SNAPBoxBeam Technical Summary

Straight steel box girder bridges are modeled as 2D finite element systems using beam elements. The global X-axis is in the longitudinal direction of the bridge to the right. Y-axis is upward. The local coordinate system is the same as the global system. Right-hand rule is applied for Z-axis.

Beam Element

Figure 2-1 Coordinate System and Beam Element

Beam elements used in the model have 2 nodes. Y-Translation (Deflection) and Z-Rotation are the two degrees of freedom taking into account for each node.

Finite element formulation for the two-node beam elements is as follows:

[K^e]{u} ={ f}

where [K^e] is a 4x4 element stiffness matrix, {u} is a 4x1 nodal displacement vector, and {f} is a 4x1 nodal force vector respectively.

For the element stiffness matrix, users can find it in many textbooks. However, for composite construction, different stiffnesses are used for different stages.

Material Model

Linear elastic material model is assumed for steel and concrete.

In the program, concrete is transformed to steel.

Users shall input the material properties of steel and concrete in the program using Material Properties input command. There are default values for the material properties in the Material Property Definition dialog box.

Section Model

In non-composite stage, concrete deck does not have contribution to the element stiffness. The weight of the concrete deck will apply on the steel section only.

For the superimposed dead load, which is sustained, creep effect is considered according to AASHTO requirements. The deck concrete is transformed to steel in terms of 3n, where n is the ratio of modulus of elasticity between steel and concrete.

For live load, deck concrete is transformed to steel in terms of 1n.

Effective concrete slab width which contributes to the element stiffness of the composite section is calculated in accordance with the AASHTO requirements as the smallest of:

One-fourth of the span length

Center to center distance between beams/girders

Twelve times the minimum structural depth of slab

In dead load positive moment region, the element section is assumed to be composite for superimposed dead load and live load if users specify the structures as composite. In negative moment region, users could define the percentage of concrete deck contribution for composite section, and the negative moment reinforcement could be provided.

Users have to define the typical bridge section dimensions including the beam spacing, deck slab thickness etc which are used to calculate the effective deck slab width and live load distribution factor etc.

Users shall define the girder section dimensions in Girder Section dialog box, and then use Select Element command and Assign Section command to assign Girder sections to each element. See Step-by-Step Tutorial.

Restraints

Restraints at piers and abutments are assumed to be fixed in y-direction only. The rotations are released. Because the X-translation of nodes is not considered in the model, the longitudinal translation freedom is irrelevant.

The program will automatically provide a hinge at the far left end of the girder, and rollers at each pier and the far right end of the girder.

Loads

Users can define load information using Loads definition command. It will prompt the Load Definition dialog box.

For weight of concrete deck and steel girder itself, users can specify the detail factor to take into account of the addition weight of integral wearing surface, cross-frame steel, stiffeners etc.

Users can define as many as necessary superimposed dead load cases. It could be distributed or concentrated load and applied on 1n or 3n section.

The program supports AASHTO standard H, HS, Alternate Loading and HL93 vehicle live loads. It also supports sidewalk live load.

The program will automatically calculate the load distribution factors and impact factors (dynamic allowance) in accordance with the AASHTO codes.

Structural Analysis

High-Speed Solver

SNAPBoxBeam is incorporated with a high-speed solver for static finite element analysis of structures. There is no limit on structure size, but it relies on the system configuration of your computer.

Sign Convention

SNAPBoxBeam adopts the following convention of the general practice.

Deflection: Positive (Upwards), Negative (Downwards)

Rotation: Positive (Counter-Clockwise), Negative (Clockwise)

Moment: Positive (Bottom Fiber in Tension), Negative (Top Fiber in Tension)

Shear: Positive (Clockwise), Negative (Counter-Clockwise)

Reaction: Positive (Upwards), Negative (Downwards, Uplift)

Stress: Steel: Positive (Tension), Negative (Compression)

Concrete: Positive (Compression), Negative (Tension)

Analysis Procedure

Following chart shows the analysis procedure used by SNAPBoxBeam.

