Linear Dynamic Analysis and Seismic Evaluation of RC Building

SPRING 2016

LINEAR DYNAMIC ANALYSIS AND SEISMIC EVALUATION OF A FULL-SCALE RC MODEL Earthquake-Resistant Design

Abhinanda Dilip, Abhishek Salkar, Qudsia Wahab

University of California, Berkeley

1

Table of Contents ABSTRACT ................................................................................................................................................. 2

INTRODUCTION ....................................................................................................................................... 2

PAST RESEARCH ..................................................................................................................................... 3

PROBLEM STATEMENT AND OUTLINE ........................................................................................... 4

DETAILS OF FULL-SCALE MODEL TESTED ON SHAKE TABLE ............................................... 6

Materials Used .................................................................................................................................... 7

Setting of Specimen ............................................................................................................................ 7

MODELING IN SAP2000 .......................................................................................................................... 8

SMRF .................................................................................................................................................. 8

Shear Walls ......................................................................................................................................... 9

Loading ............................................................................................................................................... 9

RESPONSE-SPECTRUM ANALYSIS IN SAP2000 ............................................................................. 12

CALCULATIONS AND RESULTS........................................................................................................ 16

Girder 1 (2nd Floor) .......................................................................................................................... 16

Column 1 (1st Floor) ......................................................................................................................... 19

Exterior Joint Shear (1st Floor) ....................................................................................................... 22

Wall (1st Floor) ................................................................................................................................. 24

SERVICEABILITY CHECKS ................................................................................................................ 26

Special Moment Resisting Frames.................................................................................................. 28

Special Shear Walls.......................................................................................................................... 33

PERFORMANCE OF FULL-SCALE MODEL TESTED ON SHAKE TABLE ............................... 36

Performance of Columns on 1st floor ............................................................................................. 36

Performance of Girders and Joints on 2nd, 3rd and 5th floors ................................................... 36

Performance of Shear Wall on 1st Floor......................................................................................... 38

REFERENCES .......................................................................................................................................... 39

ACKNOWLEDGMENTS ........................................................................................................................ 39

APPENDIX ................................................................................................................................................ 40

2

Linear Dynamic Analysis and Seismic Evaluation

of a Full-Scale RC Model Abhinanda Dilip1, Abhishek Salkar1 and Qudsia Wahab1

1Graduate Student, Department of Civil and Environmental Engineering, University of California, Berkeley,

Berkeley, CA 94720

ABSTRACT

It is a well known fact that Japan is one of the most seismically active countries in the world.

There have been 11 earthquakes with a moment magnitude of over 7.0 since 2010 in Japan. As a

result, Japan invests significant amount of resources in advancing knowledge and technology in

the area of seismic design of structures. In this project, a ten-story structure was modeled in

SAP2000. The structure had SMRFs in the longer direction and RC shear walls in the shorter

direction as its lateral force resisting systems. The structure was modeled to represent the

behavior of a full scale model that was tested on the E-Defense Shake Table at the Hyogo

Earthquake Engineering Research Center, Japan. Capacities and demands were obtained at

critical members and joints using ACI 318-11 and SAP2000 respectively. Time period of the

structure and other important parameters were obtained using ASCE 7-10. Appropriate spot

checks were applied to determine if the structure conformed to the ASCE 7-10 requirements and

the shake table test results were compared to SAP2000 results.

Keywords: Seismic Design, ASCE 7-10, ACI 318-11, RC Building, SMRF, Special Shear Wall

INTRODUCTION

Earthquake engineering is an interdisciplinary branch of engineering that designs and analyzes

structures, such as buildings and bridges in order to make them more resistant to earthquakes.

Early stages of earthquake engineering and earthquake resistant design were shaped by major

earthquakes that occurred in the early 20th century such as the 1906 San Francisco earthquake

(Figure 1-a) in the United States, the 1908 Messina earthquake in Italy and the 1923 Kanto

earthquake (Figure 1-b) in Japan [1]. The immediate reaction of structural engineers to the idea

of earthquake resistant design was to approximate the seismic action by static horizontal forces

that will be resisted elastically. The first such report was prepared by the commission formed by

the Italian government after the 1908 Messina earthquake and recommended designing the

building to withstand a static horizontal force of approximately 10% of the total building weight.

This method was then adopted by building codes worldwide. The Los Angeles Building Code

adopted in 1943 addressed the importance of the height of the building for estimating the seismic

response for the first time. Thus, a "building flexibility" associated with the number of stories

was introduced. In 1952, 20 years after the development of the concept of response spectra, the

period of vibration of the building was introduced as a means of determining the base shear

coefficient. In 1957, a coefficient considering the inherent ductility and energy dissipation

characteristics of structures was introduced in the base shear equation. It was not before 1978

that seismic hazard was explicitly considered in the seismic design recommendations, namely by

3

Cornell who developed contour maps for effective peak acceleration (EPA) and peak velocity

(EPV). A period-dependent lateral force coefficient based on the ground motion spectrum was

proposed to be used in the structural design similar to the design spectrum that is used today.

Further, the introduction of a response modification factor permitted the use of an elastic force

design that is expected to respond inelastically.

Figure 1 (a) 1906 San Francisco Earthquake and (b) 1923 Kanto Earthquake

The US Geological Survey (USGS) estimates that several million earthquakes occur in the world

each year. Many earthquakes go undetected because they hit remote areas or have very small

magnitudes [2]. Experience has shown that reinforced concrete structures have great advantage

in such situations. The successful performance of a large number of reinforced concrete

buildings in earthquake zones in the U.S. and around the world has proved that it is possible to

design structures with the resilience to withstand earthquakes of relatively high magnitude. It is

uneconomical to design a structure to respond in the elastic range to the inertial forces caused by

the maximum considered earthquake. Accordingly, the design seismic lateral forces prescribed in

ASCE 7-10 are less than the elastic response inertial forces caused by the intended design

earthquake. The purpose of these detailing and proportioning requirements is to avoid all forms

of brittle failure and insures that the structure will have sufficient inelastic deformability. This is

to enable the structure to survive without collapse when subjected to several cycles of loading

within the inelastic range. ASCE 7-10 will be extensively used ahead in this project.

PAST RESEARCH

The ten story structure considered in this project consists of RC SMRF’s and RC Special Shear

Walls in the longer and shorter directions, respectively. Reinforced concrete special moment

frame concepts were introduced in the U.S. starting around 1960 [3]. It was not until 1973 that

the Uniform Building Code first required use of the special frame details in regions of highest

seismicity [4]. The earliest detailing requirements are remarkably similar to those in place today.

Studies related to modeling of reinforced concrete walls date back to the 1970s. Cervenka and

Gerstle (1971, 1972) tested a number of RC shear walls under monotonic and cyclic loading.

They also developed a model for reinforced concrete based on these experimental results.

4

PROBLEM STATEMENT AND OUTLINE

The main objective of this project is to model a ten-story structure to represent a full-scale model

which was tested on the E-Defense Shake Table in Japan and check if it conforms to the ASCE

7-10 and ACI 318-11 requirements. The procedure for this project has been briefly summarized

below (Figure 2).

Figure 2 – Procedure followed for this project

A report was obtained using the USGS website. The DBE and MCE response spectra (Figures 3

and 4) along with other important information from the report have been summarized below:

The structure was modeled using SAP2000 and non-linear geometry effects were taken into consideration.

The structure was assumed to be located at 1916 Shattuck Avenue at Berkeley in order to represent a seismic zone similar to Japan.

The response spectra, peak ground acceleration and other important parameters were obtained using the USGS website. The soil was assumed to be stiff (Site D).

The time period of the structure, importance factor, risk category, seismic design category and necessary information was obtained using the ASCE7-10 requirements.

Capacities of critical members and joints were obtained using ACI 318 code provisions and compared to demands obtained from SAP2000 analysis to determine

if the structure was adequate. ASCE 7-10 requirements were used.

The results from SAP2000 analysis were also compared to the results from the shake table test.

5

Table 1 – USGS Summary of Parameters

SMS 2.373g

SM1 1.480g

SDS 1.582g

SD1 0.987g

TL 8 seconds

PGA 0.914g

Figure 3 – Design Response Spectrum

Figure 4 – Maximum Considered Earthquake (MCER) Response Spectrum

6

DETAILS OF FULL-SCALE MODEL TESTED ON SHAKE TABLE

A full scale model of the ten story RC structure was tested on the E-Defense Shake Table at the

Hyogo Earthquake Engineering Research Center, Japan in 2010. The structure remained stable

after the test but sustained severe damage. The lateral force resisting system of the structure

consisted of SMRF’s in the longer (Y) direction and special shear walls up to the first 7 stories in

the shorter (X) direction. The total floor area is 1297m2. The plan and elevation of the structure

have been shown below (Figure 5) along with the loading on the structure (Table 2).

Figure 5 – Plan and Elevation of the Structure

Table 2 - Weight and Seismic Loads

7

Materials Used

The materials used for the structure have been shown below (Table 3 and Figure 3).

