## 5.4 MATERIAL PROPERTIES

### 5.4.1 General

Designs should be based on the material properties cited herein and on the use of materials that conform to the standards for the grades of construction materials as specified in AASHTO LRFD Bridge Construction Specifications.

When other grades or types of materials are used, their properties, including statistical variability, shall be established prior to design. The minimum acceptable properties and test procedures for such materials shall be specified in the contract documents.

The contract documents shall define the grades or properties of all materials to be used. C5.4.1

According to AASHTO LRFD Bridge Construction Specifications, all materials and tests must conform to the appropriate standards included in the AASHTO Standard Specifications for Transportation Materials and Methods of Sampling and Testing and/or the standards of the American Society for Testing and Materials.

Occasionally, it may be appropriate to use materials other than those included in the AASHTO LRFD Bridge Construction Specifications; for example, when concretes are modified to obtain very high-strengths through the introduction of special materials, such as:

• Silica fume,

• Cements other than Portland or blended hydraulic cements,

• Proprietary high early strength cements,

• Ground granulated blast-furnace slag, and

• Other types of cementitious and/or Pozzolanic materials.

In these cases, the specified properties of such materials should be measured using the testing procedures defined in the contract documents.

### 5.4.2 Normal and Structural Lightweight Concrete

#### 5.4.2.1 Compressive Strength

For each component, the specified compressive strength, fc, or the class of concrete shall be shown in the contract documents.

Design concrete strengths above 10.0 ksi shall be used only when allowed by specific articles or when physical tests are made to establish the relationships between the concrete strength and other properties. Specified concrete with strengths below 2.4 ksi should not be used in structural applications.

The specified compressive strength for prestressed concrete and decks shall not be less than 4.0 ksi.

For lightweight structural concrete, air dry unit weight, strength and any other properties required for the application shall be specified in the contract documents.

C5.4.2.1

The evaluation of the strength of the concrete used in the work should be based on test cylinders produced, tested, and evaluated in accordance with Section 8 of the AASHTO LRFD Bridge Construction Specifications.

It is common practice that the specified strength be attained 28 days after placement. Other maturity ages may be assumed for design and specified for components that will receive loads at times appreciably different than 28 days after placement.

It is recommended that the classes of concrete shown in Table C1 and their corresponding specified strengths be used whenever appropriate. The classes of concrete indicated in Table C1 have been developed for general use and are included in AASHTO LRFD Bridge Construction Specifications, Section 8, “Concrete Structures,” from which Table C1 was taken.

These classes are intended for use as follows:

Class A concrete is generally used for all elements of structures, except when another class is more appropriate, and specifically for concrete exposed to saltwater.

Class B concrete is used in footings, pedestals, massive pier shafts, and gravity walls.

Class C concrete is used in thin sections, such as reinforced railings less than 4.0 in. thick, for filler in steel grid floors, etc.

Class P concrete is used when strengths in excess of 4.0 ksi are required. For prestressed concrete, consideration should be given to limiting the nominal aggregate size to 0.75 in.

Class S concrete is used for concrete deposited underwater in cofferdams to seal out water.

Strengths above 5.0 ksi should be used only when the availability of materials for such concrete in the locale is verified.

Lightweight concrete is generally used only under conditions where weight is critical.

In the evaluation of existing structures, it may be appropriate to modify the fc and other attendant structural properties specified for the original construction to recognize the strength gain or any strength loss due to age or deterioration after 28 days. Such modified fc should be determined by core samples of sufficient number and size to represent the concrete in the work, tested in accordance with AASHTO T 24 (ASTM C 42).

For concrete Classes A, A(AE), and P used in or over saltwater, the W/C ratio shall be specified not to exceed 0.45.

The sum of Portland cement and other cementitious materials shall be specified not to exceed 800 pcy, except for Class P (HPC) concrete where the sum of Portland cement and other cementitious materials shall be specified not to exceed 1000 pcy.

Air-entrained concrete, designated “AE” in Table C1, shall be specified where the concrete will be subject to alternate freezing and thawing and exposure to deicing salts, saltwater, or other potentially damaging environments. There is considerable evidence that the durability of reinforced concrete exposed to saltwater, deicing salts, or sulfates is appreciably improved if, as recommended by ACI 318, either or both the cover over the reinforcing steel is increased or the W/C ratio is limited to 0.40. If materials, with reasonable use of admixtures, will produce a workable concrete at W/C ratios lower than those listed in Table C1, the contract documents should alter the recommendations in Table C1 appropriately.

