The RAM Structural SystemTM, V8iRelease 13.0

RAM ConcreteTM

Shear Wall Design Verification Example

Bentley Systems, Inc.2744 Loker Avenue West, Suite 103

Carlsbad, CA 92010Telephone: (760) 431-3610Toll Free: (800) 726-7789

RAM Concrete Shear Wall Design Verification Example

Table of Contents1 Overview.....................................................................................32 Wall Design Forces used by RAM Concrete...............................53 Design of Walls for Shear.........................................................124 Design of Walls for Axial-Flexural Forces...............................145 Special Boundary Element Extents...........................................166 Special Boundary Tie Design....................................................19

1 Overview

This document is intended to provide technical verification for the analysis and design results within the RAM Concrete Shear Wall design module for a sample RAM Structural System model. This example utilizes RAM Structural System v8i, r13.0, which is available for download on Bentley Select as of December 16th, 2008. The model used in this document is available upon request by emailing Josh Taylor at Josh.Taylor@bentley.com.

The scope of this document is limited to providing sufficient technical background so that the user may reproduce the design results and calculations performed in the design module. This document does not intend to exhaustively report the design results for the entire model.

Figure 1 – RAM Frame 3D view showing wall and floor slab mesh

Figure 2 – Model 3D view showing only walls

Model Properties

Model Overview: (4) full stories plus (1) partial story (62”-0” total height) 195’ long by 75’ wide footprint 9” concrete flat slab floors 12” + 18” interior concrete shear walls Perimeter special moment frames: 20” wide by 24” deep beams with 20” square columns

Design Criteria: IBC 2006

o Bearing Wall System – Special Reinforced Concrete Shear Wallso Occupancy Category “I”o Site Class “C”

ACI 318-05o Special Reinforced Concrete Walls & Special Moment Resisting Frames

Floor Loads: Office: 25 psf superimposed dead, 60 psf reducible live Storage: 5 psf superimposed dead, 150 psf storage Roof: 20 psf superimposed dead, 20 psf roof

Wind Loads: Exposure: B Basic Wind Speed: 90 mph Topographical Factor, Kzt = 1.0 Directionality Factor, Kd = 0.85

Seismic Loads: Equivalent Lateral Force Procedure Response Modification Coefficient, R = 5.0 Displacement Amplification Factor, Cd = 5.0 Importance Factor, I = 1.0 Ss = 1.00, S1 = 0.30

Frame Analysis Assumptions: All floors treated as semi-rigid diaphragms with maximum mesh node spacing of 4 ft P-Delta effects considered with scale factor of 1.0 Out-of-plane wall stiffness ignored

2 Wall Design Forces used by RAM Concrete

Verify Section Cut SC2H:133.

Figure 3 shows a screen shot of the View/Update dialog for Wall Design Group 2. The currently selected Section Cut is SC2H:133 (at the base of the wall) and the tabular data in the Results page reflect this Section Cut, as does the cross-section view at the bottom center. The worst case interaction value for axial/flexural design is produced by Load Combination 260, 0.9D – 1.4E6, as shown directly above the tabular data sheet. Vertical reinforcement within wall boundaries is colored red in the 3D view box (upper left). Confinement ties are shown in boundary regions in the cross section sketch.

Figure 3 – RAM Concrete Shear Wall View/Update, Axial/Flexural results

The term E6 in the controlling load combination 0.9D – 1.4E6 represents the load case EQ_IBC06_X_+E_-0.3Y_+E_F from the RAM Frame analysis. The applied story forces for this load case are shown in the RAM Frame Loads and Applied Forces report below.

Figure 4 – RAM Frame Loads and Applied Forces report

Load case E6 coincides with the full X-Direction seismic story force applied coincidentally with 30% of the Y-direction seismic story force, with both loads applied at an eccentricity that generates a positive Z-axis moment. This is illustrated in Figure 5.

Y

X

Fx0.3FY

Figure 5 – Orientation of applied loads with respect to mass center for seismic load case E6

The design forces at the Section Cut SC2H:133 can be verified, among other means, by forming a Wall Group in RAM Frame of the same extents as the Section Cut. The resultant forces at the base of the Wall Group for each load case or load combination can then be processed.

