Purdue UniversitySchool of Civil EngineeringGraduate School

Torrenova BuildingStructural Design

Gerardo Aguilar

Santiago Pujol

J. Paul Smith

Feb. 2001

GENERAL DESCRIPTION

Torrenova is an 8-story office building with two stories for parking underneath the ground level. The

building will be constructed in the city of Los Angeles, California, United States. The structural design

presented herein was carried out based on the architectural layout depicted in the attached drawings and in

compliance with the provisions of the ACI-318-1999 and UBC-97 codes. Modifications in the original

dimensions and location of structural elements were suggested as described next.

DIMENSIONS AND NOTATION

An approximate dynamic analysis was used to evaluate the structural adequacy of the given

configuration and to propose dimensions for structural elements. The objective of the design was twofold: 1)

to satisfy requirements for lateral displacements stated in the UBC-97 code and 2) to limit the level of

damage that may occur during an earthquake. A target value of 1% for maximum inter-story drift ratio was

set with these two goals in mind.

The original structural configuration (dimension and location of structural elements), as suggested

by the architects, was found unsatisfactory in terms of structural performance under seismic loading. As a

consequence, different structural configurations were proposed and evaluated. The configuration described

herein was selected as the more convenient in an agreement with the other parts of the project (architect

and owner).. Fig. 1 shows a general plan of the structural system chosen including a notation system that is

used hereafter. Figure 1 and the drawings attached summarize all the properties of the different structural

elements.

Beams were proposed to be 0.30-m wide and 0.80-m deep. A one-way slab floor system with

beams running in the North-South direction was suggested. Joists spanning in the East-West direction were

preliminary dimensioned to be 0.55-m deep and 0.20-m wide. In all cases, the preliminary thickness

suggested for beams and joists satisfies the minimum required by the ACI 318-99 code (ACI 318-99 Section

9.5). Slab thickness in between joists was selected as 0.10-m.

The columns of the system proposed are 0.80-m square. This dimension was selected so that

colomns are stronger than beams. Dimensions of proposed structural walls ranged from 0.30- to 0.45-m

thick, and from 1.20- to 3.00-m long as shown in Fig. 1.

The structural configuration described is the result of a “trial and error” process. This process was

carried out until all the conditions on serviceability and strength described in UBC-97 were met.

NOTATION

East-West (E-W) and North-South (N-S) directions are as defined in Fig. 1. Hereafter, dimensions

and direction of forces are referred to this coordinate system. Moments in one particular direction produce

bending in the corresponding plane. For example, an “EW moment” produces bending in a plane containing

the EW axis (see Fig. 1).

Columns and walls are identified with a single number (from 1 to 19) as indicated in Fig. 1.

Beams are identified with two numbers corresponding to the identification numbers of the columns

or walls at both ends of the beam.

Frames are identified by the labels of the axes in Fig.1.

MODELING ASSUMPTIONS

Two computer programs were used in the structural analysis. A preliminary dynamic analysis of the building

was carried out using SARSAN Version 1.971. Additional dynamic and static analyses were carried out

using RISA-2D Version 5.1b2. The following assumptions were used in the modeling process:

In each direction (NS and EW) and for dynamic analyses, the building structure was considered as a

series of two-dimensional wire frames connected by rigid links. The wire frames had 10 stories. These

series of two-dimensional frames were analyzed independently in the two orthogonal directions: East-

West and North-South.

In order to find design member forces, the building structure was considered as a series of two-

dimensional independent wire frames loaded separately.

The presence of retention walls at the first two stories (underneath the ground) was taken into account

by connecting a very stiff 2-story element to the 10-story wire frames. This element extended from the

base of the building (located at the lower level of the second basement) to the base of first floor.

The base (Bottom of 2nd basement) of all vertical elements was assumed fixed.

Girders were assumed to be rigid from the face of their supports to the center of the connecting column

or wall.

Columns and walls were assumed to be rigid from the bottom to the top of connecting beams.

Theproperties of the beams were computed based on a T-shape cross section with a flange thickness

of 0.10 m and an overhanging flange width of 16 times the thickness of the slab (ACI318-99 Section

8.10.2) for interior beams and 6 times the thickness of the slab for exterior beams (ACI318-99, Section

8.10.3).

1 Copyright (c) Rational Systems, Inc. 1990-19942 Copyright © 2000, RISA technologies

LOADS AND LOAD COMBINATIONS

Basic loads and load combinations were calculated based on the UBC-97 code, Chapter 16. It was

assumed that the frames in N-S direction carry all the gravity loads.

GRAVITY LOADS

Dead load includes self-weight of the structure, partitions and finishes. The volumetric weight of

concrete was assumed to be 2400 kg/m3. Partition loads were taken as 300 kg/m2. Loads representing the

weight of finishes were assumed to be 100 kg/m2 for the first two stories (at the ground level), and 150 kg/m2

for the remaining stories. All roof loads were taken as 300 kg/m2.

For the computation of dead loads, an equivalent slab thickness of 0.20 m was assumed. This

average thickness corresponds to a slab thickness of 0.10-m and 0.55-m-thick joists spaced 0.90-m

(standard spacing).

Live loads were taken as 250 kg/m2 (UBC-97 Section 1607). Snow loads of 50 kg/m2 were

considered (ANSI A58.1-1982. Return period = 50 years). Table 1 summarizes the gravity load

considerations involved in the analysis.