The specified strengths shown in Table C1 are generally consistent with the W/C ratios shown. However, it is possible to satisfy one without the other. Both are specified because W/C ratio is a dominant factor contributing to both durability and strength; simply obtaining the strength needed to satisfy the design assumptions may not ensure adequate durability.

### Table C5.4.2.1-1 Concrete Mix Characteristics By Class.

Class of Concrete | Minimum Cement Content | Maximum W/C Ratio | Air Content Range | Coarse Aggregate Per AASHTO M 43 (ASTM D 448) | 28-Day Compressive Strength
pcy | lbs. Per lbs. | % | Square Size of Openings (in.) | ksi
A A(AE) | 611 611 | 0.49 0.45 | — 6.0 ± 1.5 | 1.0 to No. 4 1.0 to No. 4 | 4.0 4.0
B | 517 | 0.58 | — | 2.0 to No. 3 and No. 3 to No. 4 | 2.4
B(AE) | 517 | 0.55 | 5.0 ± 1.5 | 2.0 to No. 3 and No. 3 to No. 4 | 2.4
C C(AE) | 658 658 | 0.49 0.45 | — 7.0 ± 1.5 | 0.5 to No. 4 0.5 to No. 4 | 4.0 4.0
P P(HPC) | 564 | 0.49 | As specified elsewhere | 1.0 to No. 4 or 0.75 to No. 4 | As specified elsewhere
S | 658 | 0.58 | — | 1.0 to No. 4 | —
Lightweight | 564 | As specified in the contract documents

#### 5.4.2.2 Coefficient of Thermal Expansion

The coefficient of thermal expansion should be determined by the laboratory tests on the specific mix to be used.

In the absence of more precise data, the thermal coefficient of expansion may be taken as:

• For normal weight concrete: 6.0  10–6/°F, and

• For lightweight concrete: 5.0  10–6/°F

C5.4.2.2

The thermal coefficient depends primarily on the types and proportions of aggregates used and on the degree of saturation of the concrete.

The thermal coefficient of normal weight concrete can vary between 3.0 to 8.0  10.0–6/°F, with limestone and marble aggregates producing the lower values, and chert and quartzite the higher. Only limited determinations of these coefficients have been made for lightweight concretes. They are in the range of 4.0 to 6.0  10–6/°F and depend on the amount of natural sand used.

Additional information may be found in ACI 209, ACI 343 and ACI 213.

#### 5.4.2.3 Shrinkage and Creep

##### 5.4.2.3.1 General

Values of shrinkage and creep, specified herein and in Articles 5.9.5.3 and 5.9.5.4, shall be used to determine the effects of shrinkage and creep on the loss of prestressing force in bridges other than segmentally constructed ones. These values in conjunction with the moment of inertia, as specified in Article 5.7.3.6.2, may be used to determine the effects of shrinkage and creep on deflections.

In the absence of more accurate data, the shrinkage coefficients may be assumed to be 0.0002 after 28 days and 0.0005 after one year of drying.

When mix-specific data are not available, estimates of shrinkage and creep may be made using the provisions of:

• Articles 5.4.2.3.2 and 5.4.2.3.3,

• The CEB-FIP model code, or

• ACI 209.

For segmentally constructed bridges, a more precise estimate shall be made, including the effect of:

• Specific materials,

• Structural dimensions,

• Site conditions, and

• Construction methods.

C5.4.2.3.1

Creep and shrinkage of concrete are variable properties that depend on a number of factors, some of which may not be known at the time of design.

Without specific physical tests or prior experience with the materials, the use of the empirical methods referenced in these Specifications cannot be expected to yield results with errors less than 50 percent.

##### 5.4.2.3.2 Creep

The creep coefficient may be taken as:

(5.4.2.3.2-1)

in which:

(5.4.2.3.2-2)

where:

H = relative humidity (percent)

k c = factor for the effect of the volume-to-surface ratio of the component specified in Figure 1

k f = factor for the effect of concrete strength

t = maturity of concrete (day)

t i = age of concrete when load is initially applied (day)

In the absence of better information, H may be taken from Figure 5.4.2.3.3-1.

f'c= specified compressive strength at 28 days (ksi)

C5.4.2.3.2

The methods of determining creep and shrinkage, as specified herein and in Article 5.4.2.3.3, are taken from Collins and Mitchell (1991). These methods are based on the recommendation of ACI Committee 209 as modified by additional recently published data.