Figure 6 – RAM Frame Wall Group numbers

The forces at the base of RAM Frame Wall Group 2 are listed in Table 1.

Table 1 –Forces at base of RAM Frame Wall Group 2

Load Condition P (kips) Mxx (k-ft) Myy (k-ft)Dead 810.34 142.76 961.85X_+E_-0.3Y_+E_F -394.38 3625.83 20855.040.9D - 1.4E6 1281.44 -4947.68 -28331.39

Note: The RAM Frame Wall Group forces listed above are taken at the wall base, and thus the moments will be slightly larger in magnitude than the corresponding moments at Section Cut SC2H:133, which is located 6 in above the base.

Figure 7 through Figure 12 show RAM Frame screen shots for Wall Group 2 forces for each load case for axial loads and moments.

Figure 7 – Wall axial forces for Dead Load case from RAM Frame

Figure 8 – Wall major moments for Dead Load case from RAM Frame

Figure 9 – Wall minor moments for Dead Load case from RAM Frame

Figure 10 – Wall axial forces for seismic load case from RAM Frame

Figure 11 – Wall major moments for seismic load case from RAM Frame

Figure 12 – Wall minor moments for seismic load case from RAM Frame

Design shear forces can be verified in a similar manner. For Section Cut Segment SC2H:133A, the controlling load combination is 224, 0.9D + 1.4E6. For Section Cut Segment SC2H:133B, the controlling load combination is 157, 1.2D + 1.4E11. The design shear forces are summarized in Table 2. The term E11 represents the load case EQ_IBC06_-0.3X_+E_Y_+E_F from RAM Frame.

Table 2 – Section Cut Segment Forces

Section Cut Segment Load Condition V (kips)SC2H:133A Dead 0.56

-0.3X_+E_Y_+E_F 583.180.9D + 1.4E6 816.86

SC2H:133B Dead 6.54-0.3X_+E_Y_+E_F 334.121.2D + 1.4E11 475.62

3 Design of Walls for Shear

Verify Section Cut Segment SC2H:133A.

Figure 13 – RAM Concrete Shear Wall View/Update – shear design results

The shear strength calculation is per ACI 318-05, Sections 11.10.6 (as specified in the design criteria setting) and 11.10.9. The relevant parameters are summarized in Table 3:

Table 3 – Summary of parameters used in shear strength equations

Parameter Value Commentsf’c 8,000 psih 18.0 in Wall ThicknessLw 20.0 ftd 16.0 ftNu 177.18 kips Axial force acting on Section Cut SC2H:133 for LC 0.9D + 1.4E6Vu 816.86 kips Shear acting Section Cut Segment SC2H:133A for LC 0.9D + 1.4E6Mu 18849.63 k-ft Moment acting Section Cut Segment SC2H:133A for LC 0.9D + 1.4E6

Equation (11-29):

Equation (11-30):

Equation (11-30) controls

Horizontal reinforcing is (2) curtains of #5@12” o.c. Thus,

As = 2 x 0.307 in2 = 0.614 in2

Vn = 819.80 + 589.44 = 1409.24 kips

Equation 11.10.3 limits Vn to:

Thus,Vn = 0.75 x 1409.24 = 1056.93 kips

4 Design of Walls for Axial-Flexural Forces

Verify Section SC2H:133.

= 0.65Ag = 20.5’x12x18” + 8.25’x12x12” = 5616 in2

As = 175.0 in2 (see table below)

The reinforcing zones in each wall panel are summarized in Table 4.

