T6: Cracking due to Restraints

Question 1

What are the two restraint cases (ie. time-scales), and what restraints do they apply to?

Answer 1

Short-term case
- Edge, end, internal restraint situations

Long-term case:
- Edge, end restraint situations

Question 2

Describe the design process for the short-term case (8 steps).

How does it vary for the long-term case?

Answer 2

For long-term case, repeat the procedure with long-term values

Question 3

[NAQ] design process

Answer 3

Question 4

What causes non-structural cracking (x3)

Answer 4

• Non-structural cracking due to thermal or shrinkage strains
• Caused when the concrete contracts/shrinks, and is restrained from doing so
• The restraining effect creates tensile strains; if it exceeds TS capacity of concrete it cracks

Question 5

Name two different ways restraints are provided?

Answer 5

• By the existing ground (in the case of a foundation or cast-on-grade floor slab)
• By the previously cast concrete

Question 6

What type of external restraint is this?

Answer 6

Combined restraint

Question 7

What type of external restraint is this?

Answer 7

Edge restraint

Question 8

What type of external restraint is this?

Answer 8

End restraint

Question 9

What type of external restraint is this?

Answer 9

Combined restraint

Question 10

In this combined restraint case, which is the dominant restraint in each zone?

Answer 10

Zone 1: Edge

Zone 2: End

Zone 3: Combined

Question 11

How does steel reinforcement control internal cracking (x2)?

Answer 11

• The reinforcement distributes the tensile strains along the reinforcement
• This keeps crack widths to an acceptable surface width

Question 12

What is an alternative (to the provision of large areas of rebar) measure to prevent internal cracking?

And why?

Answer 12

Providing movement joints
- reduces the degree of restraint
.

Question 13

For internal/restraint cracking, what are the three main effects that need to be considered?

Answer 13

• Early thermal contraction
• Shrinkage
• Longer-term thermal movements

Question 14

What causes early thermal contraction?

When is the most critical period?

Answer 14

Caused by the concrete cooling down from the peak temp. to ambient temp.
- peak temp. is generated by the exothermic hydration reaction

Most critical period usually about 3 days after pouring

Question 15

What are two types of shrinkage that need to be considered?

What time do they occur?

Answer 15

Autogenous shrinkage
- occurs during early stage of hydration, and over a longer period of time than ETC
- typically within first 28 days after pouring

Drying shrinkage
- usually only considered after 28 days (after pouring)

Question 16

What causes longer-term thermal movements?

Answer 16

Seasonal changes in the ambient temp.

Question 17

Which internal/restraint cracking effects fall into the short-term case, and which into the long-term case?

What are the timescales for both cases?

Answer 17

Short-term:
- early thermal contraction
- autogenous shrinkage effects
- occur within first 3 days after pouring

Long-term:
- 28-day values of autogenous and drying shrinkage strains considered together
- longer-term thermal movements

Question 18

Why type of restraint is this?

What is the most common example of this form?

Answer 18

External edge restraint

When a wall is cast on a previously cast foundation

Question 19

For an external edge restraint, how does the degree of restraint vary with distance from the joint between the new cast/ existing concrete?

Answer 19

Degree of restraint decreases with distance…
- as L/H increases, degree of restraint increases

Question 20

How can an external edge restraint cause cracking (x2)?

Answer 20

Due to early-age strains AND longer-term movements

Question 21

What does this equation represent?

Answer 21

Used to determine the edge restraint at a joint between newly cast/existing concrete

Question 22

If the relative areas of influence (A_old, A_new) are difficult to define, what is recommended?

Answer 22

It is recommended that the relative area is assumed to be in proportion to the relative thickness (h_old, h_new) of the wall and slab

Question 23

When does max. crack width of an external edge restraint occur?

Answer 23

At a height from the base equal to 10% of the length of the wall

Question 24

When do external edge restraints usually occur?

Give three examples

Answer 24

Tend to occur when relatively thin, flexible concrete members (usually slabs) are cast against much stiffer forms of concrete construction

• A suspended floor slab cast between rigid walls and/or columns
• Floor slabs in building cast into lift shaft cores/stair wells
• A thin ground slab cast on piles

Question 25

Where was end restraint theory evolved from?

Answer 25

The behaviour of **axially reinforced concrete prisms** subjected to uniaxial tension NB. for many years, same theory was employed for edge restraint members as well

Question 26

Describe the difference between end and edge restraints, with respect to: a) where cracking is max/min

Answer 26

End - **uniform** along the member Edge - **max. at base**, and varies along height and length

Question 27

Describe the difference between end and edge restraints, with respect to: b) whether the crack reduces the stiffness globally or locally

Answer 27

End - crack reduces the stress and member stiffness **globally** Edge - crack reduces the stress and member stiffness only locally

Question 28

Describe the difference between end and edge restraints, with respect to: c) what crack width is a function of

Answer 28

End (uniform) - function of **concrete tensile strength** and **steel reinforcement** Edge (max. at base) - function of **imposed strain** and **degree of restraint**

Question 29

In what type of elements do internal restraints occur?