Other applicable references include Rusch et al. (1983), Bazant and Wittman (1982), and Ghali and Favre (1986).

The creep coefficient is applied to the compressive strain caused by permanent loads in order to obtain the strain due to creep.

Creep is influenced by the same factors as shrinkage, and also by:

• Magnitude and duration of the stress,

• Maturity of the concrete at the time of loading, and

• Temperature of concrete.

Creep shortening of concrete under permanent loads is generally in the range of 1.5 to 4.0 times the initial elastic shortening, depending primarily on concrete maturity at the time of loading.

Figure 5.4.2.3.2-1 Factor kc for Volume to Surface Ratio.

In determining the maturity of concrete at initial loading, ti, one day of accelerated curing by steam or radiant heat may be taken as equal to seven days of normal curing.

The surface area used in determining the volume to area ratio should include only the area that is exposed to atmospheric drying. For poorly ventilated enclosed cells, only 50 percent of the interior perimeter should be used in calculating the surface area.

Figure 1 is based on the equation below (PCI 1977):

(C5.4.2.3.2-1)

The maximum V/S ratio considered in the development of Figure 1 and Eq. C1 was 6.0 in. Based on research presented by the PCI Committee on prestress losses in 1975, creep remains nearly constant for V/S ratios greater than 6.0 in. Therefore, V/S should be limited to 6.0 in. in Eq. C1.

5.4.2.3.3 Shrinkage

For moist cured concretes devoid of shrinkage-prone aggregates, the strain due to shrinkage, εsh, at time, t, may be taken as:

(5.4.2.3.3-1)

where:

t = drying time (day)

k s = size factor specified in Figure 2

k h = humidity factor specified in Figure 1 and Table 1

C5.4.2.3.3

Shrinkage of concrete can vary over a wide range from nearly nil if continually immersed in water to in excess of 0.0008 for thin sections made with high shrinkage aggregates and sections that are not properly cured.

Shrinkage is affected by:

• Aggregate characteristics and proportions,

• Average humidity at the bridge site,

• W/C ratio,

• Type of cure,

• Volume to surface area ratio of member, and

• Duration of drying period.

If the moist-cured concrete is exposed to drying before five days of curing have elapsed, the shrinkage as determined in Eq. 1 should be increased by 20 percent.

For steam-cured concrete devoid of shrinkage-prone aggregates,

(5.4.2.3.3-2)

Figure 5.4.2.3.3-1 Annual Average Ambient Relative Humidity in Percent.

Large concrete members may undergo substantially less shrinkage than that measured by laboratory testing of small specimens of the same concrete. The constraining effects of reinforcement and composite actions with other elements of the bridge tend to reduce the dimensional changes in some components.

Figure 5.4.2.3.3-2 Factor ks for Volume-to-Surface Ratio.

Figure 2 is based on the equation below (PCI 1977):

(C5.4.2.3.3-1)

The maximum V/S ratio considered in the development of Figure 2 and Eq. C1 was 6.0 in. When the V/S ratio exceeds 6.0 in., a value of 6.0 in. may be used in Figure 2 or Eq. C1. If a more detailed analysis is required, when the V/S ratio exceeds 6.0 in., then the alternate provisions of Article 5.4.2.3.1 may be used. For nonsegmental structures, the added refinement may not be warranted.

### Table 5.4.2.3.3-1 Factor k h for Relative Humidity.

Average Ambient Relative Humidity % | kh
40 | 1.4 3
50 | 1.2 9
60 | 1.1 4
70 | 1.0 0
80 | 0.8 6
90 | 0.4 3
100 | 0.0 0

The values in Table 1 may be approximated by the following equations:

• For H < 80%

(C5.4.2.3.3-2)

• For H ≥ 80%

(C5.4.2.3.3-3)

### 5.4.2.4 Modulus of Elasticity

In the absence of more precise data, the modulus of elasticity, Ec, for concretes with unit weights between 0.090 and 0.155 kcf, may be taken as:

(5.4.2.4-1)

where:

w c = unit weight of concrete (kcf)

f'c= specified strength of concrete (ksi)

C5.4.2.4

See commentary for specified strength in Article 5.4.2.1.

