
0.36
[email protected]
0.38
[email protected]***
I
* For h, = 40 - 2.5 = 37.5 ft based on load division
= 15 in. if horizontal
bending controlled.
** tmin.
***
See following
pages for
design
of other
,.
vertical
between
horizontal
and vertical
bending.
steel.
. ..-.
. ,.
.
-- . .
3-6
Vertical
Steel at Wall-to-Footing
Connection
In sidewalls
- outside steel at center of sidewalls:
VVC = 13.80 kips/ft
MVC = 24.9 ft kips/ft
= 18 - 3.5 =14.5 in.
d
Direct compressive force:
Weight of riser above footing
= 175.0 kips
Pressure = 175.0/(57.75 - 18.75) = 4.48 ksf
NC = 4.48 x 18/12 = 6.72 kips/ft
Analysis for required
steel:
d"
= 1812 - 3.5 = 5.5 in.
MS
= 24.9 + 6.72 x 5.5/12 = 28.0 ft kips/ft
thus A = 1.30 in.2/ft
and As = 1.30 - 6.72/20 = 0.96 in.2/ft
= $
CO
Use
= 3.11 in./ft
= *
#[email protected] (A, = 1.29,
CO =
5.50)
Check steel required
at first
construction
joint:
Neglect change in wall thickness
from 18 in. to 15 in.
6 in. below joint,
treat as though t = 18 in.
gx=&i
(3.5)
at
=
0.?2
= 0.307
e+'(sinSX)
e+'(cospX
+ sinSX) = 0.559
MVX = - 13.8 (3.81)(0.307)
+ 24.9 (0.559) = - 2.3 ft kips/ft
Thus, moment passes through zero a short distance below the
first
joint.
Extend, by the use of dowels, the #[email protected] the usual
lap distance above the first
joint.
In endwalls - inside steel at center of endwall:
t/D = 18130 = 0.600 therefore
KY = 0.255
B
= (
1
4 x 0.255
%o =
3.840
x
2
1l/4
x c2.514
(2.52)2
(1 -w)
1
=2.52
=11.3
f't kips/ft
Revised
u-65
3-7
Analysis
l
,
..
c
for
required
Ms = 11.3 + 6.72 x 5.5/12 = 14.4 ft kips/ft
thus A = 0.64 in2/ft
< required
and As = 0.64 - 6.72/20 = 0.30 in2/ft
for
Vertical
Steel for Moment from Embankment Loading
Determine 'heighted"
width of endwall for use in evaluating
ment loadings:
7(4.17) = 29.19
lO(4.50)
lO(5.00)
= 45.00
= 50.00
3(5.50)
= 16.50
140.69
The moment to be resisted
B =140*6p
T & S
embank-
= 4 69 ft
l
30
is:
M = 0.0125(4.6p)hs3
l
steel:
= 0.0586
hs3 f-t kips
Because of the conduit entrance,
the vertical
T & S steel in the downstream endwall is not effective
below the first
construction
joint,
nor
above it until the required
embedment length is reached (taken as 2.0 ft
or approximately
30 #6 bar diameters).
Hence this T 8~ S steel is only
checked for values of h, s 34.5 ft.
Table 3-2, in which:
AS
=
&
in2
shows the analysis.
Since this analysis
over estimates the required
steel, the usual T 8~ S steel in the downstream endwall is considered
adequate for hx 5 34.5 ft even th ough the indicated
required
A, at
h, = 34.5 ft is somewhat greater than the A, provided.
Table
M
hS
7
12
17
l
3-2.
20
101
289
22
625
24.5 862
Vertical
loading
steel for moment from embankment
at usual closed sections.
t
3D+t
10
8.33
8.50
8.50
8.75
8.75
12
12
15
15
As
0.1
0.6
l-7
3.6
4.9
2(D+2t)
8.33
9.00
9.00
10.00
10.00
As provided
1
in2/ft/surfacc
#[email protected] = 0.25
#5912 = 0.31
#[email protected] = 0.31
$46912 = 0.44
#[email protected] = 0.44
Revised
?t
1
for
11-65
T&S
3-8
For values of h, > 34.5 ft, assume the steel in the downstream 3 ft of
the sidewalls
is effective
in resisting
the moment and use (3D + t/2)
as the moment arm. Thus for h(-.)
