power point presentation thermal gradient

Thermal Stresses

Thermal Stresses in Concrete

P.K. Mehta and P.J.M. Monteiro, Concrete: Microstructure, Properties, and Materials


Introduction

Importance

Technological Aspects

Case Study – LA Cathedral



History

Original work of Roy W. Carlson, R.E. Davis, M. Polivka, etc.

How to measure stresses and strain in dams?



Thermal stresses

where:σt: tensile stressKr: degree of restraintE:elastic modulusα: coefficient of thermal expansion∆T: temperature changeϕ: creep coefficient

σ t =K r

E1 + ϕ

α∆T



Degree of Restraint ( Kr )

A concrete element, if free to move, would have no stress.

In practice, the concrete mass will be restrained either externally by the rock foundation or internally by differential deformations.

For example, there will be full restraint at the concrete-rock interface ( Kr = 1.0), however, as the distance from the interface increases, the restraint will decrease .

The same reasoning can be applied to determine the restraint between different concrete lifts.



Degree of Restraint

When dealing with a non-rigid foundation, ACI-207.2R recommends the following multipliers for Kr

multiplier =1

1+Ag E

Af Ef

where:Ag: gross area of concrete cross sectionAf: area of foundation or other restraining element. (For

mass concrete on rock, Af can be assumed as 2.5 Ag.)Ef: modulus of elasticity of foundation or restraining element.E: modulus of elasticity of concrete.



Coefficient of Thermal Expansion



Temperature Evolution

∆T = placement temperature of fresh concrete + adiabatic temperature rise - ambient or service temperature - heat

losses.



Temperature of fresh concrete

Precooling of fresh concrete is a good method of controlling the subsequent temperature drop.

Chilled aggregates and/or ice shavings are specified for making mass concrete mixtures in which the temperature of fresh concrete is limited to 10 oC or less.

During the mixing operation the latent heat needed for fusion of ice is withdrawn from other components of the concrete mixture, providing a very effective way to lower the temperature.

Use of liquid nitrogen.

Cast at night or early in the morning



Adiabatic temperature rise

The rate and magnitude of the adiabatic temperature riseis a function of the amount, composition and fineness of cement, and its temperature during hydration.

Finely ground portland cements, or cements with relatively high C3A and C3S contents show higher heats of hydration than coarser cements or cements with low C3A and C3S.

Use of pozzolanic materials to replace cement.



Heat Losses

Heat losses depend on the thermal properties of concrete, and the construction technology adopted. A concrete structure can lose heat through its surface, and the magnitude of heat loss is a function of the type of material in immediate contact with the concrete surface.

Numerical methods can be use to compute the temperature distribution in mass of concrete



Introduction of heat equation

Heat flux in the x-direction

Thermal Balance

Addition of the flux variation in the three-directions determines the amount of heat introduced in the interior of the element per unit time:

∂

∂xk∂T∂x

+∂

∂yk∂T∂y

+

∂

∂zk∂T∂z

dx dy dz

If the material is homogeneous

k∂2 T∂x2

+∂ 2 T∂y2

+∂2 T∂z2

dx dy dz

For a material with mass density r and specific heat c, the increase of internal energy in the element is given by:

ρ c dx dy dz

∂T∂t



Thermal Balance

k∂2 T∂x2

+∂ 2 T∂y2

+∂2 T∂z2

= ρ c

∂T∂t

Now consider the case when there is heat generation inside the material. The equation when added to the quantity of heat generated in the interior of the element per unit of time -wdxdydz - can be equated with the increase of internal energy in the element.

k∂2 T∂x2

+∂ 2 T∂y2

+∂2 T∂z2

+ w = ρ c

∂T∂t



Simple example from ACI



Example



Example for dams: Itaipu Dam



General Information

Ambient Conditions

Yearly average temperature 21 C

Maximum Temperature 40 C

Mimimum Temperature -4 C

Volume of materials

Concrete 12.3 million m3

Earth moving 23.6 million m3

Rock excavation 32.0 m3

Embankments 31.7 million m3



General Information

River BasinArea 820,000 km2Average annual precipitation 1,400 mmAverage discharge at Itaipu 9,700 m3/s

ReservoirArea 1,350 km2Volume 29 billion m3Length 170 kmDamMaximum height 196 mTotal length 7,760Generating UnitsQuantity 18Capacity 700 MW



Diversion of the Paranáriver was achieved by the

construction of a channel 2 km long, 150 m wide, and 90 m deep on the left river

bank.

Paraná River



Two arch dams were built to protect the channel structures

from floods.

Arch Dams



AND THEN…

the two arch dams built to protect the

structures from flood were

simultaneously exploded in just 3

seconds

Complexsite

In November of 1979, a monthly production of 340,000 m3 was achieved. In 1980, the yearly production was 3 million cubic meter.

Seven aerial cables with an span of 1300 m were used for transporting concrete in 8 m3 buckets.



To reduce the amount of concrete in the dam, the

center of the block is hollow

The spillway, with a length of 483 m, was designed for a maximum discharge capacity of 62,220 m3/s.



Characteristics for the concrete for the thermal study

35.860 days

29.828 days

20.47 days

17.23 days

MPaCompressive strength

2537 kg/m3Density of the concrete

1.71 kcal/m.h CThermal conductivity

0.22 kcal/kg CSpecific heat of the concrete



Concrete Mixture Proportions

2.9Superplasticizer

41938-mm CA

74219-mm CA

373Artificial sand

556Natural sand

154Water

290Cement

Kg/m3



Thermal stresses in Itaipu dam

Finite element mesh (before processing) for the spiral box inside the dam.

Courtesy from Selmo Kuperman, Itaipu Binacional, Themag Engenharia e Gerenciamento



Thermal stresses in Itaipu dam

Finite element mesh after processing




Isotherms after 300 hours




Isotherms after 500 hours




Detail of the locations where the maximum temperature developed


power point presentation thermal gradient

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