DESIGN OF VERTICAL SHEAR IN TRANSFER PLATES 1

Transcription

1 Structural Concrete Software System TN271_transfer_plate_shear_ DESIGN OF VERTICAL SHEAR IN TRANSFER PLATES 1 Bijan O Aalami 2 Shear normal to the plane of a transfer plate (vertical shear) is generally high in magnitude and requires special treatment. This Technical Note describes a procedure used for its design. The procedure described is followed by a numerical example. The shear design in transfer plates, in concept, is no different from the general philosophy of structural engineering design. A designer ensures that: (i) there exists an uninterrupted load path from each load on the structure to the foundation; and (ii) each load path has the strength to carry the forces it is calculated for; and (iii) the structure is provided with adequate ductility to redistribute the forces and develop the load paths envisaged by the designer. The following outlines the selection of load paths to be used for design of vertical shear, and the determination of the required reinforcement along the path length. In flat slab construction common to commercial and residential buildings, the slab proper is generally strong enough to resist the calculated vertical shear. Occasionally, slabs may have to be reinforced against punching in the vicinity of supports. The significantly larger shear demand in transfer plates oftentimes requires that a distinct grid work of physical or virtual beam spines be provided and designed to direct the shear flow to the supports. Once a grid work of shear spines is envisaged, the force in each of the spines is determined and the associated reinforcement calculated. The spines can extend beyond the soffit of a slab, as is the case of physical beams, or they can be fully concealed within the slab thickness (virtual beams). In both variations, the determination of shear force to be carried by each spine and the design process are the same. STRUCTURAL MODEL Figure 1a shows the plan of a slab corner supported on a column. The arrows indicate the direction of principal vertical shear. The intensity of vertical shear increases closer to the support. Figure 1b shows a region in the slab, referred to as shear spine, reinforced to resist vertical shear. The shear spine terminates at the shear flow boundary that encircles the support and must be adequate to sustain the entire shear associated with the support it encircles. Figure 1a shows the plan of a slab corner supported on a column. The arrows indicate the direction of principal vertical shear. The intensity of vertical shear increases closer to the support. 1 Copyright 2007 ADAPT Corporation 2 Professor Emeritus, San Francisco State University; Principal, ADAPT Corporation support@adaptsoft.com 1733 Woodside Road, Suite 220, Redwood City, California, 94061, USA, Tel: (650) Fax (650)

2 (a) Shear flow in slab next to column (b) Shear design components FIGURE 1 VERTICAL SHEAR FLOW NEXT TO A SUPPORT At any design section shown in Fig, 1b, the demand actions on the section and the resistance provided by the section are illustrated in Fig. 2 FIGURE 2 ACTIONS ON A DESIGN SECTION Where, on the demand side the actions are: Vu Mu Nu = Demand shear; = Demand moment; and = Demand axial force. On the resistance side the actions are: C = compression zone force; 2

3 T Vc Vs P = Tensile force of longitudinal reinforcement; = shear force resistance provided by concrete; = shear resistance provided by shear reinforcement; and = force in post-tensioned tendons. The focus of this Technical Note is the determination of the reinforcement associated with Vs. The prerequisites for the validity of the procedure described herein are: The section must have adequate reinforcement to resist the tensile force T; The compression zone of the section must be adequate to resist the compression force C; The concrete section and strength must be adequate to develop the internal compression strut shown in Fig. 2. This is controlled by the maximum shear Vu that a section is permitted to resist. Different building codes impose a limit on Vu, in order to avoid crushing of concrete 3. Consider the transfer plate shown in Fig. 3. Its longer side is 25m. It has a thickness of 1.50m and supports a multi-story tower above it. The shear transfer in the plate is envisaged to be through the shear spines shown in Fig. 4. The spines are considered continuous along the perimeter of the plate between the column supports. The noncontinuous spines from the columns toward the interior of the plate are extended far enough to where the slab on its own can resist the vertical shear. The provision of shear spines and the length of their extension are somewhat similar to the shearhead used in common residential and commercial floor systems (Fig. 5). The shearheads terminate, where the capacity of slab is adequate to resist the demand shear. (a) View of transfer plate (b) Deflection of plate under selfweight FIGURE 3 VIEW OF TRANSFER PLATE 3 As an example ACI-318 (chapter 11) controls the crushing of concrete by limiting the value of Vs not to exceed [(2/3)* f c]*b w *d, where b w is the width of the design section 3

4 (a) View of shear spines (b) Design sections of shear spines FIGURE 4 PLAN OF SHEAR SPINES AND DESIGN SECTIONS OF EACH FIGURE 5 AN EXAMPLE OF SHEARHEAD REINFORCEMENT The shear spines start at a distance a from the face of support (Fig. 6). The distance a depends on whether the plate is conventionally reinforced or post-tensioned. ACI-318 (Chapter 11) suggests the following: For conventionally reinforced concrete (RC) a = d For post-tensioned plates (PT) a= h/2 Where h is the total depth of the section and d is distance of between the compression fiber and the centroid of tension, but not less than 0.8h (ACI-318). The value of design shear in each instance is determined at distance a. The shear reinforcement calculated at distance a is continued to the face of support. 4

