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Section 3: Strut-and-Tie Method

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Geometric Constraints

The angle between compression struts and tension ties must be greater than 26 degrees.

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Structural Analysis

Do not use Strut and Tie Modeling for standard girders and bent caps. Strut and Tie Modeling is appropriate to use when designing footings, dapped beam ends, post-tensioning anchorage zones, deviation diaphragms, bents that use high load bearings, and other special designs.

Place nodes at applied loads and reactions. More nodes can be added as long as the tension ties are located where reinforcement is normally placed. In general, nodes need to be located at the center of the tension ties and compression struts. If there is sufficient concrete in the incoming member the strut can be considered within both members, such as in the case with a column and a footing, and the nodes can be placed where the two members meet.

A 3 dimensional truss can be broken into multiple 2 dimensional trusses to be analyzed. When analyzing the 2 dimensional trusses, use the same reactions as the 3 dimensional truss, but recalculate the applied loads so equilibrium is satisfied.

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Design Criteria

When designing broad members that are uniformly loaded on one end and discretely loaded on the other end, use Article 5.10.9.4.

Development length for the tension tie reinforcement must be in accordance with Articles 5.6.3.4.2 and 5.11.2.

Nodal geometry is needed to analyze the capacity of a strut and the capacity of the node itself; however, if the node is significantly large, such as with a column and a footing, no nodal analysis is needed. If nodal analysis is needed, use Article 5.6.3.5.

Replace Article 5.6.3.3.3 with the following:

• For struts with reinforcement satisfying Section 5.6.3.6:

but not greater than the minimum of1

• and 0.85

• For struts without reinforcement satisfying Section 5.6.3.6:

but not greater than the minimum of

and 0.85

The nominal capacity of a strut shall be taken as:

where:

• Pn = nominal capacity of a strut (kip)
• = efficiency factor
• = specified compressive strength (ksi)
• Ac = cross-sectional area of the strut at the face of the node (in2)
• = angle between the compressive strut and the adjoining tie (deg)
• = length of the node adjoining the strut. For CCC and CCT nodes and for CTT nodes from Figure 5.6.3.3.2-1.
• ws = width of the strut at the face of the node (Figure 5.6.3.3.2-1)

Replace Figure 5.6.3.3.2-1b "(b) Strut anchored by bearing and reinforcement" with the following figure:

Figure 5-1. Strut Anchored by Bearing and Reinforcement (CCT node)

Replace Figure 5.6.3.3.2-1 "(a) x-x" (cross section) with the following figure:

Figure 5-2. CTT node and abutting strut width limitations

Replace Article 5.6.3.6 with the following:

• Structures and components or regions thereof, except for slabs and footings, which have been designed in accordance with the provisions of Article 5.6.3, and using the efficiency factor associated with reinforced struts (Equation A-7) shall contain crack control reinforcement in an orthogonal grid. Horizontal reinforcement alone shall be used. The spacing of the bars in the strut reinforcement shall not exceed 12.0 in.
• The amount of reinforcement within a strut shall be calculated as2:

Where:

• = equivalent reinforcement perpendicular to the strut axis
• AsH = total of horizontal reinforcement in a strut within spacing sH(in2)
• b = width of the member (in)
• sH = spacing of horizontal reinforcement (in)
• AsV = total area of vertical reinforcement in a strut within a spacing, sV (in2)
• sV = spacing of vertical reinforcement (in)
• The minimum amount of reinforcement in a strut shall be taken as3:

Where:

• Pu = factored load in a strut (kip)
• fy = yield strength of the reinforcement within a strut (ksi)
• b = width of the member transverse to the plane of the strut-and-tie model
• l = length of the strut
• m = slope of the angle of compression dispersion (Figure 5-3)

Figure 5-3. Dispersion of compression in a bottle-shaped strut (View is perpendicular to the plane of the dispersion of compression)

Guidelines

The tension tie reinforcement must be close enough to the drilled shaft to be considered in the truss analysis. Therefore, the tension tie reinforcement must be within a 45 degree distribution angle (i.e. no more than dc away from the member on either side).

Use strut bearing lengths proportional to the amount of load carried by the strut at a node.

Conservatively assume the width of a strut in a CCC node, hs, as the height of the compression block.

1. Brown, Michael et al. "Design for Shear in Reinforced Concrete Using Strut-and-Tie Models," Report No. FHWA/TX-06-0-4371-2, Appendix A, Equation A-7.

2. Brown, Michael et al. "Design for Shear in Reinforced Concrete Using Strut-and-Tie Models," Report No. FHWA/TX-06-0-4371-2, Appendix A, Equation A-14.

3. Brown, Michael et al. "Design for Shear in Reinforced Concrete Using Strut-and-Tie Models," Report No. FHWA/TX-06-0-4371-2, Appendix A, Equation A-15.