3. Deep Beam (Transfer Girder) Analysis - spWall Software

spWall is a program typically used for the analysis and design of reinforced concrete shear walls, tilt-up walls, bearing and architectural precast walls. Additionally, the program can be used to analyze and design deep beams, transfer girders, coupling beams, corbels, pile caps, and other non-standard concrete elements with geometric discontinuity.

spWall uses a graphical interface that enables the user to easily generate complex models. Graphical user interface is provided for:

• Structural member geometry (including any number of openings and stiffeners)

• Material properties including cracking coefficients

• Loads (point, line, and area),

• Support conditions (including translational and rotational spring supports)

spWall uses the Finite Element Method (FEM) for the structural modeling, analysis, and design of slender and non-slender reinforced concrete members subject to static loading conditions. The member is idealized as a mesh of rectangular plate elements and straight-line stiffener elements. Members of any geometry are idealized to conform to geometry with rectangular boundaries. Plate and stiffener properties can vary from one element to another but are assumed by the program to be uniform within each element.

Six degrees of freedom exist at each node: three translations and three rotations relating to the three Cartesian axes. An external load can exist in the direction of each of the degrees of freedom. Sufficient number of nodal degrees of freedom should be restrained in order to achieve stability of the model. The program assembles the global stiffness matrix and load vectors for the finite element model. Then, it solves the equilibrium equations to obtain deflections and rotations at each node. Finally, the program calculates the internal forces and internal moments in each element. At the user’s option, the program can perform second order analysis. In this case, the program takes into account the effect of in-plane forces on the out-of-plane deflection with any number of openings and stiffeners.

In spWall, the required flexural reinforcement is computed based on the selected design standard (ACI 318-14 is used in this example), and the user can specify one or two layers of wall reinforcement. In stiffeners and boundary elements, spWall calculates the required shear and torsion steel reinforcement. Member concrete strength (in-plane and out-of-plane) is calculated for the applied loads and compared with the code permissible shear capacity.

For illustration and comparison purposes, the following figures provide a sample of the input modules and results obtained from an spWall model created for the reinforced concrete deep beam (transfer girder) in this example.

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Figure 16 - spWall Interface

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Figure 17 - Assigning Supports for Deep Beam (spWall)

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Figure 18 - Assigning Dead Loads for Deep Beam (spWall)

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Figure 19 - Assigning Live Loads for Deep Beam (spWall)

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Figure 20 - Solve and Mesh Options (spWall)

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Figure 21 - Loads and Reactions (kips) (spWall)

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Figure 22 - Service Vertical Displacement (in.) (spWall)

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Figure 23 - Service Dxyz Displacements Contour (in.) (spWall)

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Figure 24 - Internal Axial Forces X-Direction (Nxx) (kips) (spWall)

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Figure 25 - Internal Axial Forces Y-Direction (Nyy) (kips) (spWall)

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Figure 26 - Internal Shear Forces (Nxy) (kips) (spWall)

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Figure 27 - Required Horizontal Reinforcement (Asx) (in.2/ft) (spWall)

Table 1 - Required and Provided Horizontal Reinforcement Based on spWall Results

Horizontal As,provided based on As,min

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Increment

Elements

As, in.2/ft

As,required, in.2

Reinforcement

As,provided, in.2

1

408 - 744

0.60

0.50

2#5 @ 10 in.

0.62

Horizontal As,provided based on As,required

Increment

Elements

As, in.2/ft

As,required, in.2

Reinforcement

As,provided, in.2

2

360

0.85

0.81

4#5

1.24

312

1.58

3

264

2.35

1.83

4#7

2.40

216

3.15

4

168

4.02

3.00

4#8

3.16

120

4.97

5

72

6.01

4.39

4#10

5.08

24

7.17

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Figure 28 - Required Vertical Reinforcement (Asy) (in.2/ft) (spWall)

Table 2 - Required and Provided Vertical Reinforcement Based on spWall Results

Zone

Elements

As, in.2/ft

As,required, in.2

Reinforcement

As,provided, in.2

1

337 - 344

0.60

0.50

#4 Stirrups (4 legs) @ 10 in.

0.80

2

345 - 355

1.41

1.17

#6 Stirrups (4 legs) @ 10 in.

1.76

3

356 - 365

0.60

0.50

#4 Stirrups (4 legs) @ 10 in.

0.80

4

366 - 376

1.41

1.17

#6 Stirrups (4 legs) @ 10 in.

1.76

5

377 - 384

0.60

0.50

#4 Stirrups (4 legs) @ 10 in.

0.80

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33

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Figure 29 - Summary of Provided Reinforcement (spWall)

The previous figure shows the recommended reinforcement configuration selected for educational and illustration purposes. The provided reinforcement configuration can vary based on engineering judgement taking into account the configuration practicality, erection flexibility, number of girders, steel tonnage allowance and the project complexity. Note that the strength reduction factor used in the STM is 0.75 compared with 0.90 used in the FEM.

The STM is used to check strength limit states, however, structural members should be checked for serviceability requirements. The ACI code allow the use of traditional elastic analysis (along with STM) for deflection checks. On the other hand, the FEM adopted by spWall reports deflection values for the entire model without the need of using other methods to complete the design (δmax = 0.038 in. for this example as shown in Figure 22).