BRIDGE INSIGHT THE COMPLETE GUIDE TO TEMPERATURE …

VOL. 03

TEMPERATUREGRADIENT

THE COMPLETE GUIDE TO

BRIDGE INSIGHT

midas Bridge

The CompleteGuide toTemperatureGradient

CONTENTS

01. What is Temperature Gradient?

2

02. Code Provisions for Temperature GradientLoad on Bridges

3

03. Features in midas Civil for TemperatureGradient Load

6

04. FAQ’s for using Temperature Gradientin midas Civil

9

05. Sample Calculations

11

06. Common Mistakes While AssigningTemperature Gradient Loads in midas Civil

15

The Complete Guide to Temperature Gradient BRIDGE INSIGHT The Complete Guide to Temperature Gradient BRIDGE INSIGHT

What isTemperature Gradient?

-

01

Code Provisions forTemperature Gradient

Load on Bridges

Every code has given certain provisions for temperature gradient loads. Some of them have been listed below.

02

Fig. 1.2 Heat transfer mechanisms

2 3

The heat exchange between the bridge boundary and the

environment is very complex, as shown in Fig 1.1. It is composed

of three principal mechanisms: solar radiation, convection, and

thermal irradiation. Solar radiation is generally considered to be

the most important one among the three mechanisms.

Fig. 1.2 displays the main mechanisms of heat transfer in a

bridge structure: absorption of solar radiation (directly or

reflected) and convection of the ambient air temperature is

natural environmental sources that affect temperature

variations over the depth and width of concrete bridge girder

sections. The exposed surfaces are heated, and in the case of

cross-sections optimized for minimal material with maximum

structural capacity, nonlinear temperature distributions are

produced within the cross-sections and induce self-equilibrat-

ing stresses that can affect the structure’s appearance.

02-1.Indian code(IRC 6:2017)

01-1. IntroductionThe daily changes in ambient temperature and solar radiation intensity lead to differential temperature in bridge superstructures.

These temperature gradient loads induce stresses throughout the depth of the bridge deck. If the top of a beam heats up relative to

the bottom, it tends to expand, while the bottom of the beam would resist this expansion. If the beam is restrained, bending

moment and shear force are generated, leading to additional stresses in the statically indeterminate structure.

Fig. 1.1 Heat exchange between the boundary and the environment

Fig. 2.1 Design Temperature Differences for Concrete Bridge Decks in IRC6:2017

Fig. 2.2 Temperature Differences across Steel and Composite Section in IRC6:2017

The Complete Guide to Temperature Gradient The Complete Guide to Temperature GradientBRIDGE INSIGHT BRIDGE INSIGHT

We can conclude with this that all renowned structural design codes do consider this temperature non-lin-earity. However, the magnitude of temperature and even the units for measurement considered can be different.This has been incorporated in midas Civil in a generalized way to accommodate all possible standards.

4 5

02-2.Eurocode(EN 1991-1-5 (2003))

02-3.AASHTO Code(AASHTO LRFDBridge DesignSpecifications)

4 5

Zone

1

2

3

4

T1 (°F)

54

46

41

38

T2 (°F)

14

12

11

9

Fig. 2.3 Temperature differences for bridge decks Type 1: Steel Decks

Fig. 2.4 Temperature differences for bridge decks Type 2: Composite Decks

Fig. 2.5 Temperature differences for bridge decks Type 2: Concrete Decks

Fig. 2.6Positive Vertical Temperature Gradient in

Concrete and Steel Superstructures

Table 2.3 Basis for Temperature Gradients


Features in midas Civil forTemperature Gradient Load

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03

There are two ways to apply the temperature gradient in midas Civil as per the element type, section type and temperature inputs.

Temperature Gradient Beam section Temperature

03-1.TemperatureGradient

The temperature gradient analysis is applicable for elements with bending stiffness such as

beam and plate elements. In the case of a beam element, enter the temperature difference and

the corresponding distance between the extremities of the element with respect to the local y

and z-axes. In the case of a plate element, the temperature gradient can be represented by the

temperature difference between the upper and lower faces of the plate and the plate thickness.

The gradient temperature produces the following equivalent moments.

As shown in fig 3.1, we can specify the temperature differences between the tops and bottoms

of beam or plate elements for thermal stress analysis.

Where, α is the linear thermal expansion coefficient, E is the modulus of elasticity, I is the

moment of inertia about the relevant axis of the beam element, ΔT is the temperature differ-

ence between the two extremities (outermost faces) of the element, h is the distance between

the two extremities of the beam section, t is the thickness of the plate and υ is the Poisson's

Ratio.