Table 3 (a) – Concrete and (b) - Steel

Figure 6 (a) – Concrete and (b) - Steel

Setting of Specimen

The first six floors and the rest of the floors (floor 7 to roof) were constructed separately as two

different specimens. These two specimens were taken to the testing site and connected together

on the shake table as illustrated below (Figure 7).

Figure 7 – Two separate specimens of the structure to be connected on shake table

8

MODELING IN SAP2000

A finite element model of the building was generated in SAP2000 and analyzed under

earthquake forces. The first floor of the building was not included in the model as it had no

contribution to the inertia forces. The supports were defined to be restrained against translation

and rotation in all three directions. All connections except gravity-only beams were modeled as

fixed connections as shown below (Figure 8).

Figure 8 – (a) Plan View and (b) Elevation (SMRF and Shear Wall Direction)

SMRF: The SMRF was modeled with frame elements and were meshed at intermediate joints

and at frame intersections. The local axes of the members were oriented such that axis 3-3 was

the major bending axis. Sections were defined from the structural drawings and material

properties were chosen according to the story levels (Figure 9 (a)). The insertion point of the

beams was set at the top-centre of slab to include the slab in the effective flange width (Figure 9

(b)). End length offsets were defined from connectivity with a rigid zone factor of 1.0 and panel

zones were defined at the joints. Flexural stiffness modifiers of 0.7 and 0.5 were assigned to the

columns and the beams respectively, to account for cracking.

9

Figure 9 – (a) Typical Column Section and (b) Frame Insertion Point

Shear Walls: The shear walls were modeled as thin shell elements with both membrane and

plate bending characteristics. The transition between the shear wall and moment frame at the 8th

story level was captured by modeling a frame element at the transition line. The shell elements

were meshed using automatic area meshing at edge points and edge constraints were generated.

Stiffness modifiers of 0.5 and 0.7 were assigned for the membrane and bending behaviors,

respectively. In order to constrain the rotation of the beams framing into the walls, rigid links

were defined at the boundary of vertically adjacent wall segments using frame elements with

flexural rigidity of 100 times that of the other beam elements (Figure 10 (a)).

Figure 10 – (a) Rigid Links at Shear Walls and (b) Mass Source Definition

Loading: The element self-weight was included in the dead load pattern. Additional joint loads

were defined under dead load pattern to include the weight of the cantilevered slab edges. Live

loads were added as surface loads on the slab elements. For modal analysis, all loads under the

10

dead load pattern and and 50% of loads under live load pattern were defined in the mass source

(Figure 10 (b)). The response spectrum for DBE intensity level was generated from USGS

website and the parameters including soil type were defined in the response spectrum function.

SAP2000 generates the response curve (Figure 11). Load cases were defined for modal analysis,

combined modal response spectrum analysis in the X( shear wall) and Y (SMRF) directions

(Figure 12). Nonlinear geometry effects were also included by using the stiffness matrix at the

end of P-Δ geometry under dead load, for all load cases (Figure 13).

Figure 11 – Response Spectrum Definition in SAP2000

Figure 12 – Definition of Load Cases Figure 13 – Inclusion of non-linear geometry effects

11

For the response spectrum cases, the spectrum was scaled using appropriate reduction factor and

scaling factor to match with the base shear obtained from equivalent lateral force procedure in

both directions (Figure 14).

Figure 14 – Scaling of Response Spectrum in X and Y Directions

Load combinations were defined as per ASCE 7-10 including effects of seismic forces

simultaneously occurring in orthogonal directions. Envelope case was defined to obtain the

critical maximum and minimum analysis results (Figure 15).

Figure 15 – Defining Load Combinations in X and Y Directions as per ASCE 7-10

12

RESPONSE-SPECTRUM ANALYSIS IN SAP2000

Response-spectrum analysis (RSA) is a linear-dynamic statistical analysis method which

measures the contribution from each natural mode of vibration to indicate the likely maximum

seismic response of an essentially elastic structure. It is the representation of the maximum

response of idealized single degree freedom system having certain time period and damping

during earthquake ground motions [5]. The maximum response plotted against un-damped

natural period for various damping values can be expressed in terms of maximum absolute

acceleration, maximum relative velocity or maximum relative displacement. Response-spectrum

analysis provides insight into dynamic behavior by measuring pseudo-spectral acceleration,

velocity, or displacement as a function of structural period for a given time history and level of

damping. It is practical to envelope response spectra such that a smooth curve represents the

peak response for each realization of structural period. Response-spectrum analysis is useful for

design decision-making because it relates structural type-selection to dynamic performance.

Structures of shorter period experience greater acceleration, whereas those of longer period

experience greater displacement. Structural performance objectives should be taken into account

during preliminary design and response-spectrum analysis. The main limitation of response

spectra is that they are only universally applicable for linear systems. Response spectra can be

generated for non-linear systems, but are only applicable to systems with the same non-linearity.

As it has been mentioned earlier, the ten story structure consists of SMRF’s in the Y (longer)

direction and Special RC Shear Walls up to the seventh story in the X (shorter) direction as its

lateral force resisting systems. In order to determine if the lateral force resisting system in the X

direction behaved like a dual system or not, earthquake loading was applied in the X direction.

The columns in the X direction were found to take 15% of the base shear. ASCE 7-10 [6]

Section 12.2.5.1 provisions state that the moment frames should be capable of resisting at least

25% of the design seismic forces in order for the system to be considered as a dual system.

Hence, the lateral force resisting system in the X direction was treated as a Bearing Wall System.

The Mass Source was defined to include 100% of the dead load and 50% of the live load. The

dead load only included the self weight of the structure while the live load was defined under

load patterns. Once the mass source was defined, modal analysis of the structure was performed

in SAP2000 in X and Y directions.

The fundamental period of the structure was found to be 0.538 seconds in the X direction (Figure

16 (a)) and 0.947 seconds in the Y direction (Figure 16 (b)). The mass participation of the first

mode was found to be 73.43% and 78.25% in the X and Y directions, respectively. As we see,

the mass participation in both directions was less than 90% as required by Section 12.9.1 ASCE

7-10. A total of 60 modes were considered for analysis such that the mass contribution added up

to 99% of the mass of the structure as required for this project.

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Figure 16 - (a) Deformed Shape in the fundamental mode in X-direction and (b) Deformed

Shape in fundamental model in Y- direction

Section 12.8.2 ASCE 7-10 Code Provisions were used in order to determine the fundamental

periods and the upper limits of time periods that could be considered for the structure. Section

12.8.2.1 of ASCE 7-10 states that the fundamental period of the structure is given by:

Ta = Cthnx (1)

Where

hn = structural height of the structure

Ct and x = Period parameters obtained from Table 12.8.2 of ASCE 7-10 (shown below)

14

Using the equation (1), the fundamental periods in the two directions were found to be:

X-direction Ta = 0.04880*(27.45)0.75 = 0.585 sec

Y-direction Ta = 0.04660*(27.45)0.90 = 0.918 sec

Section 12.8.2.1 of ASCE 7-10 also states an upper limit on the fundamental periods that can be

used for a structure given by:

Tlimit = CuTa (2)

Where,

Ta = Fundamental Period of structure obtained from the above equation

Cu = Coefficient for upper limit on calculated period obtained from Table 12.8.1 of ASCE 7-10

(shown below)

Using equation (2), the upper limits for calculated periods in the two directions were found to be:

X-direction Tlimit = 1.4 * 0.585 = 0.819 sec

Y-direction Tlimit = 1.4 * 0.918 = 1.285 sec

All the values of fundamental periods obtained in SAP2000 and ASCE7-10 (including the upper

limits) have been summarized below (Table 4)

Table 4 – Comparison of Fundamental Periods from SAP2000, drawings and ASCE 7-10

Ta (ASCE 7-10) T (drawings) T (SAP2000) Tlimit (ASCE 7-10)

X-direction 0.585 sec 0.610 sec 0.538 sec 0.819 sec

Y-direction 0.918 sec 0.800 sec 0.947 sec 1.285 sec

It is observed that all the calculated fundamental periods are below the upper limits obtained

from ASCE 7-10. Hence, the time periods obtained from SAP2000 analysis were used.

The base shears were found to be 1784.43 kN and 804.11 kN in the X and Y directions,

respectively. Section 12.8 of ASCE 7-10 was used to calculate the seismic base shear using the

Equivalent Lateral Force Method. The seismic base shear is given by:

V = CsW

15

Where

V = Seismic base shear

W = Weight of the structure (7683.19 kN)

Cs = Base Shear Coefficient given by

Cs = (𝑆𝑑𝑠

𝑅

𝐼𝑒

)

The building falls under risk category II according to Table 1.5-1 of ASCE 7-10. The importance

factor, Ie of the building was determined to be 1.00 from Table 1.5-2 of ASCE 7-10. The

response modification factor, R was found to be 5 and 8 in the X and Y directions, respectively

from Table 12.2-1 of ASCE 7-10.

The upper and lower limits of Cs are given by:

Cs, max = 𝑆𝑑1

𝑇(𝑅

𝐼𝑒) for T < TL = 8sec

Cs, min1 = 0.5𝑆1

(𝑅

𝐼𝑒)

Cs, min2 = 0.044SDSIe > 0.01

The base shear values obtained from the above equations using ASCE 7-10 have been

summarized below (Table 5).