Distributed gravity loads on each frame at different levels of the building are shown in Table 2. The

tributary width assumed for each frame is also included in that table. For frame C, the tributary widths

assumed for the central bay (denoted as C, C. bay) was different from the width assumed for the external

bays (denoted as C, E. bays) to account for the opening in the slab proposed by the architect. The self-

weight of columns and walls was considered in the analysis by including point loads at each story level.

EARTHQUAKE EQUIVALENT LOADS

Equivalent lateral loads associated with earthquake actions were calculated according to Section

1630.2 of UBC-97 code. Story weights were obtained as the total dead load from Tables 1 and 2. Table 3

summarizes the calculation procedure following the UBC-97 Code. Table 4 shows the lateral load

distribution (for stories above ground level).

For a given direction of analysis, the possible effect of the eccentricity of the lateral loads with respect to

the center of stiffness and the possible effects of accidental torsion (UBC-97 Section 1630.6) were taken into

account by distributing all lateral loads among frames according to distribution factors obtained as follows:

The relative lateral stiffness of each frame was first obtained.

A system of frames in parallel is then modeled as an infinitely stiff beam supported by springs with

elastic constants equal to the relative lateral stiffness of the frames. The springs are separated from one

another the same distance than the frames themselves.

A unit load is then applied at an abscise equal to 0.45L, L being the length of the hypothetical beam

analyzed (for the NS direction, L is the distance from frame F to frame B). The reaction at every spring

is the distribution factor corresponding to +5% eccentricity with respect to center of mass for the

corresponding frame (as required by UBC). The distribution factor for –5% eccentricity was obtained

similarly by applying the unit load on the hypothetical beam at an abscise equal to 0.55L.

Table 5- shows the lateral load distribution on each frame for two cases: eccentricity with respect to the

center of mass of 5% and –5%.

WIND LOADS

Wind loads were calculated according to UBC-97 Code Sections 1615 through 1625. Table 6

summarizes the calculation involved and the distribution of loads for both, EW and NS direction.

LOAD COMBINATIONS

Load combinations according to UBC-97 Section 1612 were used for the structural analysis of the

structure in two perpendicular directions (NS and EW). Combinations of factored loads are given by

Equations (12-1) through (12-6) of the code. Live loads were placed in both consecutive and alternate spans

(alternate along the length and the height of the building). Six cases of live load were considered.

STRUCTURAL ANALYSIS AND DESIGN FORCES

The structural analysis of the structure for the load combinations described in UBC-97 was carried

out using RISA-2D. Table 7 provides the minimum and maximum force values (in NS and EW direction as

applicable) on each structural element.

DESIGN

STIFFNESS

The structure was proportioned so that the maximum story drift that may happen during an

earthquake is limited to a reasonably small value. The maximum initial (uncracked sections) period of the

structure has been computed to be about 0.6 s. The maximum story drift calculated as per UBC-97 Section

1630.9.2 is 1% (Tables 8 and 9).

STRENGTH

For an average floor area of 440 m2, the reliability redundancy factor (UBC Eq. 30-3) is more

than 1.25 if a member in the structure carried more than 40% of the shear in any story. For dual systems,

the UBC states that the value of need not to exceed 80percent of the value obtained from Eq. 30-3. No

member in the structure carries more than 40% of the shear in any story as computed in the structural

analysis. This implies that NO amplification of the earthquake design forces above the level under

consideration as specified in section UBC-97 1630.2 is required.

All members were proportioned for an assumed concrete design strength of 5000 psi (350 kgf/cm2).

All steel was assumed to have a minimum yield stress of 60000psi (4200 kgf/cm2).

Flexure and Axial Load

Design Forces

All elements (beams, columns and walls) were proportioned so that their nominal flexural strength

is greater than the corresponding moments obtained in the analysis described before (linear response,

cracked sections). Design axial forces were obtained in the same manner.

Computed Nominal Strength

The nominal flexural strength of all members was computed based on the following assumptions:

At any section, normal strains are distributed linearly.

Steel bars and the concrete around them undergo the same strains.

The stress-strain behavior of steel is described with the expression:

f s={Es εs for εs≤ f yE sf y for ε s≥f yE s

The stress-strain behavior of concrete is described with the expression:

f c=¿¿f c ,max={ f c

' for beams

0 .85 f c' for columns

The nominal flexural strength corresponds to the moment for which the computed maximum strain in

the concrete is 0.003.

All elements (including columns) were designed for the maximum moments obtained from the

analysis and zero axial load. In order to support axial loads, all elements were proportioned so that the

maximum axial load computed in the analysis was less than the balanced axial load (load at which yielding

of the main reinforcement is reached and the maximum strain in the concrete reaches 0.003 simultaneously)

and less than 35 % of the axial strength of the member (Computed as .85f’c(Ag-As)+fyAs).

All vertical elements were designed to be stronger than the beams framing into them. The minimum ratio

Mc/Mb, for the entire frame, is larger than 1.2 (Table 10). (ACI Eq. 21-1, UBC Eq. 21-1). (Mc and Mb are

defined in Fig. 2. Mb, Fig. 3, is calculated for maximum beam moments of 1.25 times the flexural strength.

McMIN, Fig 3, stands for the flexural strength of a column for zero axial load).

The reinforcement ratio As/Ag in any column or concrete wall is not less than 1.1%. The maximum

reinforcement ratio in any column is 1.8 %. These are within the limits set by ACI-318 (21.4.3) and UBC

(1921.4.3.1).

