حساب مقدار القوى الناتجة عن الزحف والانكماش للجسر
Understanding Creep and Shrinkage in bridge design
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خلاصة
حساب الزحف والانكماش Creep and Shrinkage |
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LRFD_Design_Example.pdf 4.4
Bearing Pad Design 4.4.1
Abutment (Exp.) Bearing Pad Design
page 36 من
التحليل نحصل على أربع قيم لكل مجاز Beam shortening (PL/AE) Concrete shrinkage loss, final Concrete creep loss, final Initial total prestress loss منها
نحسب الاستطالة لكل مجاز هكذا Δspan_1= Beam
shortening (Concrete shrinkage loss, final
+ Concrete creep loss, final) /
Initial total prestress loss نجمع
استطالات المجازين ΔCr
Sh= Δspan_1 + Δspan_2 |
|
قلنا
من التحليل نحصل على أربع قيم لكل مجاز كيف؟ من هذا المثال PrecastBeamExample-1.pdf وهذا مثال FlatSlabExample.pdf |
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5. SUBSTRUCTURE AND FOUNDATION DESIGN LRFD_Design_Example_New Mexico PRESTRESSED CONCRETE GIRDER BRIDGE DESIGN.pdf page 43 عندنا ثلاثة مجازات , استطالة
المجازات الطرفية تحمل من قبل الركائز الطرفية تبقى لدينا استطالة المجاز الوسطي
فقط تحمل بواسطة الركيزتين الوسطيتين أي ان كل ركيزة ستحمل نصف إزاحة المجاز
الوسطي المحسوبة أعلاه As calculated above Δspan_2= 0.385in. ΔLCR&SH
= Δspan_2 / 2 = 0.385in / 2 = 0.1925
in |
Alaska
Bridges and Structures Manual September
2017
Alaska_bridge_manual.pdf
11.
Structural Systems and Dimensions
11.4.
General Design Considerations
11.4.7.
Foundation Considerations
Settlement
Limits
Experience
demonstrates that bridges can
accommodate
more settlement than traditionally
allowed in
design due to creep, relaxation, and
redistribution
of force effects. LRFD Article
10.6.2.2.1
mandates that settlement criteria be
developed
consistent with the function and type of
structure,
anticipated service life, and consequences
of
unanticipated movements on service performance.
12. Loads and Load Factors
12.3.
Transient Loads
12.3.1. General
The LRFD
Specifications recognize 19 transient loads,
which integrate
static water pressure, stream pressure,
buoyancy, and
wave action as water load, WA. The
LRFD
Specifications elevate creep, settlement,
shrinkage, and
temperature (CR, SE, SH, TU, and TG)
in importance
to “loads,” being superimposed
deformations
which, if restrained, will result in force
effects. For
example, restrained strains due to
increasing
uniform temperature induce compression
forces.
14.
Structural Concrete page 139
14.4.
Prestressed Concrete Girders
14.4.1. General
The generic
word “prestressing” relates to a method of
construction in
which a steel element is tensioned and
anchored to the
concrete. Upon release of the
tensioning
force, the concrete will largely be in
residual
compression and the steel in residual tension.
There are three
methods of applying the prestressing
force, as
discussed below. Only two of these
methods,
pretensioning and post-tensioning, are
acceptable, and
a combination of these two methods is
acceptable if
approved by the Chief Bridge Engineer.
Pretensioning: In the
pretensioning method,
tensioning of
the steel strands is complete before
placing the
concrete. When the concrete surrounding
the steel
strands attains a specified minimum strength,
the strands are
released thereby transmitting the
prestressing
force to the concrete by bond-and-wedge
action at the
girder ends. The initial prestress is
immediately
reduced due to the elastic shortening of
the concrete.
Further losses will occur over time due
to shrinkage
and creep of concrete and relaxation of
prestressing
steel.
The generic
word “prestress” is often used to mean
“pretensioning”
as opposed to “post-tensioning.”
Post-Tensioning:
In
the post-tensioning method,
tensioning of
the steel is accomplished after the
concrete has
attained a specified minimum strength.
The tendons,
usually comprised of numerous strands,
are loaded into
ducts cast into the concrete. After
stressing the
tendons to the specified prestressing
level, they are
anchored to the concrete and the jacks
are released.
Several
post-tensioning systems and anchorages are
used in the
United States; the best information may be
directly
obtained from the manufacturers.
Post-tensioned
concrete is also subject to losses from
shrinkage and
creep, although at a reduced magnitude
because a
significant portion of shrinkage usually
occurs by the
time of stressing, and the rate of creep
decreases with
the age at which the prestress is
applied. After
anchoring the tendons, the ducts are
pressure filled
with grout, which protects the tendons
against
corrosion and provides composite action by
bonding the
strand and the girder. Post-tensioning can
be applied in
phases to further increase the loadcarrying
capacity and
better match the phased dead
loads being
applied to the girder.