Table 5 – Summary of Base Shear Calculations using ASCE 7-10

T (sec) Cs Cs,max Cs, min V=CsW

SMRF 0.947 0.1978 0.1303 0.0690 1000.98 kN

Shear Wall 0.538 0.3164 0.3670 0.0987 2430.96 kN

The base shear values obtained using ASCE 7-10 were compared with the base shear values

obtained from SAP2000 analysis. The comparison has been summarized below (Table 6).

Table 6 – Comparison of Base Shear Values from SAP2000 and ASCE 7-10

V (ASCE 7-10) V (SAP2000)

SMRF 1000.98 kN 780.5850 kN

Shear Wall 2430.96 kN 1754.678 kN

As it can be seen, the values obtained from SAP2000 were found to be lower than those of the

code. Therefore, the values obtained from analysis were increased by a factor of 1.2448 and

1.3623 for SMRF and Shear Wall directions, respectively. The building was analyzed for these

forces and member forces were obtained for the critical load combinations. A few members were

picked and demand versus capacity ratios were checked to understand the strength level of the

building per ASCE and ACI 318 provisions.

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CALCULATIONS AND RESULTS

Girder 1 (2nd Floor)

The girder spans the EW direction with a span of 4000 mm. SAP2000 is used to find the design

moment, Mu. In SAP2000, the girders of the moment frame are modeled with no moment

releases at column intersections. The girders are designed using a rectangular cross-section

(Figure 17 (a)) ignoring any reinforcement in the slab, which gives a conservative result. The

following calculations adhere to ACI 318-11 [7] and ASCE 7-10.

Moment:

Design at Support (Rectangular Cross-Section):

Given From SAP2000:

From load combinations, the maximum negative moment is 304 kN-m

From load combinations, the maximum positive moment is 290 kN-m

Reinforcement:

Longitudinal reinforcement – 22 mm dia. bars

Transverse reinforcement – 10 mm dia. stirrups

𝜑 = 0.9 (moment)

𝜑 = 0.75 (shear)

∈𝑠 ≥ ∈𝑦

Parameters:

𝑓𝑐′ = 42 𝑀𝑃𝑎 → 𝛽1 = 0.745 (Figure 17 (b))

𝑓𝑦 = 345 𝑀𝑃𝑎

𝑓𝑦𝑡 = 295 𝑀𝑃𝑎

𝐸𝑠 = 200000 𝑀𝑃𝑎

∈𝑐 = 0.003

𝑑 = 550 − 61 = 489 𝑚𝑚

ℎ = 550 𝑚𝑚

𝑏 = 350

Cover = 61 mm

Figure 17 – (a) Rectangular cross section, (b) 𝛽 values from concrete compressive strength

17

Rectangular Design:

∈𝑠

(𝑑−𝑐)=

∈𝑐

𝑐 → ∈𝑠= 0.003 (

𝑑

𝑐− 1)

∈𝑠′

(𝑐−𝑑′)=

∈𝑐

𝑐 → ∈𝑠 ′ = 0.003 (1 −

𝑑′

𝑐)

𝑇𝑠 = 𝐴𝑠𝑓𝑦

𝐶𝑐 = 0.85𝑓𝑐′𝑏𝛽1𝑐

𝐶𝑠′ = 𝐴𝑠′ 𝐸 ∈𝑠

o +↺ ∑ 𝐹 = 0 → 0.85𝑓𝑐′𝑏𝛽1𝑐 + 𝐴𝑠′𝐸 ∗ 0.003 (1 −

𝑑′

𝑐) − 𝐴𝑠𝑓𝑦 = 0

o 9314 c2 +615815 c – 80968267 =0

o c = 65.9 mm

Check:

Moment:

o + ↺ ∑ 𝑀 = 0

o 𝑀𝑛 = 0.85𝑓𝑐′𝑏𝛽1𝑐 ∗ (𝑑𝑠 − 0.425𝑐) + 𝐴𝑠′𝐸 ∈𝑐 (1 −

𝑐𝑜𝑣𝑒𝑟

𝑐) (𝑑𝑠 − 𝑐𝑜𝑣𝑒𝑟)

o 𝑀𝑛+= 246 𝑘𝑁 − 𝑚

o 𝑀𝑛−= 303 𝑘𝑁 − 𝑚

o 𝑀𝑢 > 𝜑 𝑀𝑛 Girder is NOT adequate for flexure

Phi Factor:

o ∈𝑠

(𝑑−𝑐)=

∈𝑐

𝑐 → ∈𝑠= 0.003 (

𝑑

𝑐− 1) = 0.0188

o ∴ ∈𝑠 > 0.005 → 𝜑 = 0.9

Shear:

Given From SAP2000:

Vu = 𝑀𝑝𝑟1+𝑀𝑝𝑟2

𝐿𝑛+

𝑤𝐿𝑛

2 = 228 kN.

Vu ≤ 𝜑(𝑉𝑠 + 𝑉𝑐)

o 𝑉𝑐 = 2√𝑓𝑐′𝑏𝑤𝑑

o 𝑉𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑠

𝑠

o 𝑉𝑛 = 𝑉𝑠 + 𝑉𝑐

o 𝜑𝑉𝑛 = 347 𝑘𝑁

o 𝑉𝑢 ≤ 𝜑 𝑉𝑛 Girder is adequate for shear

The calculations were done in excel. The rest of these calculations have been provided in the

Appendix. The results from SAP2000 analysis for Girder 1 have been shown below (Figure 18).

The demands capacity ratios were then obtained and have been summarized in Table 7.

18

Figure 18 – SAP2000 results for girder G1

Table 7 – Demand Capacity Ratios for Flexure and Shear

D/C FOR MOMENT AND SHEAR

Mu/ΦMn (+) Mu/ΦMn (-) V

2nd Floor

G1 1.31 1.12 0.66

G2 0.99 1.04 0.66

3rd Floor

G1 1.31 1.12 0.76

G2 1.02 1.07 0.76

5th Floor

G1 1.24 1.33 0.86

G2 1.21 1.03 0.77

As it can be seen from the above table, most of the D/C in flexure are greater than 1, which

means that they don’t meet the demand requirements as per ACI 318. D/C ratios for shear are all

lower than 1, and therefore the girders are sufficient in shear.

19

Column 1 (1st Floor)

The column considered is C1 on grid A1 and spans from level 1 to 2. The size of the column is

550 mm x 550 mm and its height is 2800 mm. SAP2000 is used to find the design moment, Mu

and axial force, Pu. SAP2000 is also used to generate a P-M interaction diagram (Figure 19) for

the cross section. The following calculations adhere to ACI 318-11 and ASCE 7.

Reinforcement:

Longitudinal reinforcement – (20) 22 mm dia. bars

Transverse reinforcement – 10 mm dia. Hoops @ 100 mm o.c.

Parameters:

𝑓𝑐′ = 42 𝑀𝑃𝑎



𝐸𝑠 = 200000 𝑀𝑃𝑎

Figure 19 - P-M Interaction Diagram of the Column

As it can be seen in the graph, some of the demand points lie outside of the P-M interaction

diagram, suggesting that the column does not have adequate capacity to resist applied loads.

(Pu, Mu) > Φ (Pn, Mn)

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 200 400 600 800 1000 1200

Axi

al F

orc

e, P

(kN

)

Moment, M (kN-m)

C1: P-M Interaction Diagram

Pu,Mu

ΦMn, ΦPn

Pn,Mn

20

Column Shear Calculations

Vu ≤ Φ Vn

- Φ = 0.75

- Vn = Vc + Vs

𝑉𝑐 = 2 (1 +𝑁𝑢

2000𝐴𝑔) 𝜆 √𝑓 ′𝑐 𝑏𝑑

𝑉𝑠 = 𝐴𝑣𝑓𝑦𝑡 𝑑

𝑠

Φ Vn = 464 kN

Vu = 244 kN

Vu < Φ Vn Column is adequate for shear

The calculations were done in excel. The rest of the calculations have been provided in the

Appendix. The SAP2000 analysis for Column 1 has been shown below (Figure 19). The demand

capacity ratios for axial-moment and shear were then obtained and have been summarized below

(Table 8)

Figure 19 – SAP2000 analysis of column C1

Table 8 – Demand Capacity Ratios for Axial, Moment and Shear

D/C FOR AXIAL-MOMENT

AND SHEAR

P-M V

C1 1.16 0.42

C2 1.51 0.70

21

SAP2000 analysis results for column 1 have been illustrated below (Figures 20 and 21).

