حساب مقدار الازاحة الناتجة عن التغير الحراري للقسم العلوي من الجسر
Understanding temperature variations in bridge design
Reference: New Mexico Department of Transportation (NMDOT)
Forces, stresses, and
movements in bridge components and members due to temperature variations (both
atmospheric and in construction materials) must be calculated and provided for in such items as
elastomeric bearing pads,
expansion bearing devices,
deck joint sealing systems,
and deck joint openings.
* Generally
the effect of temperature gradient need not be considered
|
خلاصة حساب
مقدار الازاحة الناتجة عن التغير الحراري للقسم العلوي من الجسر Summary
of total superstructure movement due to
temperature 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. Thermal expansion
coefficient conversions are given by: Steel: ΔL = L×0.000078×ΔT Concrete: ΔL = L×0.000072×ΔT where: L = Length of the bridge that
will move due to temperature changes (ft.) Each abutment will receive half of
the total bridge movement. L = 44 ft. + 43.75 ft. = 87.75 ft. ∆T = 80° F the Design Guide also says, “The
thermal movement used in the design of elastomeric bearing pads shall be not
less than 75% of the total anticipated movement due to temperature ∆L = 87.75 ft.´ 0.000072 ´ 80°F ´ 75% = 0.38in. The total superstructure movement due
to temperature, shrinkage, and creep is then: Δs = 0.38 + ΔCreep SH= 0.65 in. |
Creep: Increase in strain with time due to a sustained load Creep
Concrete Creep - The time
dependent increase of strain in hardened concrete
subjected to sustained stress is defined as concrete creep
armoring
angles and an elastomeric compression seal.
prestress loss. The loss from elastic shortening should be included in both initial and total loss computations.
Normal
Weight Concrete—Concrete having a
weight between 0.135 and 0.155 kcf.
Elastic—A structural material behavior in which the ratio of stress to
strain is constant, the material returns to its original unloaded state upon
load removal.
Inelastic—Any structural behavior in which the ratio of stress and strain is
not constant, and part of the deformation remains after load removal.
Yield
Line—A plastic hinge
line.
Yield
Line Method—A method of
analysis in which a number of possible yield line patterns are examined in
order to determine load-carrying capacity
Stiffness—Force effect resulting from a unit deformation
Lightweight Concrete—Concrete containing lightweight aggregate and having an air-dry unit weight not exceeding 0.120 kcf, as determined by ASTM C567. Lightweight concrete without natural sand is termed “all-lightweight concrete” and lightweight concrete in which all of the fine aggregate consists of normal weight sand is termed “sandlightweight concrete.”
Masonry
Plate The bottom steel
plate that connects the bridge bearing to the pedestal
Pedestal
A concrete or built-up metal member constructed on top of a bridge seat or pier
for the purpose of providing a bearing seat at a specific elevation
Plastic
Deformation Displacements that
occur outside the elastic range of the member, where the member does not return
to its original undeformed shape when the load is removed.
Redundant Containing multiple load paths such that if a failure occurs in
any one member, the structure would not collapse. (Typically refers to bridge
superstructure.)
Retrofit Work done to an existing structure for the purpose of upgrading
details that do not meet current standards.
AADT Average Annual Daily Traffic
ADT Average Daily Traffic
ADTT Average Daily Truck Traffic
reference:
Dornsife, R.J. "Expansion Joints."
Bridge Engineering Handbook.
Ed. Wai-Fah Chen and Lian Duan
Boca Raton: CRC Press, 2000
Expansion Joints
ch25 هذا هو Expansion Joints.pdf
25.2 General Design Criteria
Expansion joints
must accommodate movements produced by concrete shrinkage and creep, post-
tensioning shortening, thermal variations, dead and live loads, wind and
seismic loads, and structure settlements. Concrete shrinkage, post-tensioning
shortening, and thermal variations are generally taken into account explicitly
in design calculations. Because of uncertainties in predicting, and the
increased costs associated with accommodating large displacements, seismic
movements are usually not explicitly included in calculations.
Expansion joints
should be designed to accommodate all shrinkage occurring after their instal- lation. For unrestrained concrete, ultimate shrinkage
strain after installation, b, may be estimated
as 0.0002 [1]. More-detailed
estimations can be used which include the effect of ambient relative humidity
and volume-to-surface ratios [2]. Shrinkage shortening of the bridge deck, Dshrink, in
mm, is calculated as
Δshrink= (b)· (µ)· (Ltrib)
· (1000 mm/m) (25.1)
where
Ltrib
=tributary length of structure subject to shrinkage; m
b = ultimate shrinkage strain after expansion joint
installation; estimated as 0.0002 in lieu of more-refined calculations
µ = factor
accounting for restraining effect imposed by structural elements installed
before slab is cast [1]
= 0.0 for steel
girders, 0.5 for precast prestressed concrete girders, 0.8 for concrete box
girders and T-beams, 1.0 for flat slabs
Thermal
displacements are calculated using the maximum and minimum anticipated bridge
deck temperatures. These extreme values are functions of the geographic
location of the structure and the bridge type. Thermal movement, in mm, is
calculated as
Dtemp= (a)· (Ltrib)· (dT) · (1000 mm/m) (25.2)
where
α= coefficient of thermal expansion;
0.000011 m/m/°C for concrete and 0.000012 m/m/°C for steel
Ltrib
= tributary length of structure subject to thermal variation; m
dT = temperature variation; °C
Any other predictable movements following
expansion joint installation, such as concrete post- tensioning shortening and
creep, should also be included in the design calculations.
