Concrete beams prestressed by pre-tension

The BSE Bridge Structural Engineering software allows users to perform the analysis, design, verification and evaluation of concrete beams prestressed by pre-tension. The pre-tension module performs with a minimum of effort for users the design, verification and evaluation of prestressed concrete beams. In fact, once the geometric data and the materials are given by users, via the pre-tension module, the program takes care of generating the model automatically. Thus, the time required to create a model is reduced to a minimum.

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Technical specifications

Through a set of simple and appropriate forms, the analysis, design verification and evaluation of precast concrete bridge girders with pre-tension is carried automatically by the BSE Software according to the following specifications:
• The supported codes are CSA S6-14 and CSA S6-19
• Standard AASHTO, NEBT, NBPS and CPCI sections and custom precast sections.
• Automatic and custom transverse strands layouts.
• Straight strands with one or two raised points.
• Standard and custom moving load envelopes for truck and/or lane loads.
• Pre-tension losses calculated with specified code or through a step-by-step method.
• Design of precast girders for multiple span bridges with composite slab action.
• Design of stirrups along girders and design of steel reinforcement at supports.
• Account for thermal effects
• Account for the secondary effects from creep and shrinkage.
• Deflection of girder according to time.

The pre-tension module combines the results obtained for the highway live load with other types of loads applied to a structure (dead weight, additional dead loads and live loads) to obtain a global solution as well as the corresponding envelopes.
Model parameters

The pre-tension toolbar contains the commands to operate the prestressed bridge girder design module. The module allows to design such beams according to the CSA S6-14 and CSA S6-19 codes using standard AASHTO, CPCI, NEBT and NBPS sections as well as custom precast cross sections. The module supports standard highway moving loads and custom moving loads.

– Custom precast section predefined shapes include the narrow top flange, the wide top flange and the bulb tee sections.
– Narrow Top Flange: Custom precast sections with narrow top flange similar to AASHTO-II sections.
– Wide Top Flange: Custom precast sections with wide top flange similar to AASHTO-V sections.
– Bulb Tee: Custom precast sections similar to NEBT standard sections.
Verification of input fields
Because the pre-tension module is automated, a list of verifications done during the start of the solution is listed below.
The summary of the input data contains the following tables:
General: Gap between Spans, Reinf. ratio at interior supports

Strands: Nominal Diameter (dn), Cross section area(At), Steel Ultimate Stress (fpu), Initial Stress in Strands (fpi= ratio of fpu), Steel Elastic Modulus (Eps)

Moving Load: Lateral Distribution Coefficient, Dynamic load allowance: Concentrated, Dynamic load allowance: Uniform

Slab: Concrete Compression Strength (f’cd), Concrete density, Reinforcement Yield Stress (fy), Slab width (b), Slab Thickness (t), Haunch thickness (th)

Stiffener Beams: Height (hr), Thickness (tr), Density

Stirrups: Area of a Stirrup (Av), Yield Stress of Stirrups (fv)

Thermal Gradients: Maximum Thermal Gradient, Minimum Thermal Gradient

Losses: Relative Humidity, Area of Ordinary, Reinforcement Bars (As), Time T1 must be superior to -20.0 days, Time T4 must be equal to 0.0 days, Time T1 to T7 must be chosen in increasing order, Time T7 must be inferior to 400 days

Span Data: Span Length (Lp), Number of Stiffener -Beams between Supports, Additional Dead Loads 1 and 2, Live Load (Other than moving loads), Initial Concrete Resistance of Beams (f’co), Concrete Resistance of Beams at 28 days (f’c28), f’co resistance must be inferior or equal to f’c28, Concrete density of Beams, Number of Straight Strands (Ns), Number of Inclined Strands (Ni), (Ni) or (Ns) Value must be superior to zero, Support distance from Raised Point L1 or L2, Eccentricity of strands at Center (ec), Minimum Dist. of Inclined Strands to Bottom, Distance C1 and C2, Supports Tension (T)

