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Summary ofACI 318-02 Appendix A

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

A dapped beam end shown in Figure 1 is to be designed to transmit a factored vertical reactionforce of 60 kips and a factored horizontal reaction force of 12 kips to the support. The verticalreaction is assumed to act 2 in. from the left end of the beam. The beam is 16 in. wide andmade from 6 ksi concrete (normal density) and 60 ksi steel reinforcement.

Figure 1(Click here to view a larger image)

Define the D-region and Calculate the Forces Acting on the Boundary of the Region:The extension of the D-region is assumed to be one member depth plus the extended part, i.e.30 + 6 = 36 in. The forces at the right end are a moment of 60(36-2) + 12(15-14) = 2052 k-in.,an axial tension force of 12 kips, and a shear force of 60 kips. Figure 1 shows the forces actingon the D-region.Determine the bearing plate dimensions:Choose a 4 in. 4 in. 5/8 in. steel angle placed across the width of the beam at the support.

The bearing plate area is and the bearing stress isSince this is less than the bearing stress limit, i.e.

the bearing size is adequate.

Establish the Strut-and-Tie Model:The geometry of the assumed truss is given in Figure 2.

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Figure 2(Click here to view a larger image)

The location of strut BE centerline is dictated by the required compressive block height a atmidspan and is assumed to be 3 in. from the top of the beam. Similarly, the center of tie AD isdictated by d at midspan and is assumed to be 3 in. from the bottom of the beam.Tie BC is located just far enough from the dap face to distribute the steel reinforcement and isassumed to be located 6 in. from the dap face. Tie EF is assumed to be 18 in. from tie BC.Node D is the meeting point of struts BD, DE, CD, and tie AD.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 AB AD BC BD' BE CD CF DE' EF'Force (kips) -82.6 +68.7 +102 -56.1 -19.5 -127 +76.5 -75 +60

Design the Tie:

The area of reinforcement required for tie AD is Choose4 #6 bars,

The area of reinforcement required for tie BC is Try touse 4 #5 two-legged, closed stirrups at 2 in. o.c.,

The area of reinforcement required for tie CF is Assumethat #8 bars are used for the midspan bottom reinforcement, use 3 #8,

The area of reinforcement required for tie EF is Try touse 4 #4 two-legged stirrups at 4 in. o.c.,

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Check the Struts:The struts will be checked by computing the strut widths and then checking whether they fit inthe space available.The stresses in all the struts are conservatively limited to

Hence, the required width for strut

AB is Choose a width of 3 in. for strut AB. The required width

for strut BD is Select a width of 2 in. for strut BD. The required

width for strut CD is Select a width of 4 in. for strut CD. The

required width for strut DE is Select a width of 3 in. for strut DE.

The required width for strut BE is Choose a width of 1 in. forstrut BE.As shown in Figure 3, all the strut widths fit into the outline of the disturbed region. Thus, thissolution is accepted. Note that Figure 3 also summarizes the strut stress demands and limits (inbrackets).

Figure 3(Click here to view a larger image)

Design the Nodal Zones and Check the Anchorages:To anchor tie AD, the steel is welded to the steel angle. To satisfy the stress limits in nodes Aand D, the tie reinforcement must engage an effective depth of concrete at least equal to

This requirement is easily satisfied since the nodal zone available is 4 in.The required anchorage length for tie AD at the right end is

Provide beyond point D, which isassumed as anchor point.The steel provided for tie CF is 3 #8. The required development length for #8 bars is

but the available development length is onlyabout 6 2.5 + 3 = 6.5 in. The force that can be developed in 3 #8 bars is

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which is less than the required tie CF force of 76.5 kips. Thus,

provide horizontal U bars to anchor the force. The area required is Use 2 #6 Ubars placed above the #8 bars.Other Detailing Considerations:To improve crack control and ductility, a minimum amount of horizontal reinforcement parallelto and above tie AD will be provided. If the dapped end is treated as a corbel, the required areaof such additional reinforcement would be Provide 2 #4 Ubars, distributed over two-thirds of the effective depth.Summary of the Design:The reinforcement details for the dapped beam end designed using the strut-and-tie modelaccording to Appendix A are shown in Figure 4.

Figure 4(Click here to view a larger image)

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Q & A | Related LinksThis page was created and is maintained by Tjen TjhinUniversity of Illinois at Urbana-ChampaignLast update: June 01, 2002

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