Figure 20 – Axial Force Results for Column C1 in SAP2000

Figure 21 – Bending Moment and Shear Force Results for Column C1 in SAP2000

22

Exterior Joint Shear (1st Floor)

Column Shear

𝑀𝑝𝑟𝑔2 + 𝑀𝑝𝑟𝑔1 + ((𝑀𝑝𝑟𝑔1 + 𝑀𝑝𝑟𝑔1

𝐿𝑛) ∗

𝑑𝑐

2+ (

(𝑀𝑝𝑟𝑔2 + 𝑀𝑝𝑟𝑔2

𝐿𝑛) ∗

𝑑𝑐

2− 𝑉𝑐𝑜𝑙 ∗ 𝐻 = 0

Where,

Mprg1 - Probable moment of girder 1 (G1)

Mprg2 - Probable moment of girder 2 (G2)

Ln – clear span of the beam

H – Height of the column between inflection points

Vcol = 323 kN

Joint Shear

Vcol – Vjoint - –𝑀𝑝𝑟𝑔1

𝑑𝑔1+

𝑀𝑝𝑟𝑔2

𝑑𝑔2 = 0

Demand on the joint Vu = 1397 kN

ΦVn = Φ 𝛶√𝑓′𝑐 𝐴𝑗𝑜𝑖𝑛𝑡

Φ = 0.85

𝛶 = 15 (exterior joint), 12 (corner joint)

23

Capacity of the joint Vn = 2075kN

Demand < Capacity Joint is adequate

Calculations were done in excel. Please refer to the Appendix for these calculations.

The Vcol, Vjoint and D/C for exterior and corner joints have been summarized below (Table 9).

Table 9 - Joint Shear Summary

JOINT DESIGN

Vcol (kN) Vjoint (kN) ΦVn (kN) D/C

Exterior 323 1397 2075 0.67

Corner 161 699 1660 0.42

As seen from the table, the demand capacity ratios were found to be comfortably less than 1.

This suggests that the joints are adequate for resisting the loads. The location of the joint which

was considered for calculations illustrated above has been shown below (Figure 22)

Figure 22 – Location of the joint considered for illustrated calculations

24

Wall (1st Floor)

The wall cross section considered is W23 on grid B-C between levels 1 and 2. The length of the

wall is 1800 mm and its thickness is 230 mm. SAP2000 is used to find the design moment, Mu

and axial force, Pu. Xtract and Excel are used to generate a P-M Interaction Diagram (Figure 23)

for the wall. The following calculations adhere to ACI 318-11 and ASCE 7.

Reinforcement:

Boundary

Longitudinal reinforcement – (8) 19 mm dia. bars

Transverse reinforcement – 10 mm dia. Hoops @ 100 mm o.c.

Distributed

Longitudinal reinforcement – 13 mm dia. Bars @ 250 mm o.c.

Transverse reinforcement – 10 mm dia. Bars@ 150 mm o.c.

Parameters:

𝑓𝑐′ = 42 𝑀𝑃𝑎



𝐸𝑠 = 200000 𝑀𝑃𝑎

Figure 23 - P-M Interaction Diagram of the Wall

-5.00E+06

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

- 2 . 0 0 E + 0 5 0 . 0 0 E + 0 0 2 . 0 0 E + 0 5 4 . 0 0 E + 0 5 6 . 0 0 E + 0 5 8 . 0 0 E + 0 5 1 . 0 0 E + 0 6

AX

IAL

FOR

CE,

P (

N)

MOMENT, M (N-M)

W1: P-M INTERACTION DIAGRAM

Mn, Pn

ΦPn, ΦMn

Mu, Pu

25

As it can be seen in the graph, the demand point lies outside of the P-M interaction diagram,

suggesting that the wall does not have adequate capacity to resist applied loads.

Pu = 971.8 kN

Mu = 828 kN-m

(Pu, Mu) > Φ (Pn, Mn)

Wall Shear Calculations

Vu ≤ Φ Vn

- Φ = 0.75

- Vnmax = 8√𝑓′𝑐 𝐴𝑐𝑣

- Vn = Vc + Vs

𝑉𝑐 =α√𝑓′𝑐 𝐴𝑐𝑣

𝑉𝑠 = 𝜌𝑡 ∗ 𝑓𝑦𝑡 ∗ 𝐴𝑐𝑣

Vnmax = 1782 kN

Φ Vn = 751 kN

Vu = 710 kN

Vu < Φ Vn Wall is adequate for shear

The calculations were done in excel. The rest of the calculations have been provided in the

Appendix. The cross sectional details of the boundary zone and the wall web have been

illustrated below (Figure 24 (a) and (b)).

Figure 24 – Cross Sectional Detail of (a) Boundary Zone and (b) Wall Web

26

SERVICEABILITY CHECKS

The model is modified for calculating deflections at the story levels by changing the stiffness

modifiers for the shear walls to 0.5 in flexure and 0.4 in shear. Torsional irregularity was not a

consideration for deflection calculations. The elastic displacements were obtained under the

strength-level design earthquake forces as specified in Section 12.8.6 of ASCE 7-10. The design

story drift (Δ) was computed as the difference of the deflections at the center of mass at the top

and bottom of the story under consideration. Section 12.9.4.2 requires that the elastic drifts be

scaled up on the basis of modal base shear. Since, the applied loads were scaled to 100% of the

prescribed base shear, the drifts were not amplified again. The deflection at Level x (δx) was

computed based on the requirements of Section 12.9.2 and using Equation 12.8-15 from Section

12.8.6 of ASCE 7-10.

δx = 𝐶𝑑 X 𝛿𝑥𝑒

𝐼𝑒

Where,

δxe = elastic displacements computed at strength-level design earthquake forces

Ie = Importance factor, 1.0 for this building

Cd = Amplification factor to obtain inelastic displacements

The amplification factors Cd for the drifts were determined from Table 12.2-1 of ASCE 7-10 and

have been summarized below (Table

Table 10 - Cd values for the building

Direction R Cd

SMRF 8 5.5

Shear wall 5 5

The allowable story drifts were obtained from Table 12.12-1 of ASCE 7-10 (shown below).

The calculated elastic and inelastic displacements at the story levels have been summarized in

Table 11 (a) and 11 (b) along the Shear Wall and SMRF directions respectively. The final

inelastic story drifts were then compared with the allowable story drifts per ASCE 7-10.

27

Table 11 (a) - Drift Calculations along Shear wall direction

Story

Level

Height,

m δxe

Inelastic

Drift,δx

Interstory

Drifts,Δx

Allowable

Drift

Limits, Δax

Limit

Satisfied

2 2.8 0.002623 0.013 0.0131 0.056 OK

3 5.4 0.007562 0.038 0.0247 0.052 OK

4 8 0.013799 0.069 0.0312 0.052 OK

5 10.6 0.020455 0.102 0.0333 0.052 OK

6 13.15 0.026897 0.134 0.0322 0.051 OK

7 15.7 0.032779 0.164 0.0294 0.051 OK

8 18.25 0.037979 0.190 0.0260 0.051 OK

9 20.75 0.043688 0.218 0.0285 0.05 OK

10 23.25 0.048523 0.243 0.0242 0.05 OK

Roof 25.75 0.051818 0.259 0.0165 0.05 OK

Table 11 (b) - Drift Calculations along SMRF direction

Story

Level

Height,

m δye

Inelastic

Drift,δy

Interstory

Drifts,Δy

Allowable

Drift

Limits, Δay

Limit

Satisfied

2 2.8 0.008602 0.047 0.0473 0.056 OK

3 5.4 0.020975 0.115 0.0681 0.052 NOT OK

4 8 0.034998 0.192 0.0771 0.052 NOT OK

5 10.6 0.048547 0.267 0.0745 0.052 NOT OK

6 13.15 0.060827 0.335 0.0675 0.051 NOT OK

7 15.7 0.072208 0.397 0.0626 0.051 NOT OK

8 18.25 0.082801 0.455 0.0583 0.051 NOT OK

9 20.75 0.091359 0.502 0.0471 0.05 OK

10 23.25 0.097499 0.536 0.0338 0.05 OK

Roof 25.75 0.101277 0.557 0.0208 0.05 OK

As seen from the comparison, the drift limits are satisfied along the shear wall direction. But in

the SMRF direction, the drifts exceed the limit for story levels 3 to 8. Hence, the ASCE

provisions for serviceability are not satisfied along the SMRF direction.

28

STRUCTURAL DETAILS VS. ACI 318-11 PROVISIONS

Special Moment Resisting Frames

Reinforcement Details

Sections 21.6.3 and 21.6.4 of ACI 318-11 provide detailing requirements of columns in special

resisting moment frames. These requirements have been briefly summarized below (Figure 26

and Table 12) [8].

Figure 26 – Column detailing requirements in SMRF’s

Table 12 – Requirements for Cross Sectional Area of Hoop Reinforcement

29

The details of the three different types of columns on the first floor of the building have been

summarized below (Table 13) to determine if their detailing conforms to the ACI requirements

provided above.

Table 13 – Detailing of Columns on first floor of building

Column 1 Column 2

Cross Section

Dimensions (mm×mm) 550×550 550×550

Area of Longitudinal Reinforcement, Ast

(mm2)

7602.65 6082.12

Spacing of Transverse Reinforcement over

length lo from each joint, s1 (mm)

100 100

Cross-sectional Area of hoop reinforcement,

Ash (mm2)

314.16 314.16

Spacing of Transverse beyond length lo

from each joint, s2 (mm)

100 100

Cover (mm) 40 40

The beams listed above were checked to determine if they conformed to the ACI 318-11

requirements mentioned in Figures 25, 26. The results have been summarized below (Table 14).