19.
Expansion Joints and Bearings
19.1.
Expansion Joints
Reference: LRFD Articles
14.4 and 14.5
19.1.2.
Expansion Joint Selection and Design
Reference: LRFD Article
14.5.3.2
Table 19-2
presents the types of expansion joints used
by DOT&PF
and their maximum joint movement.
Select the type
of expansion joint and its required
movement rating
based on the expansion and racking
demands, skew,
gap widths, and whether the joint is
new or a
retrofit.
Gap width is
the perpendicular distance between the
faces of the
joint at the road surface. Use a minimum
gap of not less
than 1 inch for steel bridges. The gap
for concrete
bridges may be less than 1 inch where
creep and
shrinkage must be considered. Use a
maximum gap
width of 4 inches for strip seals and 3
inches for
individual components of modular joints.
19.2.
Bearings page 242
19.2.1. General
Reference: LRFD Articles
14.4, 14.6, and 14.8
Movements
Bridge bearings
accommodate superstructure
movements and
transmit the loads to the substructure.
The consideration
of movement is important for
bearing design,
which includes both translations and
rotations. The
sources of movement include initial
camber or
curvature, construction loads,
misalignment,
construction tolerances, settlement of
supports, thermal
effects, creep, shrinkage, seismic,
and traffic
loading.
19.2.2. Bearing
Types
Steel-reinforced
elastomeric bearings are typically the
first option
for all new bridges. Bridges with large
movements
resulting in excessive bearing pad heights
may require
sliding surfaces.
In general, the
bridge engineer should restrain vertical
displacements,
allow rotations to occur as freely as
possible, and
either accommodate or restrain
horizontal
displacements. Distribute the loads among
the bearings in
accordance with the superstructure
analysis.
The bridge
engineer may use sole plates for steel
girders to
distribute the load uniformly.
Steel-Reinforced Elastomeric Bearings
These bearings are usually the preferred low-cost
option and require minimal maintenance.
Limit the height of steel-reinforced elastomeric
bearings to 6 inches. Provide elastomeric fixed
bearings with a horizontal restraint (typically, a row of
dowels connecting the diaphragm to the cap beam)
adequate for the full horizontal load.
Polytetrafluoroethylene
(PTFE) Sliding Surfaces
Reference: LRFD Article
14.7.2
Where
horizontal movements result in steel-reinforced
elastomeric
bearing pads exceeding the 6-inch height
limit, use a
combination bearing. These bearings use
a
steel-reinforced elastomeric pad to accommodate
rotation and a
stainless steel plate/PTFE sliding
surface to provide
translational capability. See
Appendix 19.A
for a design procedure and example.
Seismic
Isolation Bearings
There are
various types of seismic isolation bearings,
most of which
are proprietary. See the AASHTO
Guide
Specifications for Seismic Isolation Design and
the FHWA Seismic
Retrofitting Manual for Highway
Structures:
Part 1 – Bridges for detailed information.
Isolation
bearings increase the fundamental period of
vibration of
the bridge resulting in lower seismic
forces.
Although this period shift lowers the seismic
forces, it
increases the seismic displacements.
Isolation
bearings also provide improved damping
characteristics
to limit the seismic displacement
demands.
Consider cold
climate behavior when selecting
seismic
isolation bearings; the preference is to use
friction
pendulum bearings. Friction pendulum
bearings are
proprietary and require sole-source
procurement.
Chapter 23 discusses
the use of seismic isolation
bearings on
bridge rehabilitation projects.
19.2.3. Design
of Steel-Reinforced
Elastomeric
Bearings
Reference: LRFD Articles
14.7.5
Steel-reinforced
elastomeric bearings may become
excessively
large if they are designed for loads greater
than
approximately 650 kips. Although no limiting
maximum design
load is specified, the maximum
practical load
capacity of a steel-reinforced
elastomeric
bearing pad is approximately 750 kips. If
the design
loads exceed 650 kips, the bridge engineer
should check
with manufacturers for availability.
Orientation
Orient
elastomeric pads and bearings so that the long
side is
parallel to the principal axis of rotation.
Holes in
Elastomer
Do not use
holes in steel-reinforced elastomeric
bearings.
Edge Distance
For elastomeric
pads and bearings resting directly on a
concrete bridge
seat, use 3 inches as the minimum
edge distance
from the edge of the pad to the edge of
the concrete
seat.
Elastomer
Use Grade 5, natural rubber for steel-reinforced
elastomeric bearings. Indicate the bearing loads and
elastomer grade in the contract documents.
Design Method
Use the Method
B procedure in the LFRD
Specifications for the design
of steel-reinforced
elastomeric
bearings. Method B requires additional
acceptance
testing.