For all members under flexural and axial loads, a strength reduction factor of 0.7 was used. Beams were

designed using a strength reduction factor of 0.9.

Beams were proportioned assuming that a portion of the slab acts as part of them. For interior beams, a

total flange width of 1.9 m was assumed. For exterior beams, the flange width assumed was 0.9 m. Despite

the sections of the exterior beams are not symmetric with respect to a vertical axis, they were assumed to

bend only on a vertical plane when loaded in the same direction.

In beams with different amounts of reinforcement at top and bottom, the difference in reinforcement is less

than half of that required to reach “balanced strain conditions.”

The minimum amount of reinforcement either at the top or at the bottom of any of the beams is 3 #9 bars.

This corresponds to a reinforcement ratio (As/bd) of 0.9%. This is in excess of the minimum

recommended by ACI-318 and UBC-97 (.35%, Eq. 10-3, ).

The maximum amount of “tension” reinforcement in any beam is 6#10 bars. This corresponds to a

reinforcement ratio of 2.3%, which is below the maximum ratio as recommended by UBC-97 (2.5%, section

1921.3.2.1).

The strength of all vertical elements under biaxial bending was computed using the expression:

( M nx

M nx 0)α 1

+( M ny

M ny 0)α2

=1

1 = 2 = 1.15

The computed flexural and axial strengths for all elements are presented in Tables 10 and 11.

Shear

Design Forces (Fig. 2 )

Columns

Design shear forces for columns were computed assuming that:

-All columns would develop their full probable flexural capacity (1.25 times the moments calculated

for maximum axial loads, with no strength reduction factor) at their bases.

-All beams would develop 1.25 times their full flexural capacity at joint faces

-Half the moment that a beam may exert on a joint is resisted by the column in the upper story.

Although this condition is likely to take place at the base of the building only, columns in all stories

have been designed for this scenario.

Equilibrium equations for each joint have been written after projecting moments at its faces to the

geometrical center of the joint as shown in Fig. 2.

In no case the forces computed as just described were less than those computed in the analysis for

factored loads.

Beams

All beams were proportioned to resist the shear corresponding to factored gravity loads plus that

associated with development of 1.25 times the full flexural strength (with no strength reduction factor) at joint

faces. In no case these forces were less than those computed in the analysis for factored loads.

Walls

Shear forces used in the design of all walls were the larger of:

-Those obtained in the structural analysis described before and

-The shear forces that cause a moment, with respect to the base of the building, equal to 1.25

times the full flexural strength (for maximum axial load) of each wall when acting at 2/3 of the

height of the structure above ground level.

Joints

Design shear forces used to check nominal stress levels in all joints were computed based on the

assumption that all beams would yield at faces of joints.

The computed shear design forces for all the elements are presented in Tables 12 and 14.

Computed Nominal Strength

Columns

Spacing of all hoops in columns was calculated assuming Vc = 0 in UBC-97 Eq. 11-2 and = 0.85

in Eq. 11-1.

Beams

Spacing of all hoops in beams was calculated assuming Vc = 0 in UBC-97 Eq. 11-2 and = 0.85 in

Eq. 11-1.

Spacing of hoops calculated based on the required shear strength do not exceed (UBC

1921.3.3.2):

-d/4 = 17.5cm,

-Eight times the diameter of the smallest longitudinal bar = 23cm,

-Twenty four time the diameter of the hoop bars = 38cm

-30 cm.

Walls

Spacing of all hoops in columns was calculated assuming Vc = 2.(f’c)1/2.b.d in UBC Eq. 11-2 and

=0.85 in Eq. 11-1 (1909.3.4.1 does not apply because all walls have been designed for the larger of: 1) the

shear forces from the structural analysis and 2) the shear force required, when acting at 2/3 of the height of

the building above the level of the ground, to reach 1.25 times the flexural capacity of the wall at its base).

Joints

Nominal shear stresses in all column-beam joints are less than 0.85 12 (f’c)1/2.

Shear reinforcement properties for all the elements are presented in Tables 13 and 14.

DUCTILITY

Provisions in sections UBC-97 1921.4.4, and ACI 318-99 21.4.4 were followed to proportion

columns and walls so that they are likely to exhibit ductile responses during an earthquake. For beams,

provisions for confinement reinforcement given in ACI 318-99 Section 21.3.3 were followed.

Confinement Reinforcement for Columns

For all columns, the recommended spacing of transverse reinforcement for shear is less than the

maximum spacing for confining rectangular hoops to be located near joints as recommended by UBC-97

and ACI 319-99, which is the minimum of:

UBC-97 Equations (21-3) and (21-4)

Four inches (10 cm)

A fourth of the minimum member dimension

Six times the diameter of longitudinal reinforcement (ACI 21.4.4.2)

Sx as defined by Equation (21-5) of ACI 318-95:

Sx=4 in .+14 in .−hx

3≤6 in .

(where, hx is the maximum horizontal distance of legs of transverse reinforcement)

The first hoop in all the elements was placed at 5 cm from the face at the joint, which satisfies the

minimum value of 2 in. required in both codes.

