Tn 175 Implementation Of European Code

Technical Note Structural Concrete Software System TN T175

European_Code13 012604

IMPLEMENTATION OF EUROPEAN CODE IN FLOOR-PRO

ADAPT FLOOR-Pro is in full compliance with the European code EC2. This Technical Note describes the details of the code implementation in the software. The implementation is based on EC2 (ENV 1992-1-1) The implementation follows the EC2 ‘s procedure of calculating a “Demand,” referred to as “design values” for each design section, and a “Resistance,” for the same section, referred to as “design capacity.” “Design value” and “design capacity” are generic terms that apply to displacements as well as actions. These are the design terminologies used in ACI, and adopted in ADAPT literature. For consistency, they are also used in this Technical Note. For each loading condition, or instance defined in EC2, the design is achieved by making the resistance exceed the associated demand. The implementation is broken down into the following steps: • •

Strength limit state Serviceability limit state o Allowable stress limits Concrete Steel o Cracking check and reinforcement o Minimum flexural reinforcement o Deflection check

The design is performed for: • Bending of section o With or without prestressing o With or without axial loading • Punching shear • Beam shear (one-way shear) In the following, the values in square brackets “[ ]” are the factory set defaults of the program. They can be changed by the user. MATERIAL AND MATERIAL FACTORS Concrete • Cylinder strength at 28 days, as specified by user is used.

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Technical Note • •

Bilinear stress/strain diagram with the horizontal branch at αfcd [α = 0.85], maximum strain 0.0035, limit of proportionality 0.00135 Modulus of elasticity of concrete is automatically calculated and displayed by the program using fck, the relationship (2.1-15) of the code. User is given the option to override the code value and specify a user defined substitute.

Nonprestressed Steel • Bilinear stress/strain diagram with the horizontal branch at (fyk)/ γs • Modulus of elasticity is user defined [200000 MPa] • No limit on tensile strain is imposed Prestressing Steel • Bilinear stress/strain diagram with the horizontal branch at (0.90fpk)/ γs • Modulus of elasticity is user defined [190000 MPa] • No limit on tensile strain is imposed Material Factors • Concrete • Nonprestressed steel • Prestressing steel

γs = 1.50 γs = 1.15 γs = 1.15

LOAD COMBINATIONS AND DESIGN CHECKS

For the European Code, the program automatically generates the following load combinations and performs the associated design checks. • • • •

Service (quasi-permanent) condition Service (frequent) condition Strength condition Initial (transfer)

In addition to the above, the program has an option for “No code check” for conditions, when a user is interested in the response of the floor system to a user defined loading, as opposed to a code driven design check. •

No code check

The program’s automatically generated load cases and load combinations are listed below. Except for the initial (transfer) condition, that is not explicitly given in the code, the remainder of the combinations are based on EC2. •

Service (quasi-permanent) 1.00 x Self weight + 1.00 x Dead load + 0.30 x Live load + 1.00 x Prestressing

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Technical Note •

Service (frequent) 1.00 x Self weight + 1.00 x Dead load + 0.50 x Live load + 1.00 x Prestressing

•

Strength 1.35 x Self weight + 1.35 x Dead load + 1.50 x Live load + 1.00 x Hyperstatic

•

Initial (transfer) 1.00 x Self weight + 1.15 x Prestressing The factors of the initial condition are based upon the common practice of engineers in the USA.

DESIGN FOR FLEXURE WITH OR WITHOUT AXIAL LOAD Strength Check in Bending • • • • •

Plane sections remain plane. Strain compatibility is used to determine the actions on the section. Maximum concrete strain in compression is limited to 0.0035 . Maximum value for the neutral axis “x” is determined based on concrete strength of the section fcu . If a section is made up of more than one concrete material, the entire section is designed using the concrete properties of lowest strength in that section For strands that cross a design section at an angle, the change in strain in the strand due to flexing of the design section about its own axis is calculated from the following relationship: Change of strain in strand = (strain normal to the design section)*cos2θ , where θ is the angle between the design section and a normal to it. The strain in each strand is calculated separately, based on its angle with the design section Additional considerations for strain in prestressing steel o If bonded, strain is calculated using the stress/strain curve and the angle of strand with the design section o If unbonded, the strain is calculated using the same procedure as bonded tendons, but the calculated strain is adjusted as follows: • The stress increase is reduced by the factor (Ls/LT) • The stress increase is limited to (Ls/LT)100 MPa Stress in nonprestressed steel is based on stress-strain relationship assumed Trapezoidal concrete block is used with maximum stress equal to αfcd [α = 0.85] Depth of neutral axis is limited as given below: o

•

• • •

o o

For fcu <= 35 MPa For fcu > 35 MPa

x/d <= 0.45 x/d <= 0.35

Where necessary, compression reinforcement is added to enforce the above requirement • •

Average compressive stress over the compression zone is taken as 0.807fcd. The resultant of the compressive force in concrete is assumed to act a distance 0.411x from the compression face.