The minimum
elastomeric bearing length or width
shall be 6
inches. Provide a minimum of 0.25 inches
of cover at the
edges of the steel shims. Use 100
percent of the
total movement range previously
specified in
Table 19-1 for the design of bearings.
This practice
assumes that the bearing is installed at
the maximum or
minimum design temperature.
DOT&PF
practice increases the LRFD design value of
65 percent of
the total movement as specified in
LRFD Article
14.7.5.3.2.
New Mexico PRESTRESSED CONCRETE GIRDER BRIDGE DESIGN
design procedures for a three-span prestressed concrete girder
bridge
EXAMPLE NO.1: PRESTRESSED CONCRETE GIRDER BRIDGE DESIGN
4.4 Bearing Pad Design
Elastomeric bearing pads, plain or reinforced, are typically used
on bridges in New Mexico. The LRFD
Specifications give two design procedures for
reinforced elastomeric pads in Sections 14.7.5 (Method B) and 14.7.6 (Method
A). The stress limits
associated with Method A usually result in a bearing with a lower capacity than
a bearing designed using Method B. This increased capacity resulting
from the use of Method B requires additional testing and quality control. The
Department prefers to use Method A as it is a conservative design and requires
less testing (See Chapter 7 of the Design Guide).
Assume that transverse movement at all bearings will be
prevented by concrete keeper blocks or by other
methods. In addition, the pier bearings are considered fixed in the longitudinal
direction. Longitudinal movements are unrestrained at the expansion bearings. As discussed below, the Design Guide specifies temperature ranges to
be used in calculating structure movements in New Mexico.
The design method presented in the LRFD Specifications differentiates
between locations where shear deformations are permitted and where they are
not. The fixed bearings are prevented from deforming in
shear by the dowels or by other methods. At the expansion bearings,
shear deformations will occur.
===============================
4.4.1 Abutment (Exp.) Bearing Pad Design page
36
Loads
The (unfactored)
forces can be obtained from the Service I shear and moment envelope in the
program output. These same forces can be obtained using the method shown for live
load on the following page. Bearing pad design is based on live load forces
without the addition of an impact allowance.
RDL Deck. = 21.1 kips
RDL Diaphragm. = 0.1 kips
RDL Prec. DC = 3.1 kips
RDL Comp DC = 2.9 kips
RDL Comp DW = 2.5 kips
Live loads are given in the program output per lane with no distribution factor and no
impact.
These loads can be found from the Analysis screen as shown below. To find live
loads
at the abutment, select Load Case from the Type pull down. Next, in the Span
pull
down,
select span 01. Finally, from the Cases pull down, select the maximum shear
live
load (lane, truck, double truck, or permit)
shear.
As
shown in the above figure, Fy at Support 1 is 13.13 kips for the lane load.
Adding this
to
the truck load of 54.36 kips at the same support, we get a total of 67.5 kips.
This is the
load
per lane. The shear distribution factor for the beam we are designing is 0.879,
giving
us the design live load for bearings shown below.
RLL Total = 67.5 kips/Lane x DFShear = 67.5 kips/Lane x 0.879 = 59.33 kips/Beam
Structure Movement
In the longitudinal
direction, superstructure movement occurs due to the combined effects of
temperature changes plus creep and shrinkage of the prestressed girders.
Temperature: see page 38
Shrinkage and Creep:
Movement
due to shrinkage and creep can be found from time dependent losses in the
program output. The values from the program output are consolidated in the
following table.
|
Symbol |
Description |
Span 1 |
Span 2 |
|
ΔES |
Beam
shortening (PL/AE) |
0.077
in |
0.455
in |
|
ΔfpSH |
Concrete
shrinkage loss,
final |
10.88 ksi |
10.87
ksi |
|
ΔfpCR |
Concrete
creep loss, final |
7.02 ksi |
22.06
ksi |
|
ΔfpES |
Initial
total prestress loss |
8.55
ksi |
19.44
ksi |
Δspan_1= Beam
shortening (Concrete shrinkage
loss, final + Concrete creep loss, final) / Initial total prestress loss
ΔCr Sh= Δspan_1 + Δspan_2
Because
bearings at the piers are fixed, all of the movement from Span 1 and half of the
movement of Span 2 is assumed to be taken up by the bearings at Abutment 1.
Also, 50% of the total creep and shrinkage is assumed to occur before beam
erection. Steel relaxation is neglected. Calculations for both spans are shown
below. This approach is derived from the NYSDOT Bridge Manual, 1st edition
with Addendum, 2010.
Alternatively,
LRFD Specification Section 5.4.2.3 could be used
ΔCR SH = 0.081in. 0.385in./ 2 = 0.27in.
The
total superstructure movement due to temperature, shrinkage, and creep is then:
Δs = 0.38
+ 0.27 = 0.65 in.
Where 0.38 is Temperature: see page 38
End of 4.4.1 Abutment (Exp.)