Maximum spacing of transverse reinforcement legs in the direction perpendicular to the longitudinal axis of

the element is less than 14 inches (36 cm) as required by UBC-97 Section 1921.4.4.3.T

Confinement Reinforcement for Walls

The recommended spacing of transverse reinforcement for walls is less than the required for shear

strength and confinement. The maximum spacing for confinement requirements given in the UBC-97 code,

Section 1921.6.2 corresponds to a minimum reinforcement ratio of 0.25% along longitudinal and transverse

axes of the elements. In the longitudinal direction, all the reinforcement ratios chosen are higher than 1.1%.

In the transverse direction reinforcements ratios are larger than 0.25% for all the walls.

Confinement Reinforcement for beams

Requirements for confinement of beams according to ACI 318-99 Section 21.3.3.1 are satisfied as

follows:

Hooks are provided throughout the entire span (satisfies 21.3.3.1 (a) and (b)).

The first hook is located at 5 cm of the face (partially satisfies 21.3.3.2)

The suggested spacing of 7.5, 12.5, and 15 cm (constant for every element) is larger than eight times of

the minimum longitudinal bar diameter (8 x # 9 = 23 cm), 24 times diameter of hoop bars (24 x #5 =

38 cm), d/4 (70 cm /4 = 17.5 cm), and 12 inches (30.5 cm). This satisfies Sections 21.3.3.2, and

21.3.3.4

Boundary Elements

Under seismic loads and assuming nonlinear behavior of the structure, compressive strains close

or exceeding 0.003 were computed for most of the concrete walls. As a consequence, boundary elements

were provided following the detail requirements given in UBC-97 Section 19.21.6.6.6.

USE RECOMMENDATIONS

Use of flexible partitions is highly recommended. Partitions made out of clay tiles may be used

provided they do not restrain columns partially along their height.

The designers have agreed with the architects of the project that the stairs and the elevators core

will be relocated with respect to the original architectural design. This change should allow access to the

restrooms from the stairway and the restrooms to be moved to the same level where the offices are located.

REFERENCES

ACI Committee 318, Building Code Requirements for Structural Concrete (318-99) and Commentary (318R-99), American Concrete Institute, 391 p.

1997 Uniform Building Code, Volume 2, Structural Engineering Design Provisions.

Nilson, A., and Winter, G. (1994), Diseño de Estructuras de Concreto, McGraw Hill, 769 p.

Table 1. Gravity loads

Load Considerations

Partitions/Roof 300 kg/m2

Snow 50 kg/m2

Finishes 100, 150 kg/m2

Parking Live Load 250 kg/m2

Office Live Load 250 kg/m2

Table 2a. Distributed Gravity Loads (Carried by Frames in NS Direction)

Table 2b. Distributed Gravity Loads (Carried by Frames in NS Direction)

Levels 4 to 9Snow (kN/m) Live (kN/m) Total D Frame/Bay Total D Total D + L

Frame Tributary Width Slab Beam Partitions Finishes Uniform Uniform Lengthm Ave th.= 0.20m 0.80x0.30m 300kg/m2 150kg/m2 50kg/m2 250kg/m2

kN/m m kN kN

F 2.6 12 6 8 4 1 6 29 26.5 781 977E 5.1 24 6 15 8 12 53 26.5 1410 1733

C, E. Bays 4.9 24 6 15 7 12 51 20.6 1057 1299C, C. Bay 2.9 14 6 9 4 7 33 5.9 193 234

B1 5.2 25 6 15 8 1 (at ext bays) 12 54 26.5 1422 1786 4900 6100

Level 10 + Elevator (5000kg)Snow (kN/m) Live (kN/m) Total D Total D Total D + L

Frame Tributary Width Slab Beam Partitions Roof/Finishes Uniform Uniform Lengthm Ave th.= 0.20m 0.80x0.30m 300kg/m2 100kg/m2 50kg/m2 250kg/m2

kN/m m kN kN

E 6.0 0 6 0 18 3 14 24 26.5 626 1082C, E. Bays 4.9 0 6 0 15 2 12 20 20.6 421 714C, C. Bay 2.9 14 6 9 0 7 28 5.9 167 208

B 5.2 0 6 0 15 3 12 21 26.5 562 957

Assume Point Loads on Wall 6 due to live and dead load (on half the distance between frames E-C and 3.65 m overhang) = 110 (kN) 409 (kN) 409 519Elevator as Live and Dead Load on Wall 16 = 20 (kN) 30 (kN) 30 50

Roof (Spaning between Frames C and B, Center Bay of Frame C) (as Point Load on Walls 13 and 14) = 42 (kN) 50 (kN) 50 92Roof (Spaning between Frames C and B, Center Bay of Frame B) (as point Load on, Walls 17 and 18) = 91 (kN) 110 (kN) 110 201

2400 3900

Notes1- Distances Axis to Axis (m)

Wall-Frame F 5.00Frames F to E 5.10Frames E to C 5.10Frames C to B 4.70Frames B to Overhang 2.80Frame B to Wall 6.62- Subtract 2.0 m for the tributary width along

central bay of frame C to account for opening

Dead Load (kN/m)

Dead Load (kN/m)

Table 2c. Distributed Gravity Loads (Carried by Frames in NS Direction)

Level 11

Snow (kN/m) Live (kN/m) Total D Total M TotalFrame Tributary Width Slab Beam Partitions Roof Uniform Uniform Length

m Ave th.= 0.20m 0.80x0.30m 300kg/m2 100kg/m2 50kg/m2 250kg/m2kN/m m kN kN

C, C. Bay 2.4 11 6 0 0 1 6 17 5.9 101 141

Assume Point Loads on Wall 6 due to live and dead load (on half the distance between frames E-C and 3.65 m overhang) = 110 409 409 519600 700