= 40 ft:
h, = 30 ft
M = 1580 ft kips
A, = 'm
Provided
I
1580
= 9.6 in.2
by inside
steel
for
T ??cS:
#[email protected] = 0.44 x 3 x 2 = 2.6 in.2
Provided
by outside
steel
for
vertical
bending
#[email protected] = 1.20 x 3 x 2 = 7.2 in.2
Total
area provided
= 9.8 in.?,
Stability
Preliminaries
Volume outside riser
mum) section:
Between footing
7(57.75 - 38.24)
lO(57.75 - 42.75)
lO(57.75 - 50.00)
3(57.75 - 57.75)
v,
Between earth
surface
10(57.75 - 38.24)
slab walls
. .-.,
v2
Displacement
volume
slab walls
17(38.24)
lO(42.75)
10(50.00)
..-,
3(57.75)
Rough, preliminary
with a thickness
dimensions,
Analyses
wsJls but inside
and earth
=
=
=
OK
5.5 x 10.5 (the msxi-
the projected
surface:
136.6
150.0
77.5
0.0
=
= 364.1 f-t?
and crest
of covered
inlet:
= 195.1
= - 50.0
= 145.1 fte
of riser
between footing
=
and crest
of covered
inlet:
50.0
= 650.1
= 427.5
= 500.0
= 173.2
VD = 1800.8 fts
computations
indicate
a footing
Figure
of 21 inches is required.
of about 16 ft x 14 ft
3-2 shows the trial
3-9
Thus,
for the footing:
= 224
ft2
Area
Volume = 392
ft3
Weight = 58.8 kips
and the various working volumes:
vB1
= 30(2
VB; = (lo/301
x 4.25
x 10.5)
= 2680
=
vBl
ft3
have taken the
ft3 for the slab
walls from VB' instead
1
of from V2, or could
have taken it partly
from both.)
893 ft3
= 30(5.5
x 14)
= 2310 ft3
VB; = (lo/3a)
vB2
= 770 ft3
vB2
(Could
50.0
16.0
5.5
10.5
I
7
f/
/I
,I
//
,C
,
4.25
,I
A
c. g. of ftg.
5.5
riser
less
/
/
/
/
//
/
L
1 2.75
1 2.75
5.25
5.25
-I
Figure
3-2.
Plan of trial
footing.
7,
Ii
4.2:
3-10
eF=
Embankment present,
moist soil conditions:
Allowable
average pressure = 0.140 x 31.75 + 2.00 = 6.44 ksf
Allowable
maximum pressure = 0.140 x 31.75 + 4.00 = 8.44 ksf
Weighted wsll width
= 4.69 ft.
Embankment moment:
M= 0.0125 x 4.69 x (31.75)' = 1875 ft kips
Riser less footing
= 175.0 x (- 2.75) = - 481
Footing
VI = 364.1 x 0.14
vB1 = 2680 x 0.14
QB2 = 2310 x 0.14
=
=
=
=
58.8 x ( 0
> =
0
51.0 x (- 2.75)
= - 140
375.0 x (- 2.75)
= - 1030
323.0 x (+ 3.25)
982.8 kips
Moment about * of footing:
M$
= 1875 + 44 = 1919 ft kips
)= 4.3g(i.733)
pmax. =~(++$!j
(2)
Paver.
= 4.39 < 6.44 ksf,
Pmin.
= 4.39(0x67)
Paver.
pmin.
puplift
pmin. (net)
(3)
kips
= 7.62 < 8.44 ksf,
= 1.17 > 0 ksf,
OK
embankment (berm) surface:
31.75 +l.OO = 5.44 ksf
31.75 + 2.00 = 6.44 ksf
kips
kips
= -3
;"2 (1 + l; ; ';;;)
= 4.3g(1.446)
= 4.39 < 5.44 ksf, OK
= 4.39(0.554)
= 2.43 > 0 ksf, OK
= 0.0624 x 31.75 = 1.98 ksf
= 2.43 - 1.98 = 0.45 > 0 ksf,
= 6.35 < 6.44 ksf,
OK
Ebnbankment present, water surface to crest of covered inlet:
Allowable
average pressure = 5.44 + 10 x 0.0624 = 6.06 ksf
Allowable
maximum pressure = 6.44 + 10 x 0.0624 = 7.06 ksf
Previous
=982.8
+ 44
v2 = 145.1 x 0.0624
VB; = 893 x 0.0624
VB; = 770 x 0.0624
OK
OK
Embanlunent present, water surface to
Allowable
average pressure = 0.140 x
Allowable
maximum pressure = 0.140 x
M
= (30/50)(1875)
= 1125 ft
= 1125 + 44
= 1169 ft
W
b.X.
= + 1695
-t 44 ft
= 9.1 x (- 2.73) ==- 25
= 55.7 x (- 2.75) = - 153
= 48.0 x (+ 5.25) = + 252
1095.6
kips
+ 118 ft kips
OK
3-11
.