The summary of the output results includes: unfactored envelopes, factored envelopes, losses results, stresses of sections, ultimate flexural strength, continuity effects, stirrups design and deflection results.
Transverse strands layout

• Transverse strands layout for any standard or custom precast sections.
• All standard sections have built-in strands layout that can be overridden.
• The transverse strands layout must be defined for custom precast sections.
• The transverse strands layout is defined for the maximum number of strands in the section.
• When the actual number of strands used is lower than the number defined in the layout, each row of strands is filled completely before filling the next row.
• When a standard section is selected, the default built-in layout for this section is automatically fetched to ease simple modifications.
• A custom layout does not overwrite the default layout, this default layout is still be available.
• The maximum number of straight and inclined strands for standard sections are specified.
• Spacing of strands: the center to center spacing between the strands.
• Inclined strands: Number of strands per row, maximum number of rows, minimum distance to side.
• Straight strands: Minimum distance to side.
• Number of straight strands per row: a maximum of 12 rows of straight strands is allowed.
Moving loads parameters

The moving standard loads as well as all custom moving loads available are:
– CL-625 (CSA S6-14 and CSA S6-19)
– CL-625-ONT (CSA S6-14 and CSA S6-19)
– CL-675 (CSA S6-14 and CSA S6-19)
– CF3E-500 (Quebec) and CF3E-W (Quebec)
– QS660 (Quebec)
– CFHN-1500 and CFHN-W (Quebec)
– MTQ-340 (Quebec)
– CS600 (CSA S6-88)
– OHBDC (Ontario)
– Egyptian Loads

The lateral distribution coefficients wizard calculates the lateral distribution coefficients with respect to the CAN/CSA S6 requirements.
Custom moving loads

-ID: The unique identifier of the custom moving load. In most cases, this value is incremented automatically and need not be modified.

-Load Name: The name of the load. This name serves as a reference in other input forms in the program. -Truck load: The dynamic load allowance for the truck load must be specified. The axle positions and loads must be specified in the table. The loads entered correspond to the full axle loads which are twice the wheel loads. The position to enter in the table is the cumulative distance from the front axle. The first axle position is always 0. A maximum of 40 axles may be defined for each custom moving load.

-Lane load: The uniform lane load must be specified as well as the concentrated lane load. The concentrated lane load is specified as a ratio of the truck load.
Thermal gradient parameters

• Thermal gradients must be considered in the design of a multi-span bridge where there is continuity at the supports.
• Thermal gradients can generate non-negligible forces in the structure.
• Thermal gradient: This value indicates the maximum temperature difference between the top of the slab and the bottom of the beam.
• The program assumes a linear temperature gradient on the depth of the composite beam.
Slab parameters

• The concrete slab is cast in place during the construction of the bridge.
• The reinforcing steel in the slab and in the stiffener beams at supports ensure the continuity of the deck at interior supports for the additional dead loads, as well as for the live loads.
• The required dimensions of the concrete slab are defined by the user.

-Concrete Resistance (f’cd): The ultimate stress (f’c) of the slab material.
-Concrete Density: The density of the slab material which is used to determine its self-weight.
-Reinforcement Yield Stress (Fy): The yield stress of the reinforcement bars material.
-Slab Width (b): The slab width with respect to the beam analyzed. For interior beams, it is equal to the distance between the beams while for exterior beams it is equal to half the distance from the beam analyzed and the adjacent beam plus the length of the cantilever part.
-Slab Thickness (t): The thickness of the slab.
-Haunch Thickness (th): The thickness of the haunch if any.
Span data

All span data that vary from one span to another are defined by users.