Notes

1- Distances Axis to Axis (m)

Wall-Frame F 5.00

Frames F to E 5.10Frames E to C 5.10

Frames C to B 4.70Frames B to Overhang 2.80

Frame B to Wall 6.6

2- Subtract 2.0 m for the tributary width along

central bay of frame C to account for opening

Dead Load (kN/m)

Table 3. Parameters for the Computation of Earthquake Equivalent Loads

Parameter (Reference in UBC-97, Chapter 16-Division IV) Value

Ocupancy Category (Table 16-K) 1

Site Geology and Soil Characteristics (Table 16-J) SE

Site Seismic Hazard Characteristics (Table 16-I): Zone 4 Z = 0.4

Near-Source Factor (Table 16-S): 20 km to seismic source Na = 1.0Near-Source Factor (Table 16-T): 20 km to seismic source Nv = 1.0Seismic Response Coefficient (Table 16-Q): Zone 4, SE Ca = 0.36Seismic Response Coefficient (Table 16-R): Zone 4, SE Cv = 0.96

Numerical Coefficient (Tables 16-N, 16-P): 4.1.a (Concrete Shear Wall, SMRF) R = 8.50Stories 9

Height, m 30.7Weight, kg 4,260,000Period, s (Eq. 30-8)1 0.82Voriginal, (Eq. 30-4), kg 587,165Vmin, (Eq. 30-6), kg 168,696Vmin (Zone 4, Eq. 30-7), kg 160,376Vmax, (Eq. 30-5), kg 451,059

V, kg 451,059

Notes:

1: Periods for the structure in both EW and NS directions were also calculated using RISA, the obtained valuesusing cracked properties for walls, columns, and beams were

Period (NS direction) = 0.6 sec

Period (EW direction) = 0.5 sec

2: Distribution of equivalent lateral loads was conservatively carried out based on the period obtainedby using UBC-97 Eq. 30-8.

3: Cracked properties of structural elements per ACI 318-99 Sec. 10.11.1 as follows:Icr = 0.3x Ig: for Beams and WallsIcr = 0.7xIg : for Columns

Table 4. Vertical Distribution of Equivalent Lateral Loads for Earthquake

Ft = 25.9 (t)

Level, x (Story) Weigth, t Heigth, hx (m) Fx (t)

1 (3) 565.0 4.3 16.9

2 (4) 565.0 7.6 29.9

3 (5) 565.0 10.9 42.9

4 (6) 565.0 14.2 55.9

5 (7) 565.0 17.5 68.9

6 (8) 565.0 20.8 81.9

7 (9) 565.0 24.1 94.9

8 (10) 245.0 27.4 46.8

9 (11) 60.0 30.7 38.7

Table 5- Horizontal Distribution of Lateral Forces for each Frame

a. Frames in North-South Direction

Frame F Frame E Frame C Frame B

Relative Stiffness 0.32 0.20 0.15 0.33

Lateral Load applied at -0.05L to the East of Center of Mass Story Force, Fx Frame F Frame E Frame C Frame BLevel\distribution factor (t) 0.27 0.19 0.16 0.38

1 (Story 3) 16.9 4.6 3.2 2.7 6.4

2 ( Story 4) 29.9 8.1 5.7 4.8 11.4

3 ( Story 5) 42.9 11.6 8.2 6.9 16.3

4 (Story 6) 55.9 15.1 10.6 8.9 21.2

5 (Story 7) 68.9 18.6 13.1 11.0 26.2

6 (Story 8) 81.9 22.1 15.6 13.1 31.1

7 (Story 9) 94.9 25.6 18.0 15.2 36.1Level\distribution factor 0.50 0.24 0.26

8 (Story 10) 46.8 --- 23.4 11.2 12.29 (Story 11) 38.7 --- 28.3 10.5 ---

Lateral Load applied at +0.05L to the East of Center of Mass Story Force, Fx Frame F Frame E Frame C Frame BLevel\distribution factor (t) 0.37 0.21 0.14 0.28

1 (Story 3) 16.9 6.3 3.6 2.4 4.8

2 ( Story 4) 29.9 11.1 6.3 4.2 8.4

3 ( Story 5) 42.9 15.9 9.0 6.0 12.1

4 (Story 6) 55.9 20.7 11.7 7.8 15.7

5 (Story 7) 68.9 25.5 14.5 9.6 19.4

6 (Story 8) 81.9 30.3 17.2 11.5 23.0

7 (Story 9) 94.9 35.1 19.9 13.3 26.7Level\distribution factor 0.61 0.25 0.13

8 (Story 10) 46.8 --- 28.6 11.7 6.29 (Story 11) 38.7 --- 28.3 10.5 ---

b. Frames in East-West Direction

Frame 5 Frame 41 Frame 31 Frame 1

Relative Stiffness 0.47 0.03 0.03 0.47

Lateral Load applied at -0.05L to the North of Center of Mass Story Force, Fx Frame 5 Frame 41 Frame 31 Frame 1Level\distribution factor (t) 0.516 0.03 0.03 0.424