Table 14 - Summary of Beams satisfying/not satisfying ACI 318-11 Code Provisions

Code Requirements Satisfied Not Satisfied

Area of Longitudinal

Reinforcement, Ast

Column 1, Column 2 None

Spacing of Transverse

Reinforcement over length lo

from each joint, s1


Cross-sectional Area of hoop

reinforcement, Ash


Spacing of Transverse beyond

length lo from each joint, s2


Cover Column 1, Column 2 None

Strong Column Weak Beam Column 1, Column 2 None

As it can be observed from Table 14, both columns satisfied all the checks and conformed to the

ACI provisions. However, it was found that the cross sectional area of hoop reinforcement was

found to be marginally higher than the minimum requirement. Hence, we can anticipate some

amount of damage in case of earthquakes which are stronger than the design level earthquake.

This is confirmed as the full scale model which was tested at the E-Defense Shake Table was

found to have sustained considerable damage after the shake table test.

30

Beams and Joints in Special Moment Resisting Frames

Section 21.7 in ACI 318-11 provides requirements for joints in SMRF’s (Figure 27 and 28).

Even though the figures below summarize the transverse and longitudinal requirements for

beams in SMRF’s, they form a major part of joint requirements for SMRF’s. Section 21.7.3.1

also states that joints in SMRF’s should satisfy the spacing, cover and hoop reinforcement

(cross-sectional area) requirements of columns. Since the column requirements have already

been checked earlier, only the rest of the requirements have been checked in this section.

Figure 27 – Beam Transverse Reinforcement Requirements in SMRF’s

Figure 28 – Beam Longitudinal Reinforcement Requirements in SMRF’s

The details of the different types of girders on the 2nd, 3rd and 5th floors of the building have been

summarized below (Table 15) to determine if their detailing conforms to the ACI requirements

provided above.

31

Table 15 – Detailing of beams on 2nd, 3rd and 5th floors of the building

Beam 1

(2nd

floor)

Beam 2

(2nd

floor)

Beam 1

(3rd

floor)

Beam 2

(3rd

floor)

Beam 1

(5th floor)

Beam 2

(5th

floor)

Cross Section

Dimensions

(mm×mm)

350×550 350×550 350×550 350×550 350×550 350×550

Column dimension

parallel to beam

reinforcement, hc

(mm)

500 500 500 500 500 500

Area of Joint

Transverse

Reinforcement (mm2)

157.08 314.16 157.08 157.08 157.08 314.16

Spacing of Joint

Transverse

Reinforcement (mm)

150 150 150 150 150 150

Distance of first hoop

from face of

supporting member

(mm)

0 0 0 0 0 0

Spacing of hoops

(mm)

100 100 100 100 125 100

Spacing for stirrups

with seismic hooks

(mm)

100 100 100 100 125 100

Spacing of hoops at

lap splice (mm)

100 100 100 100 125 100

Spacing of

transversely

supported flexural

reinforcing bars (mm)

270 270 270 270 270 270

Distance of splice

from face of

supporting member

(mm)

862.5 862.5 875 875 875 875

Area of Top Long.

Reinforcement (mm2)

1900.66 1140.39 1900.66 1140.39 1520.53 1140.39

Area of Bottom Long.

Reinforcement (mm2)

1520.53 1140.39 1520.53 1140.39 1520.53 1140.39

32

The beams listed above were checked to determine if they conformed to the ACI 318-11

requirements mentioned in Figures 8 and 9. The results have been summarized below (Table 6).

As we observe, most of the checks were satisfied. However, the spacing of joint transverse

reinforcement was not satisfied at any of the joints. This is probably because the grade of steel

used at the joints was extremely high (785 MPa) and hence the designers probably took the

liberty of providing larger spacing. Also, the minimum distance requirement for lap splices to be

installed from the face of the supporting member was not satisfied for any of the beams. This is

probably due to difference in the Japanese and ASCE Code Provisions. The spacing of hoops at

the lap splice in the beams was satisfied by all beams except Beam 2 on the 5th floor.

Table 16 – Summary of Beams satisfying/not satisfying ACI 318-11 Code Provisions

Code Requirements Satisfied Not Satisfied

Column dimension parallel to beam

reinforcement, hc

All beams None

Area of Joint Transverse

Reinforcement

All joints None

Spacing of Joint Transverse

Reinforcement

None All joints

Distance of first hoop from face of

supporting member

All beams None

Spacing of hoops All beams None

Spacing for stirrups with seismic

hooks

All beams None

Spacing of hoops at lap splice Rest of the beams Beam 1 (5th floor)

Spacing of transversely supported

flexural reinforcing bars

All joints None

Distance of splice from face of

supporting member

None All beams

Area of Top Long. Reinforcement All beams None

Area of Bottom Long. Reinforcement All beams None

33

Special Shear Walls

In our project the structure has special reinforced concrete shear walls in its shorter (X) direction

and these shear walls go up to the first seven stories of the building. A typical special shear wall

has been shown below (Figure 29).

Figure 29 – Special RC Shear Wall Details

Section 21.9 of ACI 318-11 provides detailing requirements of boundary elements of shear walls

depending on whether they are to be detailed as ordinary boundary elements (Figure 30) or

special boundary elements (Figure 31). Since Section 21.9 of ACI 318-11 is extremely

descriptive, only the major significant provisions which matter for this project have been briefly

summarized below.

Figure 30 – Detailing requirements for ordinary boundary elements

Figure 31 – Detailing requirements for special boundary elements

34

In order to determine if specially confined boundary elements are required, we first identify the

maximum axial force demand (Pu) on the shear wall. We then calculate (Pu/Agf’c) since the gross

area (Ag) and the compressive strength (f’c) are already known to us and find the corresponding

value of (c/lw) from the graph (Figure 32).

Figure 32 – Approximate Compression Flexural Depth

Once we have obtained (c/lw), we would decide to reinforce the compression zones with special

boundary elements if the following expression is satisfied.

(𝑐

𝑙𝑤) ≥

1

900 (𝜕𝑢ℎ𝑤

)

c = largest neutral axis depth calculated for the factored axial force and nominal moment strength

𝑙𝑤 = length of the wall

ℎ𝑤 = height of the wall

𝜕𝑢 = top level design displacement

The ratio 𝜕𝑢

ℎ𝑤 should not be taken less than 0.007.

ACI 318-11 states that where special boundary elements are required, the special boundary

element reinforcement shall extend vertically from the critical section a distance not less than the

larger of 𝑙𝑤 or Mu/4Vu. Structural walls not designed according to the provisions above shall

have special boundary elements at boundaries and edges around openings of structural walls

where the maximum extreme compressive fiber compressive stresses exceed 0.2f’c and are

permitted to be discontinued when the compressive stresses are less than 0.15f’c. Shear walls are

also classified based on their (ℎ𝑤/𝑙𝑤) ratio (Table 17).

Table 17 – Classification of Shear Walls based on (𝒉𝒘/𝒍𝒘) value

Shear Wall Classification (𝒉𝒘/𝒍𝒘)

Squat Wall <1

Transition Wall 1-2

Slender Wall >2

35

The requirements for web reinforcement ratios ρl and ρt depend on the shear wall classification.

For walls with (ℎ𝑤/𝑙𝑤) less than 2 (squat and transition walls), ρl should always be equal or

higher than ρt. For other cases (slender walls), ρl is 0.0025 and ρt is calculated based on shear

requirements. Reinforcement spacing each way in structural walls should not exceed 18 inches.

The details of the shear wall in the structure have been summarized below (Table 18) to

determine if they conform to the ACI requirements provided above.

Table 18 – Summary of Shear Wall satisfying/not satisfying ACI 318-11 Code Provisions

Aspect Ratio, (ℎ𝑤/𝑙𝑤) 11.083 (Slender Wall)

900 (𝜕𝑢

ℎ𝑤) (

𝑐

𝑙𝑤)

3.16 (Special

Confinement Required)

Length of boundary element, lbe (mm) 450 (Check Satisfied)

Distance between Hoop or Tie Legs, hx (mm) 123.44 (Check Satisfied)

Hoop Spacing, s (mm) 100 (Not Satisfied)

Cross Sectional Area of Hoop Reinforcement, Ash Check Satisfied

Width of boundary element, b (mm) 230 (Check Satisfied)

Extension of horizontal reinforcement into boundary element (mm) 330 (Check Satisfied)

36

PERFORMANCE OF FULL-SCALE MODEL TESTED ON SHAKE TABLE

Performance of Columns on 1st floor

The performance of columns (corner and exterior) have been illustrated below

Figure 32 – (a) Column C1 and (b) Column C2 after the shake table test

As seen above, some cracks are pretty evident in the columns. This confirms the fact the columns

are not exactly adequate to resist the loads and validates calculations which showed some of the

demands lying outside the P-M interaction curve. However, the columns have not collapsed

either. This makes sense as the columns were found to conform to all ACI 318-11 requirements.