03-1-1.In the case of a beam element

03-1-2.In the case of a plate element

03-2.Beam sectionTemperature

Enter the temperature differences between specific locations of beam for thermal stress

analysis.

In case of Temperature Gradient, only the temperature difference between the top and bottom

of a section can be entered. However, in case of Beam Section Temperature, temperature

differences for certain locations in a section can also be considered.

6 7

Fig. 3.1 Temperature gradient in midas Civil

(a) Beam element (b) Plate element

The Complete Guide to Temperature Gradient The Complete Guide to Temperature Gradient

04-1.How to applytemperaturegradient load foruser definedsections?

Most of the time, for unsymmetrical sections we need to define the section as user defined

either as value type of section or using midas Section property Calculator. Let us consider one

example of Stress due to Temperature Gradient for Simply supported unsymmetrical slab I

girder using Section Property Calculator Tool available in midas Civil. Fig. 4.1 shows the section

as generated in the SPC tool and 4.2 shows the section imported in midas Civil.

Depending upon the non linear

temperaure profile the section will

be divided into parts given in table

4.1. Consider the temperature

gradient profile as per IRC 6:2017

shown in the fig.2.1.

03-2-1. General Section TypeIf a section for which a temperature difference is considered is not a rectangle, the section

should be transformed into an equivalent rectangular section, which produces the identical

moment due to the temperature load. And then the user needs to input the width and height

of the equivalent rectangular section as shown in fig.3.2.

03-2-2. PSC Section TypeFor PSC sections (except for Value type PSC sections) and Composite sections, which are

relatively complex but frequently used, the program automatically defines the temperature

load by dividing and transforming the corresponding zone. In case of PSC section as shown in

the figure above, the transformed rectangular zone can be automatically calculated by

selecting the PSC/Composite option instead of manual calculation.

As per IRC6:2017, we can provide the temperature gradient for PSC and Steel Composite

girders for positive and reverse temperature difference as shown in the fig. 3.3.

FAQ’s for using TemperatureGradient in midas Civil

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Some of the frequently asked questions while using temperature gradient load in midas Civil are listed here.

04

BRIDGE INSIGHT BRIDGE INSIGHT

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Fig. 3.2 Temperature Gradient and Beam Section Temperature in midas Civil

Fig. 3.3 Beam section Temperature in midas Civil

Fig. 4.1 Section in SPC Fig. 4.2 Section in midas Civil

Part

1

2

3

Area

0.380

0.363

0.162

Height

0.150

0.250

0.150

Width

2.531

1.450

1.077

Table 4.1 Area of each part


SampleCalculations

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In this section, the manual calculations verifying the beam section temperature application is provided. Since this loading is inherently non-linear, the stress for this can’t be obtained with simply flexural and axial stress equations. Instead, the eigen stresses need to be calculated. The process for this calculation would be discussed with a simple example.

05

Example 1

Given Data

Stress calculation for simply supported RCC I girder bridge for temperature gradient load.

The PSC type sections will be created 10 stress points where

the stresses can be displayed using Beam detail analysis shown

in fig. 5.1.

These final temperature, height and width for each part

will be mentioned in the table 4.2 will input in midas Civil

Beam section temperature option selecting the General

type of section as given in fig.4.3. The method of tempera-

ture input will be same as PSC/Composite section type

except the width option.

10


11

Part

1

2

3

2.531

1.450

1.077

H1

H2

H1

H2

H1

H2

Height

m

0.000

0.150

0.150

0.400

2.325

2.475

T1

T2

T1

T2

T1

T2

Temperature

deg

17.8

4

4

0

0

2.1

B

m

Table 4.2 Beam Section Temperature input in MIDAS

Fig. 4.3 General type section Fig. 5.1 Cross section of girder with temp gradient profile

= 23536

= 0.000017

= 0.375

= 450000

= 46093750000

N/mm2

/0C

m

mm2

mm4

Young's Modulus: E

Coefficient for thermal expansion:

CG of section from top: ztop

Cross section area: A

Section modulus: Iyy


For Row 1

Sample calculations for first two rows of table 5.1 are given below.

Similar calculations are done for complete height of the section and the output could be referred to in the table below.

The temperature gradient input in midas Civil as shown in the fig. 5.2 and the stress results for same are shown in fig. 5.3.