(4)
w
=
&lax.
= g
Paver.
Pmin.
puplift
Pan(net)
= 4.90 < 6.06 ksf, OK
= b.gO(O.575)
= 2.82 > 0 ksf,
= 0.0624 x 41.75 = 2.60 ksf
= 2.82 - 2.60 = 0.22 > 0 ksf,
U.25 + 118 = 1243 f-t kips
(1 + -m)
= 4.90(1.425)
Embankment present,
water surface
(riser
primed):
Allowable
average pressure = 5.44
Allowable
maximum pressure = 6.44
Previous
= logy.6
Water in riser
40 x 18.75 x 0.0624
= 46.8
Water over crest
224 x 1.25 x 0.0624
= 17.5
Slab wsJls above crest
- 29.5 x 0.0624
= -1.8
= 7.00 < 7.06
OK
OK
to bottom
of cover
+ 11.25 x 0.0624
+ 11.25 x 0.0624
0
%
= ll25
&IlSX.
= z
(1 + li
>
paver.
=
=
=
=
Pmin.
puplift
Pmin. (net)
(5)
= 5.17(1.362)
5.17 < 6.14 ksf, OK
5.17(0.638)
= 3.30 > 0 ksf,
0.0624
x 43.0 = 2.68 ksf
3*30 - 2.68 = 0.62 > 0 ksf,
=
0
= +
5
-
1158.1
; ;$;)
ksf
ksf
= - 129
x (- 2.75)
kips
- 6 = 1119 ft kips
slab
= 6.14
= 7.14
= +n8
x (- 2.75)
x (
ksf,
OK
6 ft
kips
= 7.05 < 7.14 ksf,
OK
OK
OK
No embankment placed, moist soil condition:
Allowable
average pressure = 0 + 2.00 = 2.00 ksf
Allowable
maximum pressure = 0 + 4.00 = 4.00 ksf
Riser less footing
= 175.0 x (- 2.75) = - 481
Footing
= 58.8
( 0
>=
0
233.8
kips
w
= - 481 ft kips
%lS.
z&l+
Paver.
pmin.
= 1.05 ksf < 2.00 ksf, OK
= 0.24 3 0 ksf,
= 1.05(0.230)
~$$+$-)
- 481 ft
= 1.05(1.770)
kips
= 1.85 < 4.00 ksf,
OK
OK
Revised
8-l-68
3 -12
(6)
Flotation
criteria:
Will not count on buoyant weight of submerged embankment over
footing
projections
unless needed.
weight of riser
233.8
m
weight of displaced water = 1800.8 + 392) 0.0624 =137.0
=
1.7 > 1.5, OK
Use 16 x 14 footing.
Footing
Projection
Loadings
The projection
loadings
ity analyses.
(1)
Upstream
Downstream
(2)
u
D
(3)
u
D
(4)
u
D
(5)
u
D
Design
Check on footing
In downstream
Shear:
Strength
are tabulated
Design
in the same order
as the stabil-
(7.62) - (l-75 x 0.15 + 30 x 0.14 = 4.46)
(1.17) - (4.46)
(6.35) - (4.46)
(2.43) - (4.46)
(7.00) - (4.46 + 10 x 0.0624 = 5.08)
(2.82) - (5.08)
(7.05) - (5.08 + 1.25 x 0.0624 = 5.16)
(3.30) - (5.16)
(0.24) - (1.75
(1.85) - (0.26)
x 0.15 = 0.26)
thickness required:
end of sidewall
footing
d = 3290(4.25
projection:
- d/12)
70 x 12
d = 12.6 in.
= 29.7 ft kips/ft
Moment: M = 3.29(4.25)*/2
d = 10.5 in. for balanced stresses
tf z 12.6 + 2.5 = 15.1 in.
In upstream endwsll footing
projection:
Pressure at face of endwall:
P = 3.16(X*23)
thus x = 7.85 ft
where
x = (-ha)
.
and p = 0.95 ksf
16
=
=
=
=
3.16 ksf t
3.29
J
t
1.89
2.03
4
= 1.92
t
= 2.26
= 1.89
= 1.86
$
P
4
= 0.02
= 1.59
s
t
3-13
a
Shear:
d N (31.60 + 950) (5.5 - d/12)
70 x 12
2
d -11.2
,
h
in.
+ 2.2I~(5.5)~/3
= 36.6 ft kips/ft
M = o.95(5.5)*/2
d = 11.7 in. for balanced stresses
2 11.7 + 4.5 = 16.2 in.