Performance of Girders and Joints on 2nd, 3rd and 5th floors

2nd Floor

Figure 33 – (a) Corner Joint and (b) Exterior Joint on 2nd floor after shake table test

37

3rd Floor

Figure 34 – (a) Corner Joint and (b) Exterior Joint on 3rd floor after shake table test

5th Floor

Figure 35 – (a) Corner Joint and (b) Exterior Joint on 5th floor after shake table test

As seen from Figures 33 to 35, the beam column joints look damaged with considerable amount

of cracks. This is not surprising as the spacing of joint transverse reinforcement was found not to

satisfy the minimum spacing requirements according to ACI 318-11. However, apart from

sustaining cracks, the joints did not fail on any of the floors. This validates the calculations

shown earlier which suggested that the joints were adequate to resist the anticipated loading. The

minimum distance requirement for lap splices was also found to not satisfy the ACI requirements

earlier. However, there were no signs of significant damage in the girders near the lap splice

region and hence no conclusions could be made on whether the location of the splices had any

effect on the performance of the girders.

38

Performance of Shear Wall on 1st Floor

Figure 36 – 230mm thick shear wall on first floor after shake table test

The shear cracks are pretty evident in the wall. This confirms the fact the wall is not adequate to

resist the loads and validates calculations which showed the demands lying outside the P-M

interaction curve. However, the wall has clearly not collapsed. This is not surprising as it was

found to satisfy most of the ACI 318-11 requirements except for hoop spacing

CONCLUSIONS

This project on the ten story structure had four main components to it. These components

included analysis on SAP2000 through which the demands were obtained, analysis using ASCE

7-10 requirements, calculation of member capacities and their comparison with the demands and

comparison between structural detailing provided in the drawings and ACI 318-11 detailing

requirements. The demands obtained from SAP2000 analysis were compared to the member

capacities to check if the members were adequate to resist loads. It was found that most of the

columns and walls were not satisfying the P-M Interaction curve as the demand points were

found to lie outside the P-M curve. Some of the girders were also found to not have adequate

moment capacities. The joint strength was found to be adequate to resist loads. However, the

spacing of joint transverse reinforcement did not satisfy the minimum spacing requirements of

ACI 318-11. The columns satisfied all the detailing requirements while most of the beams and

joints satisfied majority of the detailing requirements too with a few exceptions mentioned

earlier in the paper. Hence, it is observed that while most of the detailing requirements were

satisfied for the members, they were found to be inadequate in strength. Our calculations and

comparisons of structural detailing were validated by observing the performance of the full-scale

model after the shake table test in Hyogo, Japan.

39

REFERENCES

1. http://www.norsar.no/norsar/about-us/News/2011/Historical-Development-of-

Earthquake-Resistant-Design

2. http://www.cement.org/think-harder-concrete-/buildings-structures/design-aids/seismic-

design

3. Blume, J.A., Newmark, N.M., and Corning, L.H. (1961). Design of multistory reinforced

concrete buildings for earthquake motions, Portland Cement Association, Chicago, IL.

4. Moehle, J.P., Hooper, J.D., and Lubke, C.D. (2008). Seismic Design of Reinforced

Concrete Special Moment Frames: A Guide for Practicing Engineers, NEHRP Seismic

Design Technical Brief 1, Gaithersburg, MD.

5. Bagheri, B., Firoozabad, E.S., and Yahyaei, M. (2012). Comparative Study of the Static

and Dynamic Analysis of Multi-Storey Irregular Building, International Journal of Civil,

Environmental, Structural, Construction and Architectural Engineering Vol: 6, No: 11,

2012

6. ASCE (2010). Minimum design loads for buildings and other structures (ASCE 7-10),

American Society of Civil Engineers, Reston, VA.

7. ACI (2011). Building code requirements for structural concrete (ACI 318-11) and

commentary, American Concrete Institute, Farmington Hills, MI.

8. Moehle, J.P. (2014). Seismic Design of Reinforced Concrete Buildings, University of

California Berkeley, CA.

ACKNOWLEDGMENTS

The authors would like to express their very great appreciation to the following people:

1) Professor Jack P. Moehle, for allowing them to be a part of this project and providing

insight and expertise that greatly assisted the project and this paper.

2) Professor Stephen A. Mahin for expanding their knowledge of Earthquake Engineering.

http://www.norsar.no/norsar/about-us/News/2011/Historical-Development-of-Earthquake-Resistant-Design

http://www.norsar.no/norsar/about-us/News/2011/Historical-Development-of-Earthquake-Resistant-Design

http://www.cement.org/think-harder-concrete-/buildings-structures/design-aids/seismic-design

http://www.cement.org/think-harder-concrete-/buildings-structures/design-aids/seismic-design

Linear Dynamic Analysis and

Seismic Evaluation of a Full Scale

RC Model

Beam Moment and Shear Calculations

G1-1st Floor

Appendix

AD, AS, QW

MOMENT AND SHEAR CALCULATIOINSBeam Design: G1

350 x 550

f'c = 42 MPa

(4) 22 mm bars at the bottom

(5) 22 mm bars at the top

Length, L (mm) 3450 Length, L (mm) 4000

Width, b (mm) 350 Width, b (mm) 350

Depth, d (mm) 550 Depth, d (mm) 550

fyt (Mpa) 295 fyt (Mpa) 295

fy (MPa) 345 fy (MPa) 345

ᶲ factor, M 0.9 ᶲ factor, M 0.9

Rebar dia, mm 22 Rebar dia, mm 22

# of top bars 5 # of top bars 4

# of bottom bars 4 # of bottom bars 5

As 1520.530844 As 1900.663555

A's 1900.663555 A's 1520.530844

Top Cover (mm) 61 Top Cover (mm) 61

Bottom Cover (mm) 61 Bottom Cover (mm) 61

f'c (MPa) 42 f'c (MPa) 42

f'c (ksi) 6.091596 f'c (ksi) 6.091596

β 0.7454202 β 0.7454202

A 9314.025399 A 9314.025399

B 615814.992 B 256589.58

C -69564286.13 C -55651428.9

c (N.A. depth), mm 59.47059922 c (N.A. depth), mm 64.74153606

εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 246.0325431 Mn (kN-m) 302.8848554

εs 0.021667651 εs 0.019659333

ɸMn (kN-m) 221 kN-m ɸMn (kN-m) 273 kN-m

Mu+ (kN-m) 290 kN-m Mu- (kN-m) 304 kN-m

Mu< ɸMn NOT OK Mu< ɸMn NOT OK

D/C 1.31 D/C 1.12

FLEXURE (positive) FLEXURE (negative)



RC Model


G1-1st Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN

Metric System US Units

Width, b 350 mm 13.779535 in

Depth, h 550 mm 21.653555 in Calculating w

cover 61 mm 2.4015761 in slab depth 120 mm

fyt 295 MPa 42.7861215 ksi trib width 1.55 m

fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 42 MPa 6.0915834 ksi

ds 489 mm 19.2519789 in

stirrup dia 10 mm 0.393701 in

number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 100 mm 3.93701 in

Vc 207.2 kN 46.58 K

Vs 254.9 kN 57.30 K

Vn 462.0 kN 103.87 K

ɸVn 346.5 kN 77.90 K

Demands

Mpr1 307.5407 kN-m

Mpr2 378.6061 kN-m

Vu, gravity 8.02125 kN

Vu, lateral 219 KN

Vu, total 228 kN

Vu < ɸVn OK

D/C 0.66

SHEAR



RC Model


G2-2nd Floor

Appendix

AD, AS, QW


350 x 550

f'c = 42 MPa






fyt (Mpa) 295 fyt (Mpa) 295






As 1900.663555 As 1900.663555

A's 1900.663555 A's 1900.663555




f'c (ksi) 6.091596 f'c (ksi) 6.091596

β 0.7454202 β 0.7454202

A 9314.025399 A 9314.025399

B 484669.2066 B 484669.2066

C -69564286.13 C -69564286.13


εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 302.8239031 Mn (kN-m) 302.8239031

εs 0.019837883 εs 0.019837883



Mu< ɸMn OK Mu< ɸMn NOT OK

D/C 0.99 D/C 1.04




RC Model


G2-2nd Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN


Width, b 350 mm 13.779535 in




fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 42 MPa 6.0915834 ksi

ds 489 mm 19.2519789 in


number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 100 mm 3.93701 in

Vc 207.2 kN 46.58 K

Vs 254.9 kN 57.30 K

Vn 462.0 kN 103.87 K

ɸVn 346.5 kN 77.90 K

Demands

Mpr1 378.5299 kN-m

Mpr2 378.5299 kN-m


Vu, lateral 219 KN

Vu, total 227 kN

Vu < ɸVn OK

D/C 0.66

SHEAR



RC Model


G1-3rd Floor

Appendix

AD, AS, QW


350 x 550

f'c = 33 MPa











As 1520.530844 As 1900.663555

A's 1900.663555 A's 1520.530844




f'c (ksi) 6.091596 f'c (ksi) 6.091596

β 0.7454202 β 0.7454202

A 9314.025399 A 9314.025399

B 615814.992 B 256589.58

C -69564286.13 C -55651428.9


εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 246.0325431 Mn (kN-m) 302.8848554