Answer 29

They occur with **very thick** structural members E.g. large basement slabs, 2m or more thick

Question 30

Why do internal restraints occur?

Answer 30

They occur as a result of **temp. gradient** that exist between the **centre and outer edges** of the concrete pour

Question 31

At what time do internal restraints generate strains?

Answer 31

Strains generated in **very short-term** - in **first 2/3 days** after pouring the concrete - no need to consider long-term effects As the concrete cools, the thermal gradient dissipates; thermal strain gradually reduces

Question 32

Why do early age shrinkage strains (autogenous shrinkage) not need to be considered in internal restraint cases?

Answer 32

- It tends to be **fairly uniform** across the section - **Doesn't contribute to the strain gradient**

Question 33

What does this equation represent, and what is each coefficient?

Answer 33

Early-age restrained strain (ε_r) K_1 = 0.65 a_c = 12 R_1 = 0.42 (internal restraint case)

Question 34

[NAQ] CIRIA C766 guidance on a_c (coefficient of thermal expansion for the concrete) values, for different aggregate groups

Answer 34

Question 35

What affects the value of T_1 (temperature rise) when calculating early-age restrained strain?

Answer 35

- Cement content - Cement type - Section thickness - Formwork type (& if any insulation used) - Concrete placing temperature - Ambient conditions - If any cooling measured are being used NB. slides 28-32 have graphs/tables for T_1 values

Question 36

What does this equation represent?

Answer 36

Restraint factor (R_1), for the external end restraint simple case

Question 37

What is the typical value of restraint factors (R_1) for: a) **internal** restraint case b) suspended floor slabs (**external end** restraint case) c) infill walls cast between columns and/or edge beams (**external end** restraint case)

Answer 37

a) 0.42 b) 0.2 to 0.4 c) 0.8 to 1.0

Question 38

What do these values represent? What equations can alternatively be used?

Answer 38

Autogenous shrinkage strain (ε_ca) values, for 3-days and 28-days

Question 39

What does this equation represent, and what is each coefficient?

Answer 39

Long-term total restrained strain (ε_r) Or ε_r due to restrained thermal effects and autogenous shrinkage

Question 40

What is the max. value of T_2 recommended by CIRIA C766 For summer casting

Answer 40

20C (for summer casting)

Question 41

What does this equation represent, and what is each coefficient?

Answer 41

Total restrained strain (ε_4) due to restrained drying shrinkage effects K_c2 = 0.5

Question 42

What does this equation represent? When should it be considered?

Answer 42

Total strain (ε_r) This value should be considered when evaluating the requirements for longer-term crack control (28 days and later)

Question 43

What is ε_ctu What is the range of values (for different aggregate types), for early-age (3 days) and long-term (28 days) cases

Answer 43

Tensile strain capacity of concrete Early-age = 55 to 95 MPa Long-term = 100 to 175 MPa

Question 44

For estimating strain capacity for other classes (not C30/37) of concrete, what should be done to these values?

Answer 44

Question 45

What do these equations represent? What typical values for the E_cm (elastic modulus) coefficient should be used

Answer 45

Tensile strain capacity for early-age [ε_ctu(ea)] and long-term [ε_ctu(lt)] Typical stiffness coefficients in range 0.7 to 1.2

Question 46

What do these equations represent, and what is each coefficient? NB. top = EC2, bottom = C766

Answer 46

Question 47

1. What values for the k and k_c stress distribution coefficient should be used for: a) external restraint dominant case b) internal restraint dominant case 2. What values for section thickness (h) [for A_ct = 0.5h] should be used for:a) external restraint dominant case b) internal restraint dominant case

Answer 47

Question 48

[NAQ] tensile strengths of concrete

Answer 48

Question 49

What does this equation represent, and what is each coefficient?

Answer 49

Max. crack spacing [S_r,max] k_1 = 1.14 (early-age conditions, C766) ρ_p,eff = effective reinforcement ratio

Question 50

How is the effective reinforcement ratio [ρ_p,eff] calculated?

Answer 50

Using the effective reinforcement ratio

Question 51

[NAQ] calculating the effective area of concrete in tension

Answer 51

Question 52

For working out the design surface crack width (w_k), what else is needed after calculating the max. crack spacing (s_r,max)?

Answer 52

Crack-inducing strain

Question 53

What does this equation represent, and what is each coefficient?

Answer 53

Crack-inducing strain (ε_cr), for edge restraint and internal restraint conditions

Question 54

What doest this equation represent, and what is each coefficient?

Answer 54

Crack-inducing strain, for end restraint conditions NB. no end restraint question on exam

Question 55

What can be introduced if the design surface crack width is not acceptable (x5)

Answer 55

- Introduce **movement joints**, to reduce the degree of restraint - Use **aggregates with a low coefficient of thermal expansion** - Apply **concrete cooling** - Use **insulating blankets** to control the rate of cooling (for internal restraint problems) - Use **low heat cements**

Question 56

[NAQ] full movement joint

Answer 56