1 (Story 3) 16.9 8.7 0.5 0.5 7.2

2 ( Story 4) 29.9 15.4 0.9 0.9 12.7

3 ( Story 5) 42.9 22.1 1.3 1.3 18.2

4 (Story 6) 55.9 28.9 1.7 1.7 23.7

5 (Story 7) 68.9 35.6 2.1 2.1 29.2

6 (Story 8) 81.9 42.3 2.5 2.5 34.7

7 (Story 9) 94.9 49.0 2.8 2.8 40.2

8 (Story 10) 46.8 24.1 1.4 1.4 19.8

9 (Story 11) 38.7 --- --- --- ---

Lateral Load applied at +0.05L to the North of Center of Mass Story Force, Fx Frame 5 Frame 41 Frame 31 Frame 1Level\distribution factor (t) 0.416 0.03 0.03 0.524

1 (Story 3) 16.9 7.0 0.5 0.5 8.9

2 ( Story 4) 29.9 12.4 0.9 0.9 15.7

3 ( Story 5) 42.9 17.9 1.3 1.3 22.5

4 (Story 6) 55.9 23.3 1.7 1.7 29.3

5 (Story 7) 68.9 28.7 2.1 2.1 36.1

6 (Story 8) 81.9 34.1 2.5 2.5 42.9

7 (Story 9) 94.9 39.5 2.8 2.8 49.7

8 (Story 10) 46.8 19.5 1.4 1.4 24.5

9 (Story 11) 38.7 --- --- --- ---

1: Frames 3 and 4 are walls 9 and 10 respectively

Table 6- Wind Loads

a. Parameters

Parameter (Reference in UBC-97, Chapter 16-Division III) Value

Pressure coefficient (Table 16H, Method 2) Cq = 1.4

Wind stagnation pressure at 33ft (Table 16 F, wind speed = 70 mph) qs = 0.63

Importance factor (Table 16 K) Iw = 1

b. Lateral Load Distribution

Level (Story) Height Ce

(m) Exp B NS Direction EW Direction

1 (3) 4.3 0.58 36 52

2 (4) 7.6 0.72 39 56

3 (5) 10.9 0.81 44 63

4 (6) 14.2 0.88 48 68

5 (7) 17.5 0.94 51 73

6 (8) 20.8 0.99 54 77

7 (9) 24.1 1.04 56 81

8 (10) 27.4 1.08 50 84

9 (11) 30.7 1.13 18 12

Notes:

1- Ce is the combined height, exposure, and gust factor (Table 16 G, assuming Exposure type B)

2- Wind pressure calculated from UBC-97 Eq. (20-1)

Load (kN)

Table 7. Summary of Maximum Forces in Elements (For Factored Loads)

a. Columns and walls

Element Type Frames1

min max min max min max min max min max min max1 C80x80 F and 1 14,200 291,800 0 31,200 -22,000 19,600 -19,300 19,300 -50,300 43,900 -42,500 29,6002 W265x35 F 20,600 422,900 -119,300 84,600 -300,400 282,700 -12,9003 W265x35 F 20,600 422,900 -100,300 97,400 -292,400 294,400 -12,9004 C80x80 F and 5 14,200 291,800 0 31,200 -11,100 28,000 -19,600 19,600 -43,200 57,600 -42,900 30,0005 C80x80 E and 1 29,000 619,400 -52,300 38,400 -97,600 69,7006 W300x35 E 36,900 1,016,200 -295,100 208,400 -722,300 687,2007 C80x80 E and 5 29,000 619,400 -11,600 57,900 -85,400 115,90012 C80x80 C and 1 12,900 538,600 -31,300 26,200 -67,000 47,90013 W120x45 C -1,900 454,500 -26,800 48,100 -59,700 72,30014 W120x45 C -1,900 454,500 -47,000 19,300 -83,400 58,30015 C80x80 C and 5 12,900 538,600 -9,000 39,200 -58,400 78,30016 C80x80 B and 1 6,800 507,700 0 31,200 -38,200 5,800 -22,200 22,200 -69,800 55,300 -42,800 33,90017 W190x45 B 9,100 682,200 -57,800 88,800 -169,400 208,900 -14,20018 W190x45 B 9,100 682,200 -88,800 57,700 -208,800 169,000 -14,20019 C80x80 B and 5 6,800 507,700 0 31,200 -5,600 38,000 -22,500 22,500 -55,000 69,100 -43,300 34,4008 W510x45 1 41,900 1,158,000 0 156,500 -83,600 64,600 -469,100 469,100 -164,600 117,600 -1,997,900 1,997,9009 W230x30 3 0 79,300 -99,400 99,400 -281,800 281,80010 W230x30 4 0 79,300 -99,400 99,400 -281,800 281,80011 W510x45 5 41,900 1,158,000 0 156,500 -20,600 97,100 -477,700 477,700 -143,800 194,200 -2,029,700 2,029,700

MNS, kg-m MEW, kg-mPNS, kg PEW, kg VNS, kg VEW, kg

b. Beams

Element Type Frames1

min max min max min max min max min max min max1-2 B80x30E F -32,200 35,600 -25,500 25,000 -29,300 53,6002-3 B80x30E F -16,600 24,500 -27,100 27,000 -35,800 58,6003-4 B80x30E F -4,400 15,800 -25,900 26,400 -29,000 53,4005-6 B80x30I E -23,700 39,800 -54,200 53,700 -44,800 145,1006-7 B80x30I E -14,500 34,200 -53,700 54,200 -44,700 144,900