εs 0.021667651 εs 0.019659333




D/C 1.31 D/C 1.12




RC Model


G1-3rd Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN


Width, b 350 mm 13.779535 in




fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 33 MPa 4.7862441 ksi

ds 489 mm 19.2519789 in


number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 100 mm 3.93701 in

Vc 183.6 kN 41.28 K

Vs 254.9 kN 57.30 K

Vn 438.5 kN 98.58 K

ɸVn 328.9 kN 73.93 K

Demands

Mpr1 307.5407 kN-m

Mpr2 378.6061 kN-m


Vu, lateral 219 KN

Vu, total 228 kN

Vu < ɸVn OK

D/C 0.69

SHEAR



RC Model


G2-3rd Floor

Appendix

AD, AS, QW


350 x 550

f'c = 33 MPa











As 1900.663555 As 1900.663555

A's 1900.663555 A's 1900.663555




f'c (ksi) 6.091596 f'c (ksi) 6.091596

β 0.7454202 β 0.7454202

A 9314.025399 A 9314.025399

B 484669.2066 B 484669.2066

C -69564286.13 C -69564286.13


εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 302.8239031 Mn (kN-m) 302.8239031

εs 0.019837883 εs 0.019837883




D/C 1.02 D/C 1.07




RC Model


G2-3rd Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN


Width, b 350 mm 13.779535 in




fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 33 MPa 4.7862441 ksi

ds 489 mm 19.2519789 in


number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 100 mm 3.93701 in

Vc 183.6 kN 41.28 K

Vs 254.9 kN 57.30 K

Vn 438.5 kN 98.58 K

ɸVn 328.9 kN 73.93 K

Demands

Mpr1 378.5299 kN-m

Mpr2 378.5299 kN-m


Vu, lateral 219 KN

Vu, total 227 kN

Vu < ɸVn OK

D/C 0.69

SHEAR



RC Model


G1-5th Floor

Appendix

AD, AS, QW


350 x 550

f'c = 27 MPa











As 1520.530844 As 1900.663555

A's 1520.530844 A's 1520.530844




f'c (ksi) 3.916026 f'c (ksi) 3.916026

β 0.8541987 β 0.8541987

A 6861.351058 A 6861.351058

B 387735.3653 B 256589.58

C -55651428.9 C -55651428.9


εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 239.3844027 Mn (kN-m) 295.5861914

εs 0.01918239 εs 0.017018374



Mu- (kN-m) 286 kN-m

Mu< ɸMn NOT OK

D/C 1.24

D/C 1.33




RC Model


G1-5th Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN


Width, b 350 mm 13.779535 in




fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 27 MPa 3.9160179 ksi

ds 489 mm 19.2519789 in


number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 125 mm 4.9212625 in

Vc 166.1 kN 37.34 K

Vs 203.9 kN 45.84 K

Vn 370.0 kN 83.18 K

ɸVn 277.5 kN 62.38 K

Demands

Mpr1 299.2305 kN-m

Mpr2 369.4827 kN-m


Vu, lateral 211 KN

Vu, total 219 kN

Vu < ɸVn OK

D/C 0.79

SHEAR



RC Model


G2-5th Floor

Appendix

AD, AS, QW


350 x 550

f'c = 27 MPa











As 1520.530844 As 1900.663555

A's 1900.663555 A's 1520.530844




f'c (ksi) 3.916026 f'c (ksi) 3.916026

β 0.8541987 β 0.8541987

A 6861.351058 A 6861.351058

B 615814.992 B 256589.58

C -69564286.13 C -55651428.9


εc 0.003 εc 0.003

Es (MPa) 200000 Es (MPa) 200000

ds 489 ds 489

Mn (kN-m) 239.3587984 Mn (kN-m) 295.5861914

εs 0.019444146 εs 0.017018374




D/C 1.21 D/C 1.03




RC Model


G2-5th Floor

Appendix

AD, AS, QW

Conversions

1 mm 0.0393701 in

1 mm2 0.00155 in2

1 MPa 0.1450377 ksi

1 K 4.4482 kN


Width, b 350 mm 13.779535 in




fy 345 MPa 50.0380065 ksi SW 3 kN/m2

ᶲ 0.75 w 4.65 kN/m

f'c 27 MPa 3.9160179 ksi

ds 489 mm 19.2519789 in


number of legs 2

Av 157.0796 mm2 0.24347343 in2

s 100 mm 3.93701 in

Vc 166.1 kN 37.34 K

Vs 254.9 kN 57.30 K

Vn 421.0 kN 94.64 K

ɸVn 315.7 kN 70.98 K

Demands

Mpr1 299.1985 kN-m

Mpr2 369.4827 kN-m


Vu, lateral 211 KN

Vu, total 219 kN

Vu < ɸVn OK

D/C 0.69

SHEAR



RC Model

Exterior Joint Appendix

AD, AS, QW

Demand

Lc 3450 mm Lc 3450 mm 1 mm 0.0393701 in

Mpr+ 307.5406789 kN-m Mpr+ 378.5299 kN-m 1 K 4.4482 kN

Mpr- 378.6060693 kN-m Mpr- 378.5299 kN-m

h 550 mm h 550 mm

cover 61 mm cover 61 mm

d 489 mm d 489 mm

de 440.1 mm de 440.1 mm

h1 2800 mm

h2 2600 mm

dc 550 mm 21.65356

bc 550 mm 21.65356

Vcol 296.7069472 kN Vcol 323.0275 kN

Vjoint 1262.190026 kN Vjoint 1397.345 kN

Vjoint 1397 kN

Capacity

f'c (MPa) 42 Mpa

f'c (ksi) 6.091596 ksi

ϒ 15

Vn 549 K 2441.752 kN

ΦVn 2075 kN

Vjoint < Vn OK

D/C 0.67

ConversionsG1 G2

Column (C2)

JOINT SHEAR



RC Model

Interior Joint Appendix

AD, AS, QW

Demand

Lc 3450 mm

Mpr+ 307.5406789 kN-m 1 mm 0.0393701 in

Mpr- 378.6060693 kN-m 1 K 4.4482 kN

h 550 mm

cover 61 mm

d 489 mm

de 440.1 mm

h1 2800 mm

h2 2600 mm

dc 550 mm 21.65356 in

bc 550 mm 21.65356 in

Gravity Loading

Calculating w

slab depth 120 mm

trib width 1.55 m

SW 3 kN/m2

w 4.65 kN/m

Vcol 161.2980629 kN Vcol 133.3435896 kN

Vjoint 698.9747599 kN Vjoint 565.4536813 kN

Vjoint 699 kN

Capacity

f'c (MPa) 42 Mpa

f'c (ksi) 6.091596 ksi

ϒ 12

Vn 439 K 1953.402 kN

ΦVn 1660 kN

Vjoint < Vn OK

D/C 0.42

JOINT SHEAR

G1

Column (C1)

Conversions



RC Model

Column (C1) PM Interaction Diagram APPENDIX

AD, AS, QW

Demands for Envelope Case

P M3 0 6838.39 0 10520.61

KN KN-m 250.7993 6838.39 385.8451 10520.61

-1739.93 425.8359 420.4033 6474.33 646.7743 9960.51

-1729.13 176.5983 543.8825 5466.9 836.7424 8410.61

-1718.33 71.193 628.5217 4341.2 966.9564 6678.78

686.432 3031.961 1056.049 4664.56

746.52 2463.428 1008.548 3328.09

793.4803 1749.4 891.0365 1964.483

623.4142 514.8855 692.6824 572.095

329.6961 -960.9879 366.329 -1067.764

0 -2360.63 0 -2622.922

P-M3 interactionφP-φM3 interaction

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 200 400 600 800 1000 1200

Axi

al F

orc

e, P

(kN

)

Moment, M (kN-m)


Pu,Mu

ΦMn, ΦPn

Pn,Mn



RC Model

Column (C1) Shear Appendix

AD, AS, QW

Section Properties in metric system Conversions

b 550 mm 1 mm 0.0393701 in

h 550 mm 1 mm2 0.00155 in2

d 440 mm 1 MPa 0.1450377 ksi

Ag 302500 mm2 1 K 4.4482 kN

f'c 42 MPa

fy 345 MPa

fyt 295 MPa

bar 10 mm

Av/leg 78.53981634 mm2

# of legs 4

s 100 mm

Vu ≤ ΦVn

Vn = Vc + Vs

Φ 0.75

Vc = 2(1 + Nu/(2000 Ag)) λ √(f'c) bd

Nu = Pu -800.5 kN -179959.6 lbs

λ 1

Ag 468.875 in2

f'c 6.091583 ksi 6091.5834 psi

b 21.65356 in

d = 0.8 b 17.32284 in

Vc 47315.73 lbs 47.32 kips 210.47 kN

Vs = Av fyt d / s

Av/leg 0.12 in2

# of legs 4

fyt 42.78612 ksi

d 17.32284 in

s 3.93701 in

Vs 91.6721 K 407.7778 kN

Vn 138.99 K 618 kN

φVn 104.2409 K 464 kN

φo 1.25

Vu,SAP 243.75 kN

Vu, Joint Shear 161.3 Kn

D/C 0.53 OK



RC Model

Column (C2) PM Interaction Diagram APPENDIX

AD, AS, QW

P M3

KN KN-m 0 6593.84 0 10144.36

-2029.32 459.1085 239.3368 6593.84 368.2105 10144.36

-2018.52 160.3768 404.0899 6264.63 621.6768 9637.9

-2007.72 140.6808 520.5027 5292.16 800.7734 8141.78

596.8154 4237.53 918.1775 6519.27

640.0707 3025.278 984.7242 4654.27

691.4461 2491.357 934.1434 3365.82

732.7736 1887.716 822.8661 2119.805

570.309 732.214 633.6767 813.5711

304.8556 -605.648 338.7285 -672.943

0 -1888.5 0 -2098.34

φP-φM3 interaction P-M3 interaction

-4000

-2000

0

2000

4000

6000

8000

10000

12000

0 200 400 600 800 1000 1200

Axi

al F

orc

e, P

(kN

)