Moment:
tf
Assumed thickness
is OK, use tf = 21 in.
Determine footing
steel required:
T & S requires
A,(min.)
= 0.002 x 12 x 16 = 0.38 in*/ft
Design of transverse
steel (perpendicular
to sidewall):
Top steel:
d = 21 - 2.5 = 18.5 in.
Downstream:
M = 29.7 ft kips/ft
As = 1.05 in*/ft
co IT= 3290 x 4.25
= 3.53 in./ft
245 x 7/8 x 18.5
Because of the unknown thickness
of the spigot wall fitting,
this steel should not be placed under the fitting
but should
In order to provide
the
be started ahead of the fitting.
the maximum area required
per foot
same total resistance,
will have to be increased to:
1.29 in.*/ft
& =1.05
Use short length ##&?12, A, = 0.44 in.*/ft
each side of fitting
to provide
for T & S. Use #E&4, A, = 1.33 in.2/ft
for 2.5 ft
Use #6??8, A, = 0.66 in.*/ft
for
starting
ahead of fitting.
next 2.5 ft, then use #@12.
Upstream:
Use #&112, A, = 0.44 > 0.38 in.2/ft
Bottom steel:
d = 21 - 3.5 = 17.5 in.
Downstream:
M = 1.59(4.25)*/2
A, = 0.53 in.*/ft
= 14.4 ft
kips/ft
1590 x 4.25
=O = 350 x 7/t] x 17.5 = 1.26 in./ft
Use #f&6, A, = 0.88 in.*/ft.
Co = 4.71 in./ft,
Change to #[email protected] at 16 - 16(0.44/0.53)
= 2.7 say 3 ft from
downstream
end of footing.
Upstream :
Use#[email protected], As = 0.44 > 0.38 in.*/ft
Revised
8-l-68
3-14
Design of longitudinal
steel (perpendicular
to end-wall):
Top steel:
d = 21 - (2.5 f 1.0) = 17.5 in.
Use #6912, As = 0.44 > 0.38 in.'/ft
Bottom
At
M
A,
steel:
d = PII- - (3.5 + 1.0) = 16.5 in.
face of upstream endwall:
= 36.6 ft kips/ft
= 1.48 in.;?/ft
+ Ooy5) (5.5)
2
V = (3*16
Co =
350
x
11300
718 x 16.5
= 11.3 kips
= 2.24 in./ft
Use #[email protected] and #f&2,
As = 1.64 in.2/ft,
Co = 7*86 in./ft.
Drop
the #[email protected] at anchorage distance downstream qf the downstream face
of endwall.
Design of footing
steel for MVo and VVo:
At center of sidewall:
MVO = 24.9 ft kips/ft,
VVo = 13.8 kips/ft
Assume two layers of steel:
= 21 - (3.5) - (1.0) = 16.5 in.
d
= 6.0 in.
d" = 21/2 - 4.5
%. + vvo (t +-F)
= 24.9 +13.8
VVo d"/12
= 13.8
(0.625 + 0.875) = 45.6
(6.0/d
= 6.9
M,
A = 2.15 in.2/ft
A, = 2.15 - 13.8/20
= 52.5 ft kips/ft
= 1.46 in2/ft
#[email protected] (continuous
#@Z&2 (place
from sidewall
to footing
to sidewall)=
1.20
= 0.44
the #[email protected] 2 in. above this steel)
1.64 > 1.46
in2/ft
Example Plans
PlEUM,
for
consisting
of a layout sheet and three structural
detail
sheets,
the riser designed in this example are shown on the following
pages.
...
,.
-.
,” .._.
E-E
--
N01133S
n3sI~ 03~3~03 auvpws
SNVld
3ldWVi3
V-V
NOl133S
.133HS
33s
9Nl1 VET ON V 5379NV
213v&ww,y1 JO 7/K&w No,
NW-Id
d01
”
_-
w
9
ifii
-
1
t9
5TEEL
STEEL Z” FROM i-O,= OF SLAB
STEEL 2” FRaM BOTTOM OF SLAB
COVER SLAB PLAN
RISER WALL STFELNOTWOWN
E’FROM
SECTION
INSIDE FACE
B-B
re
CUTSlOE
FACE /NSlDE FACE
SECTION
A-A
STEEL 2” FROM OUTSIDE FACE
ENDWALL
STEEL Z-FROM
lN5lDE
COVER 5LAU STEEL NOT SHOWN
BAR TYPES
5m.
FACE
STEEL 2” FRO?., OUTSIDE
SECTION
ELEVATION
TYPE I
5-B
FACE
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