double corbel.pdf

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Summary ofACI 318-02 Appendix A

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Double Corbel Design per ACI 318-02 Appendix A, US Customary UnitDeep Beam (1) | Deep Beam (2) | Dapped-Beam End | Single Corbel | Double Corbel

A double corbel projecting from a 14 in. 14 in. column is to be designed to support precastbeam reaction forces at 6 in. from the face of the column. The factored vertical load to becarried is 61.8 kips. Due to restraint of beam creep and shrinkage deformations, a factoredhorizontal force of 14.3 kips is assumed to develop. The upper column carries a factored axialload of 275 kips.The concrete strength is 4 ksi (normal density), and the yield strength of reinforcement is takenas 60 ksi.

Determine the Bearing Plate Dimensions:Choose a 12 in. 6 in. 1/2 in. bearing pad. The bearing plate area is 12(6) = 72 in.2 and thebearing stress is 61.8(1000)/72 = 858 psi. Since this is less than the bearing stress limit, i.e.

the bearing size is adequate.

Choose the Corbel Dimensions:Choose a depth at the column face of 18 in. The ACI Code requires that the depth at theoutside of the bearing area is at least one-half of the column face depth. Therefore, select adepth of 10 in. at the free end of the corbel. The selected dimensions for the corbel aresummarized in Figure 1.

Figure 1(Click here to view a larger image)

Establish the Strut-and-Tie Model:To allow for load eccentricities and erection tolerances, consider the vertical load to be placed1 in. toward the edge of the corbel from center of bearing plate. Thus, the position of verticalload is 1 + 6 = 7 in. from the face of column.

Strut-and-Tie Resources Web Site - Worked Design Examples: Doub... http://dankuchma.com/stm/STM/examples/DCorbel/DCorbel.htm

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The geometry of the assumed truss is given in Figure 2. The center of the tie is assumed to belocated 2 in. from the top of the corbel. Thus, d = 18 2 = 16 in. The horizontal strut BB isassumed to lie on the horizontal line passing through the sloping end of the corbel.The location of strut CB centerline can be found by calculating the required compressive forcein strut CB, NCB, and the strut stress limit to obtain the strut width a. The strut CB force is

and the limit stress on the nodal zone B (also strut CB) is Thus, we have

This fixes the geometry of the truss and means that member AB has a horizontal projection of0.46 + 7 + 5.58/2 = 10.25 in.


Determine the Required Truss Forces by Statics:The required forces in all the members of the truss are given in the following table. Note thatpositive indicates tension, negative compression.

Member AA' AB BB' CB BDForce (kips) +54.1 -73.5 -39.8 -199.3 -137.5

Design the Tie:

The area of reinforcement required for tie AA is and the

minimum area of reinforcement is

Choose 6 No. 4 bars,


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Check the Struts:The struts will be checked by computing the strut widths and checked whether they will fit inthe space available.The stress of the diagonal strut AB is limited to

Hence, the required width for strut

AB is Select a width of 3.00 in. for strut AB.The stress of the vertical struts BD and CB and horizontal strut BB is limited to

Hence, the required widths for strut

BD and BB are andrespectively. Choose 4 in. width for strut BD and 2 in. width for strut BB. The required widthfor strut CB is equal to a, i.e. 5.58 in.As shown in Figure 3, all the strut widths fit into the outline of the corbel region. Thus, thissolution is accepted. Note that Figure 3 also shows a summary of the stress in each strut and itscorresponding stress limit (in brackets).


Calculate the Minimum Reinforcement Required for Crack Control:According Appendix A, the minimum reinforcement provided must satisfy

to be able to take as 0.75 for the diagonal struts, and the minimumspacing for the vertical reinforcement is the smallest of 12 in. or d/2.In addition, the code requires closed stirrups or ties parallel to the reinforcement required fortie AA to be uniformly distributed with 2/3 of the effective depth adjacent to tie AA, i.e. 2/3(16) = 10.67 in. Use 11 in. The area of these ties must exceed , where is thearea of reinforcement resisting the tensile force . Hence the minimum area required is

Try 3 No. 3 closed stirrups with average spacing of 11/3 = 3.67 in.


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Since this amount of reinforcement satisfies both requirements, provide 3 No. 3 closed stirrupsdistributed over a depth of 11 in. from tie AA with a concrete cover of 1 in.

Design the Nodal Zones and Check the Anchorages:The width a of nodal zone A was chosen to satisfy the stress limits on the nodal zone.To anchor tie AA, the horizontal loop is used. The detail is shown in Figure 4. To satisfy thenodal zone stress limit, the tie reinforcement must engage an effective depth of concrete atleast equal to

This limit is easily satisfied since the nodal zone available is 4 in.

The required anchorage length for tie AA is Since

this is less than the available length, i.e. 3 + 6 (1 + 3/8) = 7.63 in., the anchorage length isadequate.

Summary of the Design:The reinforcement details for the corbel designed using the strut-and-tie model according toAppendix A are shown in Figure 4.


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double corbel.pdf

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