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Technical Note •

For flanged sections, the following procedure is adopted: o o

If x is within the flange the section is treated as a rectangular If x is exceeds the flange thickness, uniform compression is assumed over the flange with its centroid at mid-depth of the flange. The stem is treated as a rectangular section

Serviceability Check •

•

For “frequent” load condition, the default stress limitations for combination of dead and live loads under service condition are the code values. These, however, can be adjusted by the user to user’s specific requirements. o

Concrete Maximum compressive stress 0.60 fck. If stress at any location exceeds, the program displays that location with a change in color (or broken lines for black and white display), along with a note on the text output.. No limit on computed “hypothetical” maximum tensile stress

o

Mild Steel The maximum allowable stress (0.80 fyk ) given in the code is used. If the calculated stress exceeds the allowable value, the program automatically adds more steel to lower the calculated stress to the code specified limit.

o

Prestressing steel The maximum allowable stress under service condition (0.75 fyk) given in the code is used. If this value exceeds, the program will display a message on the screen indicating the affected tendon, and will request the user to modify the selection.

Stress limitations used for the “quasi-permanent” load combination are as follows: o

o o

•

Concrete Maximum compressive stress 0.45 fck . If stress at any location exceeds, the program displays that location with a change in color (or broken lines for black and white display), along with a note on the text output.. No limit on the computed “hypothetical) maximum tensile stress Mild Steel None required – no check made Prestressing steel None required - no check made

Cracking check and reinforcement for crack control The minimum reinforcement for crack control ( As ) is based on section 4.4.2.2 of the code. The following values are used in the evaluation of As. σs

= yield strength of reinforcement (fyk)

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Technical Note fct,eff

= tensile strength of concrete at time of crack formation, user defined, but not less than 3 MPa

K

= for members with least dimensions <= 300 mm K = 0.80 for members with least dimension >= 800 mm K = 0.5 for other members interpolate linearly = is determined based on the maximum fiber stresses as follows:

Kc

If both faces are in compression Kc = 0.0 If both faces are in tension Kc = 1.0 If one face is in compression and the other in tension Kc = 0.4 (σt/ σc), but not greater then 0.4 Where, σt and σc are farthest fiber tension and compressions stresses respectively •

Minimum Overall Reinforcement Each design section is checked to satisfy the minimum overall reinforcement (As), using Section 5.4.2.1.1 of the code. As >= (0.60 bt d / fyk ) >= 0.0015 bt d Where d = depth specified for mild steel. If no mild steel is required, the cover specified by the user and the user’s choice of reinforcement is used to calculate “d” bt = web thickness, or section width for rectangular sections fpk is used in lieu of fyk , when section is prestressed. If both prestressing and nonprestressed steel are present, weighted average of their characteristic strength is used based on the available area of each.

•

Crack Width Limitation Calculation is based on section 4.4.2.4. It is calculated using Table 12.7 with the following considerations: o o o o

For the calculation of Єm , the values σs and σsr and Es are determined for the rebar closest to the tension face. If no rebar exists, an infinitely small amount of rebar is assumed. For k1, Φ, and ρr calculation, all rebar and bonded post-tensioning within the tension zone of the section are considered. For effective tension area of concrete Ac,eff, one third of the area of concrete below the neutral axis is used. Other parameters used are those specified in the code as follows: • β = 1.7 cracks due to loading • β1 = 1 for deformed bars • β2 = 0.5 for sustained loads • k1 = 0.8 for deformed bars • •

k2 k2

= 2 for bonded prestressing = 0.5 for bending

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Technical Note o o

No check is performed for the distribution of the calculated reinforcement on the section No check is performed for the 300 mm2 area of reinforcement noted in the code. User should check the availability of this reinforcement or its equivalent.

Using the parameters, the program calculates the design crack width (wk) of each design section. If the calculated value exceeds the allowable, reinforcement is added to that section, in order to reduce the crack width to within the allowable value. The allowable crack width depends on the “Exposure” classification. The “Exposure” classification is user defined. • • •

Crack width for nonprestressed concrete – Exposure 2 - 4 • Width is limited to 0.3 mm. Crack width for prestressed concrete – Exposure 1 - 2 • Width is limited to 0.2 mm. Crack width for decompression condition – Exposure 3 - 4 for prestressed sections • Stresses at extreme fibers are checked to be in compression

One-Way Shear Check The design is based on the following: VSd <= VRd Where, VSd = design value; and VRd = design resistance Three resistance values are calculated and checked against the design values. These are: VRd1 = design shear resistance without shear reinforcement VRd2 = maximum design shear resistance that can be carried without crushing of notional concrete compressive struts VRd3 = design shear resistance of section with shear reinforcement Code formulas are used to calculate the above values. In using the code formulas, the following considerations are observed. V / bw d o o o o o o

For bw the smallest width of the section is used Shear due to the vertical component of prestressing tendons are ignored Loss of cross-sectional area due to post-tensioning ducts is ignored Code allowed increase in shear capacity for sections that are close to a support is not implemented All available tension reinforcement is included in the calculation of As1 Curtailment lengths for longitudinal bars are not calculated

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Technical Note Punching Shear In its first release of the European Code implementation, the program uses the ACI-318-2002 formulation for punching shear check. It leads to a more conservative design. Subsequent releases will provide the option for design using EC2.

NOTATION fcd

= design value of concrete cylinder compression strength

fck

= characteristic compressive cylinder strength at 28 days

fct,eff

= tensile strength of concrete

fpk

= Characteristic tensile strength of prestressing steel [1860 MPa]

fyk

= Characteristic yield strength of steel, user-defined [460 MPa]

Ls

= span length of tendon

LT

= total length of tendon

VSd

= design shear force

VRd

= design shear resistance

x

= depth of neutral axis

wk

= design (computed) crack width

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