12-13 B80x30I C -16,200 25,600 -39,400 39,400 -28,200 78,00013-14 B80x30I C -10,400 10,100 -30,400 30,300 -39,700 55,00014-15 B80x30I C -14,400 17,800 -39,300 39,400 -28,000 77,90016-17 B80x30I B -33,000 47,100 -40,000 39,700 -30,000 75,80017-18 B80x45I B -20,700 19,200 -79,300 79,300 -105,000 117,70018-19 B80x30I B -13,300 17,000 -39,700 40,000 -30,000 75,70012-16 B80x30E 1 -53,700 53,700 -28,500 28,500 -55,900 55,9001-5 B80x30E 1 -4,800 4,800 -22,600 22,600 -49,000 49,000

15-19 B80x30E 5 -54,400 54,400 -28,900 28,900 -56,700 56,7004-7 B80x30E 5 -19,600 19,600 -23,000 23,000 -49,700 49,700

MNS, kg-m MEW, kg-mPNS, kg PEW, kg VNS, kg VEW, kg

Note: In this table, a negative moment produces tension at the bottom of the beam.

Table 8. NS Drift

Level Story height s Drift (From UBCm mm Eq. 30-17)

3 4.3 5.3 0.74%

4 3.3 11.0 1.02%

5 3.3 16.8 1.06%

6 3.3 22.4 1.00%

7 3.3 27.3 0.89%

8 3.3 31.5 0.75%

9 3.3 35.0 0.62%10 3.3 38.1 0.56%

Table 9. EW Drift

Level Story height s Drift (From UBCm mm Eq. 30-17)

3 4.3 3.0 0.42%

4 3.3 6.1 0.55%

5 3.3 9.6 0.63%

6 3.3 13.3 0.67%

7 3.3 17.0 0.67%

8 3.3 20.5 0.64%

9 3.3 23.9 0.60%10 3.3 27.0 0.56%

Table 10. Flexural Strength of Columns and Walls.

Element Type Min Pb Po Pmax/Pb Pmax/Po Mn NS Mn EW As/Ag Mn/Mu M(Pmax) Mc/Mb Mc/Mb

kgf kgf kgf-m kgf-m Biaxal kgf-m NS EW

1 C80x80 768,000 2,200,000 0.42 0.15 143,000 143,000 1.6% 1.99 2.36 1.55 230,000 2.6 2.52 W265x35 1,000,000 3,100,000 0.42 0.14 536,000 65,000 1.2% 1.25 3.53 1.08 880,000 3.93 W265x35 1,000,000 3,100,000 0.42 0.14 536,000 65,000 1.2% 1.27 3.53 1.10 880,000 3.94 C80x80 768,000 2,200,000 0.42 0.15 143,000 143,000 1.6% 1.74 2.33 1.35 230,000 2.6 2.55 C80x80 260,0006 W300x35 1,260,000 3,750,000 0.81 0.27 1,050,000 1.8% 1.02 1,760,000 4.07 C80x80 260,00012 C80x80 250,00013 W120x45 648,000 1,850,000 0.70 0.25 170,000 1.5% 1.65 290,000 1.2114 W120x45 648,000 1,850,000 0.70 0.25 170,000 1.5% 1.43 290,000 1.2115 C80x80 250,00016 C80x80 768,000 2,200,000 0.70 0.24 143,000 143,000 1.6% 1.43 2.34 1.12 250,000 2.2 2.517 W190x45 923,000 2,950,000 0.74 0.23 428,000 95,800 1.5% 1.43 4.72 1.29 720,000 2.018 W190x45 923,000 2,950,000 0.74 0.23 428,000 95,800 1.5% 1.43 4.72 1.29 720,000 2.019 C80x80 768,000 2,200,000 0.70 0.24 143,000 143,000 1.6% 1.45 2.31 1.12 250,000 2.2 2.58 W510x45 1,300,000 10,500,000 1.01 0.13 559,000 4,040,000 1.1% 2.38 1.42 1.42 7,000,000 22.39 W230x30 828,000 2,400,000 0.10 0.03 448,000 1.6% 1.11 510,00010 W230x30 828,000 2,400,000 0.10 0.03 448,000 1.6% 1.11 510,00011 W510x45 1,300,000 10,500,000 1.01 0.13 559,000 4,040,000 1.1% 2.01 1.39 1.19 7,000,000 22.3

NS EW

Mn/Mu

Table 11. Flexural Strength of Beams.

Element Type Mn+ (kgf-m) Mn- (kgf-m)(Tension at Bottom) (Tension at Top) MNS+ MNS- MEW+ MEW-

1-2 B80x30E 63,000 74,000 1.94 1.242-3 B80x30E 63,000 74,000 1.58 1.143-4 B80x30E 63,000 74,000 1.96 1.255-6 B80x30I 92,600 158,000 1.86 0.986-7 B80x30I 92,600 158,000 1.86 0.98

12-13 B80x30I 66,900 88,400 2.14 1.0213-14 B80x30I 66,900 88,400 1.52 1.4514-15 B80x30I 66,900 88,400 2.15 1.0216-17 B80x30I 66,900 88,400 2.01 1.0517-18 B80x45I 120,000 135,000 1.03 1.0318-19 B80x30I 66,900 88,400 2.01 1.0516-12 B80x30E 63,000 70,700 1.01 1.145-1 B80x30E 63,000 70,700 1.16 1.30

19-15 B80x30E 63,000 70,700 1.00 1.127-4 B80x30E 63,000 70,700 1.14 1.28

Mn/Mu

Table 12. Shear Design Forces for Columns, Walls and Joints.