Bearing Pad Design page 36
===============================
5. SUBSTRUCTURE AND FOUNDATION DESIGN
LRFD_Design_Example_New
Mexico PRESTRESSED CONCRETE GIRDER BRIDGE DESIGN.pdf page 43
As calculated
above Δspan_2= 0.385in.
ΔLCR&SH
= Δspan_2 / 2 = 0.385in
/ 2 = 0.1925 in
هذا كان ما يخص الزحف والانكماش ونكمل
موضوع الاحمال الحرارية كون الطول المشارك (المقدر 77.41 قدم) متعلق بالزحف والانكماش
كما سنلاحظ ادناه
Temperature,
creep, and shrinkage are the final loads that need to be entered. RC-PIER
contains
individual load screens for each of these. However, for this example, we have
chosen
to include the creep
and shrinkage
movement with the temperature
by calculating
a
contributing length that results in the same structural movement as the sum of
the three.
Pier 1 & 2 bearings are fixed and
each takes half the thermal, creep, and shrinkage
movement from Span 2. (Span 1 movement
is taken up by the expansion bearing at the
abutment.) من هنا نأخذ نصف طول المجاز الوسطي نصف
88 يساوي 44
Change
in temperature is specified as 80°F for concrete bridges in the Design Guide.
للتذكير هذه معادلة معامل الاستطالة بتأثير الحرارة نطبق عليها
الشرطين أعلاه
Steel: ΔL = L×0.000078×ΔT
Concrete: ΔL = L×0.000072×ΔT
From Table 3.1B for “South of I-40”, structure movement is to be
based on a temperature range from 10° F to 90° F from where Change in temperature =
90-10=80
The
Auto Load Generation screen for Temperature Load is shown below. Once all
these values are entered, click Generate.
25.6.1 Modular Bridge Expansion Joints
Modular bridge expansion joints (MBEJ),
25.6.2 Design Example 3
Given
Two
cast-in-place post-tensioned concrete box-girder bridge frames meet at an
intermediate pier where they are free to translate longitudinally. Skew angle
is 0° and bridge deck ambient temperatures range from –15 to 50°C. A MBEJ will
be installed 60 days after post-tensioning operations have been completed.
Specified creep is 150% of elastic shortening. Assume that 50% of shrinkage has
already occurred at installation time. The following longitudinal movements
were calculated for each of the two frames:
|
|
Frame A |
Frame B |
|
Shrinkage |
30 mm |
15 mm |
|
Elastic shortening |
36 mm |
20 mm |
|
Creep (1.5 × elastic
shortening) |
54 mm |
30 mm |
|
Temperature fall (20 to –15°C) |
76 mm |
38 mm |
|
Temperature rise (20 to 50°C) |
66 mm |
33 mm |
Find
MBEJ
size required to accommodate the total calculated movements and the
installation gaps
measured
face to face of edge beams, “Ginstall,” at 5, 20, and 30°C.
Solution
page 14
Elastomeric bearing overview
Shore A Durometer hardnesses of
60±5 are common, and they lead to shear modulus values in the range of 80 to 180 psi. (0.5 – 1.2 Mpa)
The shear stiffness of the bearing is its most important property since it
affects the forces transmitted between the superstructure and substructure.
Some states use a slightly different common range than stated above. See
S14.7.5.2 and S14.7.6.2 for material requirements of neoprene bearing pads.
Elastomer may be used as a plain
pad (PEP) or may be reinforced with steel. Steel reinforced elastomeric
bearings are composed of layers of elastomer and steel plates bonded together
with adhesive.
Elastomers are flexible under shear
and uniaxial deformation, but they are very stiff against volume changes. This
feature makes the design of a bearing that is stiff in compression but flexible
in shear possible. Under uniaxial compression, the flexible elastomer would
shorten significantly and, to maintain constant volume, sustain large increases
in its plan dimension, but the stiff steel layers of the steel reinforced
elastomeric bearings restrain the lateral expansion.
Elastomers stiffen at low
temperatures. The low temperature stiffening effect is very sensitive to the
elastomer compound, and the increase in shear resistance can be controlled by
selection of an elasotmer compound which is appropriate for the climatic
conditions.
The design of a steel reinforced
elastomeric bearing requires an appropriate balance of compressive, shear and
rotational stiffnesses. The shape factor, taken as the plan area divided by the
area of the perimeter free to bulge, affects the compressive and rotational
stiffnesses, but it has no impact on the translational stiffness or deformation
capacity.
The bearing must be designed to
control the stress in the steel reinforcement and the strain in the elastomer.
This is done by controlling the elastomer layer thickness and the shape factor
of the bearing. Fatigue, stability, delamination, yield and rupture of the
steel reinforcement, stiffness of the elastomer, and geometric constraints must
all be satisfied.
1 psi = 6,894.76 pascals