Self-Weight Dead Load Analysis for non-composite structure

Update the structure to 3N-composite

3N-composite Dead Load Analysis for 3N-superimposed dead load

Update the structure to 1N-composite

1N-composite Dead Load Analysis for 1N-superimposed dead load

Live Load Deflection and Reaction Analysis

Live Load Moment and Shear Analysis

Unfactored and Factored Dead Load and Live Load Combination

Unfactored and Factored Stress Analysis

Structural Design

Users can specify one of the three design methods: Allowable Stress Method (ASD), Load Factor Design Method (LFD) of AASHTO Standard Specifications for Highway Bridges and Load and Resistance Factor Design Method (LRFD) of AASHTO LRFD Bridge Design Specifications.

General Code Check

Live Load Deflection Requirements of Codes.

According to Article 10.6 of AASHTO Standard Specifications for Highway Bridges, the live load deflection due to service load and impact is limited to L/800. SNAPBoxBeam checks this requirement accordingly.

Uplift Forces at Supports

Article 3.17 of AASHTO Standard Specifications for Highway Bridges requires to check the possible UPLIFT forced at supports and to provide adequate attachment of the superstructure to the substructure. SNAPBoxBeam checks whether there are uplifts at supports according to Art.3.17.1.

Girder Depth Requirements

Article 10.5 of AASHTO Standard Specification for Highway Bridges and the Article of LRFD Bridge Design Specifications specify the requirements for girder depth ratio. SNAPBoxBeam checks these requirements automatically.

Section Ductility Requirement for Composite Girders

SNAPBoxBeam checks the ductility in accordance with Article 10.50.1.1.2 of AASHTO Standard Specification and Article 6.10.5.2.2 of LRFD Bridge Design Specification.

Overload Stress for ASD and LFD Design

Article 10.57 of AASHTO Standard Specification requires to check the overload stress.

General girder proportion is checked for LRFD.

Article 10.9 of AASHTO LRFD Bridge Design Specification requires to check the member proportion.

Flexural Capacity Check

For Allowable Stress Design, the provisions related to flexural capacity in Article 10. are applied.

For Load Factor Design, the provisions related to flexural capacity of girder sections in Article 10.51 are applied.

For LRFD, the provisions in Article 6.10.5 to 6.10.6 of LRFD Bridge Design Specifications which are applied. The flexural capacity is checked for Strength Limit State of maximum DL and Live Load.

Shear Capacity Check

Transverse stiffener information is defined by users in Details Definition dialog box, which is related to the shear capacity of the sections.

The program supports three types of transverse stiffeners: Single Plates, Plate Pairs and Angles.

In accordance with the code requirements, unstiffened web and stiffened web shear capacity are calculated and the transverse stiffener section defined by users are also checked.

For ASD and LFD design, shear capacity is only checked for maximum DL plus LL+I load case.

Fatigue Stress/Strength Check

The program checks the fatigue stress range due to truck loading, lane loading and single truck loading in ASD and LFD and determines the allowable weld details.

The program checks the fatigue stress range due HL93 truck loading in LRFD and determines the allowable weld details.

For LRFD design, web fatigue requirements for flexure and shear are also checked accordance with the code.

Constructability Check

Minimum plate thickness for constructability is checked for LRFD design.

For LRFD, the program checks the constructability for flexure and shear capacity of the girders.

Serviceability Limit State Check

Serviceability Limit State control for Permanent deflection requirements of LRFD is checked.

Shear Connector Design

The program supports three kinds of shear connectors: (1) Shear Studs, (2) Channels, and (3) Others. In reality, all types of shear connectors are covered in the program.

For shear connector design, the basic information for shear connectors is required to be defined in the Details Definition dialog box.

The spacing of shear connector is designed by the program in accordance with the Fatigue Criteria of codes, and checked with the ultimate strength.