Table 4 – Reinforcing zones in each wall panel

Section Cut Segment Wall Panel Reinf Zone Bars Steel Area (in2)SC2H:133A WP 51 Zone 1 (3) #9@4” o.c. 66.0

WP 51 Zone 2 (2) #9@12” o.c. 16.0WP 51 Zone 3 (3) #9@4” o.c. 42.0

SC2H:133B WP 54 Zone 4 (3) #9@6” o.c. 51.0175.0

kips

The worst case axial-flexural interaction is produced by load combination 260, 0.900 D - 1.400 E6, which produces the following design forces on the section:

Pu = 1281.44 kips

Globally oriented moments,MXX = -4836.35 k-ft MYY = -27,929.55 k-ft

Locally oriented moments,Mmaj = -27,929.55 k-ft Mmin = 4836.35 k-ft

k-ft

= tan-1(Mmaj/Mmin) = 170.17 CCW

Figure 14 – RAM Concrete Shear Wall View/Update – axial/flexural design results

5 Special Boundary Element Extents

Verify Section SC2H:133 under load combination 0.9D – 1.4E6.

From ACI 318-05, Section 21.7.6.2, compression zones shall be reinforced with special boundary elements where:

ACI Equation (21-8)

RAM Concrete calculates u as the average horizontal displacement at the top of the Wall Design Group minus the average horizontal displacement at the Section Cut under consideration. The average horizontal displacement at the top of Wall Design Group 2 can be verified from the RAM Frame nodal displacements report. Figure 15 shows the node numbers at the top of Wall Design Group 2. Table 5 lists the displacements at these nodes for load combination 0.9D – 1.4E6.

Figure 15 – RAM Frame node numbers at top of wall group

Table 5 – Nodal deflections from RAM Frame for controlling seismic load combination

Node Number X (in) Y (in)2 -0.8988 0.00943 -1.0565 0.00105 -0.9011 0.0947

Xavg = (-0.8988 - 1.0565 - 0.9011)/3 = -0.9521 inYavg = (0.0094 + 0.0010 + 0.0947)/3 = 0.0350 in

inu = Cde = 5.0(0.9527 in) = 4.7637 in

lw = 21.86 ft (projected length of section in direction of resultant load)

hw = 62.0 ft (overall height of Wall Design Group 2)

u/hw = 4.7637/(62x12) = 0.00640 < 0.007, thus use u/hw = 0.007 in ACI equation (21-8):

in = 5.205 ft

The required length of the boundary is specified in ACI 318-05, Section 21.7.6.4, and is equal to the lesser of:

c – 0.1lw = 5.63 ft – 0.1(21.68 ft) = 3.45 ft

c/2 = 5.63/2 = 2.82 ft

Thus the required boundary length is 3.45 ft, or 3 ’ -5.4 ” .

Figure 16 – Boundary element evaluation for load combination 0.9D – 1.4E6

In this example, boundary regions have been assigned to the Wall Panels using the Assign -> Manual Reinforcement command. They have been laid out so that the resulting boundary length exceeds the

minimum required length for each load combination as solved for above. In Figure 16, each of the boundary regions is tied off as shown in the cross section sketch at the bottom. The point of maximum compression within the Section Cut for the selected load combination is denoted with a black dot. The required boundary length is then dimensioned from that point as shown in the screen shot. If any reinforcing zones not designated as boundaries lie within this region, a design failure will be issued on the Design Warnings tab. In the scenario above, a boundary has been assigned so that the requirement is fulfilled.

The Tie/Link Design sheet provides the transverse reinforcement calculations for the each of the boundary zones that intersect the selected Section Cut.

6 Special Boundary Tie Design

The design of transverse reinforcement in confinement zones is per ACI 318-05, Section 21.4.4.

Equation (21-4),

s = 3 x 0.196 in2 = 0.589 in2

b = 18 – 2 x (1.5 + 0.50/2) = 14.5 in

Rearranging and solving for s,

in

The spacing of transverse reinforcing shall also conform to ACI 318-05, Section 21.4.4.2, which states the spacing of transverse reinforcing shall not exceed the smallest of:

a) ¼ of the minimum member dimension = 18.00/4 = 4.5 inb) 6 x the diameter of the long bar = 6 x 1.128 = 6.77 in

Therefore, the controlling maximum tie spacing for reinforcing zone 1 is 3.385 in .

Figure 17 – Boundary zone tie design for Section Cut