12 13

Fig. 5.2 Temperature gradient input in midas Civil

Table 5.1 Calculation of Eigen stresses for temperature gradient

Table 5.2 Calculation of final stresses for temperature gradient

Stress due temp. Resistance (σ) = E x α x T = 23536 x 0.000017 x 30.0 = 8.261 Mpa Force (F) = b x σ = 1.0 x 8.261 = 8.261 MN/m Axial stress due to resultant force (F/A) = 0 Mpa CG of Force from top of slab (z') = 0 m Moment of force about Top of Slab (M') = F/A x z' = 0.00 x 0.00 = 0.00 MN-m

Stress due temp. Resistance (σ) = E x α x T = 23536 x 0.000017 x 7.0 = 1.928 Mpa Force (F) = b x σ = 1.0 x 1.928 = 1.928 MN/m Axial stress due to resultant force (F/A) = 0.5 x (8.261+1.928) x (0.25-0.0)/ (450000 x 10^-6) = 2.830 Mpa

CG of Force from top of slab (z') = (2 x 1.928 + 8.261)/ (1.928 +8.261) x (1.928 -8.261)/3+1.928 = 0.099 m

Moment of force about Top of Slab (M') = F x z’ = (F/A) x A x z’ = 2.830 x 450000 /10^6 x 0.099 = 0.12625 MN-m

For Row 2

Fiber No

units

1

2

3

4

5

6

Dist. Offiber from

the top

z

m

0.00

0.25

0.25

0.50

0.75

1.00

Temp.at fiber

T

0C

30.0

7.0

7.0

0.0

0.0

10.0

Width offiber

b

m

1.0

1.0

0.2

0.2

0.4

0.4

Stress duetemp.

resistance

σ

Mpa

8.261

1.928

1.928

0.00

0.00

2.754

Force

F

MN/m

8.261

1.928

0.386

0.00

0.00

1.101

Axial stressdue to

resultant force

F/A

MPa

0.00

2.830

0.00

0.107

0.00

0.306

CG of Forcefrom top of

slab

z'

m

0.00

0.099

0.250

0.333

0.00

0.917

Moment offorce aboutTop of Slab

M'

MN-m

0.00

0.12625

0.00

0.01607

0.00

0.12625

Location

Pos - 1

Pos - 5

Mid

Pos - 9

Pos - 4

Stress due to (Mpa)

Temperature

-8.261

-1.928

0.00

0.00

-2.754

Axial

3.243

3.243

3.243

3.243

3.243

Bending

2.268

0.756

-0.756

-2.268

-3.781

Temperature + Axial + Bending

(Mpa)

-2.750

2.072

2.487

0.975

-3.291

(kg/cm2)

-28.040

21.128

25.364

9.942

-33.561

Total Force = SUM (F/A) x A = 1.45947MN = 1459.47 kNCG of force from the top of the section = SUM (M’)/ Total Force = 268.487 / 1459.467 = 0.1840 m

Moment due to temp. Effect = 1459.47 x (0.375 – 0.184) = 278.81 kNm


Common Mistakes WhileAssigning Temperature Loads

in midas Civil

06

06-1.Improper inputswhile definingtemperaturegradient load

While defining the inputs data in Beam section temperature option, we need to ensure that the

units in which the data is being feed in the software and the actual unit in the software are the

same. As it could be noted in figure 6.1, the magnitude of input clearly suggests that the input

should be in Celsius and meter unit. However, the units selected in midas Civil are Fahrenheit

and centimeter. This will clearly lead to unexpected results.

The temperature input to be provided at different heights is with reference to the initial system

temperature as indicated in figure 6.2.

06-2.Assigningtemperatureloads in constructionstage analysis

Generally, the temperature loads are defined for service condition. However, if it is required to

check temperature gradient loads in the construction stage, then we can define the tempera-

ture gradient load in a load group and activate it in a dummy stage with 0 days duration (Refer

fig. 6.3). One more dummy stage needs to be defined to deactivate the temperature loads

immediately after this to ensure that the temperature gradient load does not lead to any creep

effect in the structure.

The comparison made for final stresses at top and bottom fibers of section due to

temperature gradient shown in the table 5.3.


14 15

Fig. 5.3 Stresses at top and bottom of girder in midas Civil

Most common mistakes while defining temperature gradient loads in midas Civil are introduced here.

Summary

Table 5.3 Comparison of stresses from manual calculation and midas Civil

Stresses

Top

Bottom

Manual Calculations

-2.750

-3.291

midas Civil

-2.750

-3.291

Improper inputs while defining temperature gradient load

Assigning temperature loads in construction stage analysis

The section type selection as the General type or PSC/Composite type


16 17

Fig. 6.1 Incorrect units Fig. 6.2 Initial temperature

Fig. 6.3 Adding Temperature Gradient load in construction stage

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