5 FIGURE 6 LOCATION OF FIRST DESIGN SECTION FOR VERTICAL SHEAR A central point in the selection of shear spines is that they must form a closed perimeter around each of the supports, in order to capture the entire flow of vertical shear to the foundation. Figures 6 and 7 illustrate the boundary perimeter of the shear spines around a corner column. The values of design shear for each of the boundary segments is shown in Fig. 7-b. The distribution of vertical shear for each of the segments is illustrated in Fig. 8. (a) Delineation of shear flow (b) Shear flow values FIGURE 7 ILLUSTRATION OF BOUNDARY OF SHEAR FLOW FOR AN EDGE COLUMN 5

6 FIGURE 8 SHEAR FLOW AROUND A CORNER COLUMN CROSS-SECTIONAL GEOMETRY OF SPINE The cross-sectional geometry of each spine is not specified in building codes. Figure 9 provides a guideline for its selection. (a) Spine extends to slab boundary (b) Shear spine next to boundary FIGURE 9 GUIDELINES FOR SELECTION OF SHEAR SPINE CROSS-SECTION SHEAR REINFORCEMENT The shear reinforcement generally consists of vertical bars (J-bars) placed at regular spacing along each spine and across its width. The vertical bars are encased in a U stirrup and closed at the top as shown in Fig. 10a for an example of 8 J-bars across the width of a shear spine. Where congestion of reinforcement poses difficulty, headed bars as shown in Fig. 10b can be used. The design process is the same for both options. 6

7 (a) Vertical J-bars (b) Headed shear bars FIGURE 10 ARRANGEMNET OF VERTICAL REINFORCEMENT ACROSS THE WIDTH OF A SHEAR SPINE The mechanism for shear transfer through the vertical bars is illustrated in Fig. 11. The following conservative assumptions will be made in arriving at the shear capacity: If the slab is post-tensioned, the beneficial contribution of the vertical component of the tendons near the supports is disregarded. If post-tensioned, the beneficial contribution of precompression provided by posttensioning is not accounted for. The contribution of concrete in resisting shear is disregarded. Design shear is resisted entirely by the vertical-bar reinforcement provided (J-bars). The angle of cut in the figure is assumed 45 degrees. The parameters that impact the shear transfer are: V u s l s t A v f y γ n = design shear (kn; k); = spacing of shear bars in direction of spine; = spacing of shear bars in transverse direction; = cross-sectional area of each bar; = yield stress of each bar; = material factor; and = number of bars across the assumed fracture surface. Design shear capacity of one row of vertical bars Shear capacity = (n * Av * fy)/γ For one square meter of plan, the shear capacity will be: 7

8 Shear capacity unit plan area = (Av * fy/ γ) * (d/ s l )*(1000/ s t ) FIGURE 11 SHEAR FORCE AND THE RESISTING REINFORCEMENT EXAMPLE Determine the design shear capacity of 20mm diameter vertical bars placed at 250mm on center along the shear spine and 200 mm on center normal to it for the following condition: Thickness of concrete plate h = 4000 mm Effective depth of section 0.85 * 4000 = 3400 mm Spacing in direction of spine s l = 250 mm Spacing transverse to spine s t = 200 mm Cross section of each bar 314 mm2 Yield strength of bars 460 MPa Material factor 1.15 Design shear capacity = (314 * 460/1.15)*(3400/250)*(1000/200)/1000 = 8541 kn 8

9 DESIGN EXAMPLE Consider the transfer plate of the multi-story building shown in Fig. E-1. Views of transfer plate are shown in Fig. E2. FIGURE E-1 MULTI-STORY BUILDING WITH TRANSFER PLATE 9

10 (a) Solid 3D view of transfer plate (b) See through 3D view of transfer plate FIGURE E2 VIEWS OF TRANSFER PLATE The shear transfer for the plate was designed using virtual beam spines illustrated in Fig. E3. 10

11 FIGURE E3 ILLUSTRATION OF SHEAR SPINES FIGTURE E4 IDENTIFICATION OF SUPPORT LINES FOR EACH OF SHEAR SPINES FIGURE E5 DESIGN SECTIONS OF EACH SHEAR SPINE 11

12 FIGIRE E6 DISTRIBUTION OF SHEAR FOR THE SHEAR SPINES Table 1 shows a selection of shear reinforcement for the different regions of the shear spines for the above transfer plate. As indicated in the table, the design shear capacity of the bars varies according to the depth of the plate. TABLE 1 VERTICAL SHEAR CAPACITY FOR DIFFERENT ARRANGEMNET OF J-BARS WITH DEPTH OF CONCRETE (capacities are in kn/m2 of plan) Depth of Section J bars and Type spacing 3.5m 4m 4.5 5m A 500 mm oc B 250 mm oc C 500 mm oc D 250 mm oc