The RAM Structural SystemTM

V8i

SELECTseries1 Release 14.00.00.00

RAM ConcreteTM

Shear Wall Design Verification

Example

Bentley Systems, Inc.

2744 Loker Avenue West, Suite 103

Carlsbad, CA 92010

Telephone: (760) 431-3610

Toll Free: (800) 726-7789

RAM Concrete Shear Wall Design Verification Example

Table of Contents

1 Overview..................................................................................... 3 2 Wall Design Forces used by RAM Concrete.............................. 5 3 Design of Walls for Shear......................................................... 12 4 Design of Walls for Axial-Flexural Forces............................... 15 5 Special Boundary Element Extents........................................... 17 6 Special Boundary Tie Design ................................................... 20

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, SELECTseries1, Release 14.00.00.00, which is available for

download on Bentley SELECT.

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 & Assumptions

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

� 20” square gravity columns, plus 24” diameter circular columns at curved perimeter

Design Criteria:

� IBC 2006

o Bearing Wall System – Special Reinforced Concrete Shear Walls

o Occupancy Category “I”

o Site Class “C”

� ACI 318-08

o Special Reinforced Concrete Walls & Special Moment Resisting Frames

Floor Loads:

� Office: 25 psf superimposed dead, 60 psf reducible live, 12 psf superimposed mass

� Storage: 5 psf superimposed dead, 150 psf storage, 12 psf superimposed mass

� Roof: 20 psf superimposed dead, 20 psf roof, 10 psf superimposed mass

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

Analysis Assumptions:

� All floors treated as two-way, 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

� Rigid end zone effects ignored

� Columns braced against sidesway by walls

� Effective length factor K = 0.9 used for columns supporting bare slab only

Material Properties:

Strengths

� Floor slabs & beams: f’c = 5,000 psi, fy = 60 ksi

� Columns: f’c = 5,000 psi, fy = 60 ksi

� Walls: f’c = 5,000 psi, fy = 60 ksi (8,000 psi at lower levels of center core)

Crack Factors

� Beams: 1.00 (axial), 0.35 (flexure), 0.10 (torsion)

� Columns: 1.00 (axial), 0.70 (flexure), 1.00 (torsion)

� Walls: 0.35

� Headers: 0.20

2 Wall Design Forces used by RAM Concrete

Verify design forces on Section Cut SC2H:20.

Figure 3 shows a screen shot of the View/Update dialog for Wall Design Group 2. The currently selected

Section Cut is SC2H:20 (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 336, 0.9D – 1.4E7, 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 E7 in the controlling load combination 0.9D – 1.4E7 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 E7 coincides with the full negative X-Direction seismic story force applied coincidentally with

30% of the positive 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.

Figure 5 – Orientation of applied loads with respect to mass center for seismic load case E7

The design forces at the Section Cut SC2H:20 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 736.80 145.76 845.40

EQ_IBC06_X_-E_+0.3Y_+E_F (E7) 302.19 -3,031.10 -16,711.29

0.9D - 1.4E7 240.05 4,374.72 24,156.67

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:20, which is

located 6 in above the base. These forces can be viewed in Figure 3 immediately below the spreadsheet

area.

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 Group axial forces for Dead Load case from RAM Frame

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

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

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

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

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

Design shear forces can be verified in a similar manner. For Section Cut Segment SC2H:20A, the

controlling load combination is 156, 1.2D + 0.5Lp + 1.4E7. For Section Cut Segment SC2H:20B, the

controlling load combination is 303, 0.9D + 1.4E10. The design shear forces are summarized in Table 2.

The term E10 represents the load case EQ_IBC06_0.3X_+E_-Y_+E_F from RAM Frame.

Table 2 – Section Cut Segment Shear Forces

Section Cut Segment Load Condition V (kips)

SC2H:20A Dead -8.38

Live (positive) -4.72

EQ_IBC06_-X_+E_0.3Y_+E_F -516.86

1.2D + 0.5Lp + 1.4E7 736.02

SC2H:20B Dead 1.08

EQ_IBC06_0.3X_+E_-Y_+E_F -309.95

0.9D + 1.4E10 432.12

3 Design of Walls for Shear

Verify Section Cut Segment SC2H:20A.

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

The shear strength calculation is per ACI 318-08, Sections 11.9.6 (as specified in the design criteria setting)

and 11.9.9. The relevant parameters are summarized in Table 3:

Table 3 – Summary of parameters used in shear strength equations

Param Value Comments

f’c 8,000 psi

h 18.0 in Wall Thickness

Lw 20.0 ft

d 16.0 ft

Nu 1381.79 k Axial force acting on Section Cut SC2H:20 for LC 1.2D + 0.5Lp + 1.4E7

Vu 736.02 k Shear acting Section Cut Segment SC2H:20A for LC 1.2D + 0.5Lp + 1.4E7

Mu 13,938.67 k-ft Moment acting Section Cut Segment SC2H:20A for LC 1.2D + 0.5Lp + 1.4E7

Equation (11-27):

44.12960.204

0.1679.13811000/12'0.16"0.18000,80.13.3

43.3 ' =

××

+×××××=+=w

ucc

l

dNhdfV λ

Equation (11-28):

hdl

V

M

hl

Nfl

fVw

u

u

w

ucw

cc

−

+

+=

2

2.025.1

6.0

'