Element Type 1.25M(Pmax) Ashear Vu Vu (NS) Vu (EW) Joints (NS) Joints (EW)

(2/3hw) kgf cm2Ashear (f'c)1/2 Ashear (f'c)1/2 Ashear (f'c)1/2 12(f'c)1/2/vu 12(f'c)1/2/vu

1 C80x80 5,120 4.6 4.6 2.1 2.72 W265x35 60,219 7,420 3.23 W265x35 60,219 7,420 2.74 C80x80 5,120 4.6 4.6 2.1 2.75 C80x80 5,120 5.8 1.3 2.76 W300x35 120,438 8,400 7.17 C80x80 5,120 5.8 1.3 2.712 C80x80 5,120 5.0 1.6 2.713 W120x45 19,845 4,320 2.214 W120x45 19,845 4,320 2.215 C80x80 5,120 5.0 1.6 2.716 C80x80 5,120 5.0 4.9 2.3 2.717 W190x45 49,270 5,320 3.418 W190x45 49,270 5,320 3.419 C80x80 5,120 5.0 4.9 2.3 2.78 W510x45 479,015 18,360 5.29 W230x30 34,900 5,520 3.610 W230x30 34,900 5,520 3.611 W510x45 479,015 18,360 5.2

Note: psi units used for (f'c)1/2

Table 13. Maximum Stirrup Spacing for Columns and Walls.

Element Type s (4 #5 legs) s (4 #5 legs) s (4 #5 legs) s (4 #5 legs) sWALLS (2 #4 legs) n (For Shear) sWALLS (2 #4 legs) sWALLS (2 #4 legs) sWALLS (2 #4 legs) sWALLS (2 #4 legs)Shear Shear Confinement Recommended nMIN = 0.0025 2Base.+1st-3rd Story 2Base.+1st-3rd Story Other Stories 2Base.+1st-3rd Story Other Stories

NS (cm) EW (cm) (cm) (cm) (cm) UBC 1921.6.2.1 (cm) UBC Eq. 21-6 (cm) Max. Required (cm) Max. Required (cm) Recommended (cm) Recommended

1 C80x80 15.5 15.5 14.8 12.52 W265x35 29 0.0017 29 29 20 203 W265x35 29 0.0010 29 29 20 204 C80x80 15.5 15.5 14.8 12.55 C80x80 12.2 14.8 12.56 W300x35 29 0.0071 10 20 10 207 C80x80 12.2 14.8 12.512 C80x80 14.1 14.813 W120x45 22 0.0003 22 22 15 1514 W120x45 22 0.0003 22 22 15 1515 C80x80 14.1 14.8 12.516 C80x80 14.1 14.4 14.8 12.517 W190x45 22 0.0019 22 22 20 2018 W190x45 22 0.0019 22 22 20 2019 C80x80 14.1 14.4 14.8 12.58 W510x45 22 0.0045 12 22 10 209 W230x30 34 0.0023 34 34 20 2010 W230x30 34 0.0023 34 34 20 2011 W510x45 22 0.0045 12 22 10 20

Table 14. Design Shear Forces and Maximum Stirrup Spacing for Beams.

Element Type Vu NS Vu EW s, cm (2 #5 legs) s, cm (2 #5 legs) s, cm (2 #5 legs) s, cm (2 #5 legs) s, cm (2 #5 legs)bwd(f'c)1/2 bwd(f'c)1/2 (For Shear) (For Shear) (Min. Reinf.) Required Recommended

1-2 B80x30E 3.8 25.0 17.5 17.0 152-3 B80x30E 3.8 24.9 17.5 17.0 153-4 B80x30E 3.8 25.0 17.5 17.0 155-6 B80x30I 6.7 14.1 17.5 14.0 12.56-7 B80x30I 6.7 14.1 17.5 14.0 12.5

12-13 B80x30I 5.2 18.2 17.5 17.0 1513-14 B80x30I 5.0 18.9 17.5 17.0 1514-15 B80x30I 5.2 18.2 17.5 17.0 1516-17 B80x30I 5.2 18.2 17.5 17.0 1517-18 B80x45I 6.9 9.1 17.5 9.0 7.518-19 B80x30I 5.2 18.2 17.5 17.0 1516-12 B80x30E 4.2 22.4 17.5 17.0 155-1 B80x30E 3.9 24.5 17.5 17.0 15

19-15 B80x30E 4.2 22.4 17.5 17.0 157-4 B80x30E 3.9 24.5 17.5 17.0 15

Note: psi units used for (f'c)1/2

Fig. 1 –Dimensions and Location of Structural Elements

2-3

ASSUMED MOMENT DISTRIBUTION (Shear Design)

Mb +

Mb -

2a 2b 2b 2a

Mb

Mb=(Mb+) + m.a

m=[(Mb+)+(Mb-)]/[L-a-b]L

Mb/2

Mc

Design Shear = (Mb/2+Mc)/(h/2+hc/2)

hc/2

h/2

Fig. 2 –Dimensions and Location of Structural Elements

2a 2bMc

h/2

hc/2

h/2

h/2

Mb

Mc

Mc.(h/hc)

hc/2

Mc=2McMIN.(h/hc)

Mb=Mb

ASSUMED MOMENT DISTRIBUTION (Column Strength vs. Beams Strength Check)

MIN MIN

Fig.3. –Dimensions and Location of Structural Elements