For normal weight concrete with w c = 0.145 kcf, E c may be taken as

(C5.4.2.4-1)

5.4.2.5 Poisson’s Ratio

Unless determined by physical tests, Poisson’s ratio may be assumed as 0.2. For components expected to be subject to cracking, the effect of Poisson’s ratio may be neglected.

C5.4.2.5

This is a ratio between the lateral and axial strains of an axially and/or flexurally loaded structural element.

### 5.4.2.6 Modulus of Rupture

Unless determined by physical tests, the modulus of rupture, fr in ksi, may be taken as:

• For normal weight concrete………...

• For sand lightweight concrete……....

• For all lightweight concrete………...

C5.4.2.6

The given values may be unconservative for tensile cracking caused by restrained shrinkage, anchor zone splitting, and other such tensile forces caused by effects other than flexure. The direct tensile strength stress should be used for these cases.

### 5.4.2.7 Tensile Strength

Direct tensile strength may be determined by either using ASTM C 900, “Standard Test Method for Pullout Strength of Hardened Concrete,” or the split tensile strength method in accordance with AASHTO T 198 (ASTM C 496) “Standard Method for Splitting Tensile Strength of Cylindrical Concrete Specimens.”

C5.4.2.7

For most regular concretes, the direct tensile strength may be estimated as f r = 0.23f'c.

### 5.4.3 Reinforcing Steel

#### 5.4.3.1 General

Reinforcing bars, deformed wire, cold drawn wire, welded plain wire fabric, and welded deformed wire fabric shall conform to the material standards as specified in Article 9.2 of the AASHTO LRFD Bridge Construction Specifications.

Reinforcement shall be deformed, except that plain bars or plain wire may be used for spirals, hoops, and wire fabric.

The nominal yield strength shall be the minimum as specified for the grade of steel selected, except that yield strengths in excess of 75.0 ksi shall not be used for design purposes. The yield strength or grade of the bars or wires shall be shown in the contract documents. Bars with yield strengths less than 60.0 ksi shall be used only with the approval of the Owner. C5.4.3.1

Where ductility is to be assured or where welding is required, steel conforming to the requirements of ASTM A 706, “Low Alloy Steel Deformed Bars for Concrete Reinforcement,” should be specified. A 706 reinforcement should be considered for seismic design because of the greater quality control by which unanticipated overstrength is limited.

#### 5.4.3.2 Modulus of Elasticity

The modulus of elasticity, Es, of steel reinforcing shall be assumed as 29,000 ksi.

#### 5.4.3.3 Special Applications

Reinforcement to be welded shall be indicated in the contract documents, and the welding procedure to be used shall be specified.

Locations where epoxy coated reinforcement is to be used shall be identified in the contract documents.

### 5.4.4 Prestressing Steel

#### 5.4.4.1 General

Uncoated, stress relieved or low relaxation, seven wire strand, or uncoated plain or deformed, high strength bars, shall conform to the following materials standards, as specified for use in AASHTO LRFD Bridge Construction Specifications:

C5.4.4.1

• AASHTO M 203/M 203M (ASTM A 416/A 416M), or

• AASHTO M 275/M 275M (ASTM A 722/A 722M).

Tensile and yield strengths for these steels may be taken as specified in Table 1. Low relaxation strand shall be regarded as the standard type. Stress-relieved (normal relaxation) strand will not be furnished unless specifically ordered, or by arrangement between purchaser and supplier.

### Table 5.4.4.1-1 Properties of Prestressing Strand and Bar.

Material | Grade or Type | Diameter (in.) | Tensile Strength, fpu (ksi) | Yield Strength, fpy (ksi)
Strand | 250 ksi 270 ksi | 1/4 to 0.6 3/8 to 0.6 | 250 270 | 85% of fpu, except 90% of fpu for low- relaxation strand
Bar | Type 1, Plain Type 2, Deformed | 3/4 to 1-3/8 5/8 to 1-3/8 | 150 150 | 85% of fpu 80% of fpu

Where complete prestressing details are included in the contract documents, the size and grade or type of steel shall be shown. If the plans indicate only the prestressing forces and locations of application, the choice of size and type of steel shall be left to the Contractor, subject to the Engineer's approval.