==================================
==================================
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.
Design Code Page 39
2018_Bridge_Procedures_and_Design_Guide.pdf
3.1.7.1 Temperature
Forces, stresses, and
movements in bridge components and members due to temperature variations (both
atmospheric and in construction materials) must be calculated and provided for in such items as
elastomeric bearing pads, expansion bearing devices, deck joint sealing
systems, and deck joint openings.
New Mexico temperature ranges used
in movement and force calculations are listed in Table 3.1A.
Temperature
Ranges
|
Elevation Less than
4500 Feet Above Sea Level المناطق الحارة |
||
|
Structure Type |
Temperature Range |
Min/Max design temperature |
|
Steel |
120°F |
(0° to 120°F) |
|
Concrete |
80°F |
(10° to 90°F) |
|
Elevation Greater than
4500 Feet Above Sea Level المناطق الباردة |
||
|
Structure Type |
Temperature Range |
Min/Max design temperature |
|
Steel |
130°F |
(-20° to 110°F) |
|
Concrete |
80°F |
(0° to 80°F) |
Note: Each bridge location should
be evaluated for average temperature to make sure the elevation of 4500 ft. is applicable.
The full temperature range is used
in design of the superstructure and substructure because the structure is
anticipated to have these full movements during its life.
The thermal movement used in the
design of elastomeric bearing pads shall be not less that 75% of the total
anticipated movement due to temperature. The assumption made is that the
girders will not be placed on the pads at the upper or lower end of the
temperature range.
The designer shall specify the
range of temperature in which the girders shall be placed.
Unless a more precise method of measuring the temperature of the
girders is used, the setting temperature of the girders or bridge component
shall be taken as the average of the actual air temperature over the 24-hour period
immediately before the setting of the girders or component.
The size of deck joint seals and
required deck openings may be found in the appropriate standard drawings issued
by the Department.
These standards consider factors in
addition to temperature, such as creep and shrinkage. If the movement length of
a structure exceeds that given in the standard drawings, a special joint seal
may be required. If situations arise which require special consideration,
contact the State Bridge Engineer for assistance.
Thermal expansion coefficient
conversions are given by:
Steel: ΔL = L×0.000078×ΔT
Concrete: ΔL = L×0.000072×ΔT
where ΔL is
expressed in inches and
L is expressed in feet and
ΔT, the
change in temperature, is in °F.
Generally the effect of temperature
gradient need not be considered.
end of Design Code Page 39
=========================================
LRFD_Design_Example.pdf page 36
4.4.1 Abutment
(Exp.) Bearing Pad Design
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:
Table 3.1B of the Design Guide specifies
temperature ranges based on the values given in the LRFD Specification Section
3.12.2.
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. The Design Guide states, “The full
temperature range is used in design of the superstructure because the structure
is anticipated to have these full movements during its life.” However, the Design Guide also says, “The
thermal movement used in the design of elastomeric bearing pads shall be not
less than 75% of the total anticipated movement due to temperature.”
∆L
= L ´ 0.000072 ´ ∆T
where:
L = Length of the bridge that will
move due to temperature changes (ft.) Each abutment will receive half of the
total bridge movement.
L = 44 ft. + 43.75 ft. = 87.75 ft.
∆T = 80° F
∆L = 87.75 ft.´ 0.000072 ´ 80°F ´ 75% = 0.38in.
The total superstructure movement due to temperature,
shrinkage, and creep is then:
Δs = 0.38 + 0.27 = 0.65 in.
Where
(see page 38)
Δcreep shrinkage = ΔSPAN _1 + ΔSPAN _2 /2
ΔCR+SH = 0.081in. + 0.385in. / 2 = 0.27 in.
as follow
========================
5.
SUBSTRUCTURE AND FOUNDATION DESIGN
page 43
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 88 يساوي 44 Change in temperature is specified as 80°F for concrete bridges in the Design Guide.
The Auto Load Generation screen for Temperature Load is shown below. Once all
these values are entered, click Generate.
Remember:
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
NDOT Structural manual chapter 9Expansion joints مفصل.pdf