The following data is to be defined:
– Span Length (Lp)
– Nb. Stiffener Beams between Supports
– Additional Dead Loads 1 and 2
– Live Loads (other than moving loads)
– Initial Concrete Resistance (f’co)
– Concrete Resistance at 28 Days (f’c28)
– Concrete Density
– Strands
– Nb. Straight Strands (Ns)
-Nb. Inclined Strands (Ni)
– Strands Raise Point: Left (L1) and Strands Raise Point: Right (L2)
– Eccentricity Calculation Method
– Eccentricity of Strands at Center (Ec)
– Min. Dist. of Inclined Strands to Bottom (Dbi)
– Left Support Constant (C1) and Right Support Constant (C2)
– Support Tension (T)
Stirrup parameters
• The stirrups diameter and the yield stress of the stirrups material are defined.
• The spacing of the stirrups required to resist the shear forces is calculated.
• The stirrup spacing calculated by the program accounts for anchoring zones.
• The horizontal shear between the beam and the slab will be taken by the stirrups which will be extended in the slab.

Stiffener beams parameters
• The stiffener beams are added between the longitudinal beams.
• They enhance the lateral stability of the bridge and allow for a better distribution of forces on the width of the bridge.
• These stiffener beams are not designed by the program, their dimensions and material properties are required solely for determining their self weight.
• The number of stiffener beams between the supports can vary from one span to another.

Losses parameters

The calculation of pre-stress losses is an important part of the calculation of pre-stressed beams. The losses of pre-stress during the life of the bridge beginning with the transfer of the pre-stress to the concrete can be over 20% of the initial strand tension.

•CALCULATION METHOD: Two calculation methods of the losses are supported. The first is the method proposed by the selected design code (CSA S6). The second method, based on Picard (2001), is a step-by-step approach which determines the losses over time. The calculation of losses accounts for the losses due to relaxation, shrinkage and creep.

•RELATIVE HUMIDITY: The average annual relative humidity in the surrounding of the bridge. This value has an influence on shrinkage and creep.

•AREA OF ORDINARY STEEL BARS (As) : The area of ordinary steel bars influences the losses caused by shrinkage in the step-by-step approach. When the As is not equal to zero, the step-by-step approach tends to predict lower losses caused by shrinkage.

•CONCRETE CURE METHOD: A normal concrete cure is made at room temperature. An accelerated steam cure is a thermal treatment of the concrete allowing to accelerate its hardening cycle.

•EVENT CHRONOLOGY: The production of precast prestressed beams is made in several steps which are described below. Note that the T4 time is the reference time and is always equal to zero. Thus, the T1 to T3 times are negative and the T5 to T7 times are positive.

•TENSIONING OF STRANDS (T1): The prestressing steel is put in tension and is retained by jacks and other mechanisms of steel retention. At this step, no concrete is present. The losses by relaxation start at this time.

•CONCRETE CASTING (T2): The concrete is cast in place and the concrete cure begins. This data is considered in the calculation of concrete age for the calculation of creep losses.

•END OF CURE, beginning of shrinkage (T3) : When the cure is stopped, the surrounding humidity drop provokes the start of the shrinkage of concrete. The shrinkage occurring between time T3 and time T4 will not induce pre-stressing losses.

•TRANSFER OF PRESTRESS (Reference Time) (T4): At this step, the concrete is sufficiently resistant to support the prestressing forces. The prestressing strands are released and transfer the forces to the concrete beam. Due to the arrangement of the strands in the beam, the beam tends to camber under the effect of the prestressing forces. From this time, the losses caused by creep and remaining shrinkage begin.

•CASTING OF SLAB AND STIFFENER BEAMS (T5): At this time, the loads induced by the self-weight of the slab and the stiffener beams are held by the prestressed beam only. Once hardened, the slab acts in a composite manner with the beam to support the additional loads added later to the structure. Once the concrete slab has hardened, the program assumes the continuity at the interior supports which affects the effect of additional loads.

•ADD. DEAD LOADS 1 (edges, sidewalks and curbs) (T6): The time at which the additional loads are applied to the structure has an effect on the losses. The intensity of these loads is specified for each span in the Span Data command.

•ADD. DEAD LOADS 1 (asphalt) (T7): The time at which the additional loads are applied to the structure has an effect on the losses. The asphalt is considered as a dead load which has a load factor larger than other dead loads. It has thus been separated from other additional dead loads. The intensity of these loads is specified for each span in the Span Data command.