#### 5.4.4.2 Modulus of Elasticity

If more precise data are not available, the modulus of elasticity for prestressing steels, based on nominal cross sectional area, may be taken as:

for strand: E p = 28,500 ksi, and

for bar: E p = 30,000 ksi

C5.4.4.2

The suggested modulus of elasticity of 28,500 ksi for strands is based on recent statistical data. This value is higher than that previously assumed because of the slightly different characteristics and the near universal use of low-relaxation strands.

As shown in Figure C1, there is no sharp break in the curves to indicate a distinct elastic limit or yield point. Arbitrary methods of establishing yield strength, based on a specific set or measured strain, are generally used. The 0.2 percent offset and the 1 percent extension methods are the most common.

Figure C5.4.4.2-1 Typical Stress-Strain Curve for Prestressing Steels.

### 5.4.5 Posttensioning Anchorages and Couplers

Anchorages and tendon couplers shall conform to the requirements of Article 10.3.2 of AASHTO LRFD Bridge Construction Specifications.

Corrosion protection shall be provided for tendons, anchorages, end fittings, and couplers.

C5.4.5

Complete details for qualification testing of anchorages and couplers are included in Article 10.3.2 of AASHTO LRFD Bridge Construction Specifications.

Characteristics of anchorages and couplers related to design and detailing are summarized below from AASHTO LRFD Bridge Construction Specifications:

• Anchorages and couplers are to develop at least 95 percent of the minimum specified ultimate strength of the prestressing steel without exceeding the anchorage set movement assumed for the design. Unbonded systems are to also pass a dynamic loading test.

• Couplers are not to be used at points of sharp tendon curvature.

• Couplers are to be used only at locations shown on the contract documents or approved by the Engineer.

• Couplers are to be enclosed in housings long enough to permit the necessary movements.

• Where bonded anchorages or couplers are located at sections that are critical at strength limit state, the strength required of the bonded tendons is not to exceed the resistance of the tendon assembly, including the anchorage or coupler, tested in an unbonded state.

• Bearing stresses on concrete under anchorage distribution plates are not to exceed specified limits.

• Unless waived by the Engineer because of suitable previous tests and/or experience, qualification of anchorages and couplers are to be verified by testing.

### 5.4.6 Ducts

#### 5.4.6.1 General

Ducts for tendons shall be rigid or semirigid either galvanized ferrous metal or polyethylene, or they shall be formed in the concrete with removable cores.

The radius of curvature of tendon ducts shall not be less than 20.0 ft., except in the anchorage areas where 12.0 ft. may be permitted. C5.4.6.1

The use of polyethylene duct is generally recommended in corrosive environments. Pertinent requirements for ducts can be found in Article 10.8.2 in AASHTO LRFD Bridge Construction Specifications.

Polyethylene ducts shall not be used when the radius of curvature of the tendon is less than 30.0 ft.

Where polyethylene ducts are used and the tendons are to be bonded, the bonding characteristics of polyethylene ducts to the concrete and the grout should be investigated.

The effects of grouting pressure on the ducts and the surrounding concrete shall be investigated.

The maximum support interval for the ducts during construction shall be indicated in the contract documents and shall conform to Article 10.4.1.1 of the AASHTO LRFD Bridge Construction Specifications. Polyethylene duct should not be used on radii under 30.0 ft. because of its lower resistance to abrasion during pulling-through and stressing tendons.

The contract documents should indicate the specific type of duct material to be used when only one type is to be allowed.

#### 5.4.6.2 Size of Ducts

The inside diameter of ducts shall be at least 0.25 in. larger than the nominal diameter of single bar or strand tendons. For multiple bar or strand tendons, the inside cross-sectional area of the duct shall be at least 2.0 times the net area of the prestressing steel with one exception where tendons are to be placed by the pull-through method, the duct area shall be at least 2.5 times the net area of the prestressing steel.

The size of ducts shall not exceed 0.4 times the least gross concrete thickness at the duct. C5.4.6.2

The pull-through method of tendon placement is usually employed by contractors where tendons exceed 400 ft. in length.

#### 5.4.6.3 Ducts at Deviation Saddles

Ducts at deviation saddles shall be galvanized steel pipe conforming to the requirements of ASTM A 53, Type E, Grade B. The nominal wall thickness of the pipe shall be not less than 0.125 in.