'λ

( )37.1073120.160.18

0.12025.227

97.6380.1110.24067.53 =×××

−

+×+=cV

= (53.67 + 393.33) x 3456.0 = 1,544.84 kips

Equation (11-27) controls

Horizontal reinforcing is (2) curtains of #8@12” o.c. Thus,

As = 2 x 0.785 in2 = 1.57 in

2

20.15070.12

/'"12'0.166057.1=

×××==

s

dfAV

yv

s

Vn = 1296.44 + 1507.20 = 2803.64 kips

Equation 11.9.3 limits Vn to:

14.30911000/12'0.16"0.18000,81010 ' =×××=≤ hdfV cn

Thus,

φVn = 0.75 x 2803.64 = 2102.73 kips

Since this system is considered a Special Reinforced Concrete Shear Wall per ACI 318, the shear strength

per Section 21.9.4.1 is also evaluated,

Equation (21-7):

( )ytcccvn ffAV ρλα += '

hw/Lw = 14’/20’ = 0.7 < 1.5

thus, αc = 3.0

Acv = 0.8 x (20’ x 12 “/’) x 18” = 3456.0 in2

ρt = 1.57 in2 / (12” x 18”) = 0.007269

( ) 64.2434000,60007269.0000,80.10.30.3456 =×+×××=nV

φVn = 0.75 x 2434.64 = 1825.98 kips

4 Design of Walls for Axial-Flexural Forces

Verify Section SC2H:20.

Equation (10-2):

( )[ ]stystgcn AfAAfP +−= '

max, 85.080.0 φφ

φ = 0.65 Ag = 20.5’x12x18” + 8.25’x12x12” = 5616 in

2

As = 84.0 in2 (see table below)

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

Table 4 – Reinforcing zones in each wall panel

Segment Panel Reinf Zone Bars Zone Extents As (in

2)

SC2H:20A WP 51 Zone 1 (7) #9@6” oc ef 0’-0” to 3’-0” 14.0

WP 51 Zone 2 (13) #9@12” oc ef 3’-0” to 16’-0” 26.0

WP 51 Zone 3 (8) #9@6” oc ef 16’-0” to 20’-6” 16.0

SC2H:20B WP 54 Zone 1 (7) #9@6” oc ef 0’-0” to 3’-0” 14.0

Zone 2 (3) #9@12” oc ef 3’-0” to 7’-0” 6.0

Zone 3 (4) #9@6” oc ef 7’-0” to 8’-3” 8.0

Total 84.0

( )[ ] 95.181,220.840.600.840.56160.885.065.080.0max, =×+−××××=nPφ kips

The worst case axial-flexural interaction is produced by load combination 336, 0.9D - 1.4E7, which

produces the following design forces on the section:

Pu = 240.05 kips

Globally oriented moments,

MXX = 4,285.01 k-ft MYY = 23,797.47 k-ft

Locally oriented moments,

Mmaj = 23,797.47 k-ft Mmin = -4,285.01 k-ft

71.179,24min22 =+= MMM maju k-ft

β = tan-1(Mmaj/Mmin) = 349.79° CCW

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

5 Special Boundary Element Extents

Verify Section SC2H:20 under load combination 113, 1.2D + 0.5Lp – 1.4E3.

From ACI 318-08, Section 21.9.6.2, compression zones shall be reinforced with special boundary elements

where:

w

u

w

h

lc

δ600

≥ ACI Equation (21-8)

RAM Concrete calculates δu 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 1.2D + 0.5Lp – 1.4E3.

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 -0.14008 -0.66543

3 -0.00509 -0.66312

5 -0.14043 -0.74208

∆Xavg = (-0.14008 - 0.00509 - 0.14043)/3 = -0.09520 in

∆Yavg = (-0.66543 - 0.66312 - 0.74208)/3 = -0.69021 in

( ) ( ) 69674.00.69021-0.09520-22 =+=eδ in

δu = Cdδe = 5.0(0.69674 in) = 3.4837 in

lw = 11.93 ft (projected length of section in direction of resultant load)

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

δu/hw = 3.4837/(62x12) = 0.00468 < 0.007, thus use δu/hw = 0.007 in ACI equation (21-8):

09.34007.0600

1293.11=

××

≥c in = 2.840 ft

The required length of the boundary is specified in ACI 318-08, Section 21.9.6.4, and is equal to the lesser

of:

c – 0.1lw = 3.27 ft – 0.1(11.93 ft) = 2.08 ft

c/2 = 3.27/2 = 1.64 ft

Thus the required boundary length is 2.08 ft, or 2’-0.96”.

Figure 16 – Boundary element evaluation for load combination 1.2D + 0.5Lp - 1.4E3

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 318-08, Section 21.6.4.

Equation (21-5),

yt

ccsh

f

fsbA

'09.0=

Ash = 2 x 0.196 in2 = 0.392 in

2

b = 18 – 2 x (0.75 + 0.50/2) = 16.0 in

Rearranging and solving for s,

05.20.800.1609.0

392.00.60

09.0 '=

×××

==cc

shyt

fb

Afs in

The spacing of transverse reinforcing shall also conform to ACI 318-08, Section 21.6.4.3, 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 in

b) 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 2.05 in.

Figure 17 – Boundary zone tie design for Section Cut