Moment, M (kN-m)


ΦMn, ΦPn

Mn,Pn

Mu,Pu



RC Model

Column (C2) Shear APPENDIX

AD, AS, QW

Section Properties in metric system Conversions

b 550 mm 1 mm 0.0393701 in

h 550 mm 1 mm2 0.00155 in2

d 440 mm 1 MPa 0.1450377 ksi

Ag 302500 mm2 1 K 4.4482 kN

f'c 42 MPa

fy 345 MPa

fyt 295 MPa

bar 10 mm

Av/leg 78.53981634 mm2

# of legs 4

s 100 mm

Vu ≤ ΦVn

Vn = Vc + Vs

Φ 0.75

Vc = 2(1 + Nu/(2000 Ag)) λ √(f'c) bd

Nu = Pu -801.5 kN -180184.4 lbs

λ 1

Ag 468.875 in2

f'c 6.091583 ksi 6091.583 psi

b 21.65356 in

d = 0.8 b 17.32284 in

Vc 47301.69 lbs 47.30 kips 210.41 kN

Vs = Av fyt d / s

Av/leg 0.12 in2

# of legs 4

fyt 42.78612 ksi

d 17.32284 in

s 3.93701 in

Vs 91.6721 K 407.7778

Vn 138.97 K 618.1862 kN

φVn 104.2303 K 463.6397 kN

φo 1.25

Vu, SAP 243.75 kN

Vu, Joint Shear 323 kN

D/C 0.70 OK



RC Model

APPENDIX

AD, AS, QW

Wall (BC) Axial (N)

Moment1

(NS) -

about xx

(N-m)

Moment2

(EW) -

about yy

(N-m)

Moment2

(45 deg)

(N-m)

971795.3 827988.1

Mn Pn φMn φPn Axial Strain Mn Pn φMn φPn Mu Pu

N-m N N-m N N-m N N-m N N-m N

1.08E-10 1.90E+07 7.52E-11 1.07E+07 -2.00E-03 1.08E-10 1.90E+07 7.52E-11 1.07E+07 827988.1 971795.3

867.7 1.90E+07 607.4 1.07E+07 -1.94E-03 8.68E+02 1.90E+07 6.07E+02 1.07E+07

8593 1.88E+07 6015 1.07E+07 -1.88E-03 8.59E+03 1.88E+07 6.02E+03 1.07E+07

2.70E+04 1.85E+07 1.89E+04 1.07E+07 -1.82E-03 2.70E+04 1.85E+07 1.89E+04 1.07E+07

5.32E+04 1.80E+07 3.73E+04 1.07E+07 -1.76E-03 5.32E+04 1.80E+07 3.73E+04 1.07E+07

8.62E+04 1.75E+07 6.03E+04 1.07E+07 -1.70E-03 8.62E+04 1.75E+07 6.03E+04 1.07E+07

1.25E+05 1.69E+07 8.75E+04 1.07E+07 -1.64E-03 1.25E+05 1.69E+07 8.75E+04 1.07E+07

1.69E+05 1.62E+07 1.18E+05 1.07E+07 -1.58E-03 1.69E+05 1.62E+07 1.18E+05 1.07E+07

2.16E+05 1.55E+07 1.51E+05 1.07E+07 -1.52E-03 2.16E+05 1.55E+07 1.51E+05 1.07E+07

2.66E+05 1.47E+07 1.86E+05 1.03E+07 -1.46E-03 2.66E+05 1.47E+07 1.86E+05 1.03E+07

3.18E+05 1.38E+07 2.22E+05 9.67E+06 -1.40E-03 3.18E+05 1.38E+07 2.22E+05 9.67E+06

3.70E+05 1.30E+07 2.59E+05 9.07E+06 -1.34E-03 3.70E+05 1.30E+07 2.59E+05 9.07E+06

4.06E+05 1.23E+07 2.84E+05 8.58E+06 -1.28E-03 4.06E+05 1.23E+07 2.84E+05 8.58E+06

4.29E+05 1.17E+07 3.00E+05 8.18E+06 -1.22E-03 4.29E+05 1.17E+07 3.00E+05 8.18E+06

4.43E+05 1.12E+07 3.10E+05 7.85E+06 -1.16E-03 4.43E+05 1.12E+07 3.10E+05 7.85E+06

4.55E+05 1.08E+07 3.19E+05 7.53E+06 -1.10E-03 4.55E+05 1.08E+07 3.19E+05 7.53E+06

4.68E+05 1.03E+07 3.28E+05 7.20E+06 -1.04E-03 4.68E+05 1.03E+07 3.28E+05 7.20E+06

4.80E+05 9.91E+06 3.36E+05 6.93E+06 -9.80E-04 4.80E+05 9.91E+06 3.36E+05 6.93E+06

4.88E+05 9.60E+06 3.42E+05 6.72E+06 -9.20E-04 4.88E+05 9.60E+06 3.42E+05 6.72E+06

4.95E+05 9.30E+06 3.47E+05 6.51E+06 -8.60E-04 4.95E+05 9.30E+06 3.47E+05 6.51E+06

5.01E+05 9.02E+06 3.51E+05 6.31E+06 -8.00E-04 5.01E+05 9.02E+06 3.51E+05 6.31E+06

5.06E+05 8.77E+06 3.54E+05 6.14E+06 -7.40E-04 5.06E+05 8.77E+06 3.54E+05 6.14E+06

5.10E+05 8.52E+06 3.57E+05 5.97E+06 -6.80E-04 5.10E+05 8.52E+06 3.57E+05 5.97E+06

5.14E+05 8.27E+06 3.60E+05 5.79E+06 -6.20E-04 5.14E+05 8.27E+06 3.60E+05 5.79E+06

5.17E+05 8.05E+06 3.62E+05 5.63E+06 -5.60E-04 5.17E+05 8.05E+06 3.62E+05 5.63E+06

5.19E+05 7.85E+06 3.64E+05 5.49E+06 -5.00E-04 5.19E+05 7.85E+06 3.64E+05 5.49E+06

5.21E+05 7.68E+06 3.64E+05 5.38E+06 -4.40E-04 5.21E+05 7.68E+06 3.64E+05 5.38E+06

5.21E+05 7.54E+06 3.65E+05 5.28E+06 -3.80E-04 5.21E+05 7.54E+06 3.65E+05 5.28E+06

5.22E+05 7.40E+06 3.65E+05 5.18E+06 -3.20E-04 5.22E+05 7.40E+06 3.65E+05 5.18E+06

5.22E+05 7.25E+06 3.66E+05 5.07E+06 -2.60E-04 5.22E+05 7.25E+06 3.66E+05 5.07E+06

5.23E+05 7.10E+06 3.66E+05 4.97E+06 -2.00E-04 5.23E+05 7.10E+06 3.66E+05 4.97E+06

5.22E+05 6.93E+06 3.66E+05 4.85E+06 -1.40E-04 5.22E+05 6.93E+06 3.66E+05 4.85E+06

5.21E+05 6.77E+06 3.65E+05 4.74E+06 -8.00E-05 5.21E+05 6.77E+06 3.65E+05 4.74E+06

5.20E+05 6.60E+06 3.64E+05 4.62E+06 -2.00E-05 5.20E+05 6.60E+06 3.64E+05 4.62E+06

5.19E+05 6.44E+06 3.63E+05 4.51E+06 4.00E-05 5.19E+05 6.44E+06 3.63E+05 4.51E+06

5.16E+05 6.30E+06 3.61E+05 4.41E+06 1.00E-04 5.16E+05 6.30E+06 3.61E+05 4.41E+06

5.12E+05 6.17E+06 3.58E+05 4.32E+06 1.60E-04 5.12E+05 6.17E+06 3.58E+05 4.32E+06

5.08E+05 6.04E+06 3.56E+05 4.23E+06 2.20E-04 5.08E+05 6.04E+06 3.56E+05 4.23E+06

5.04E+05 5.90E+06 3.53E+05 4.13E+06 2.80E-04 5.04E+05 5.90E+06 3.53E+05 4.13E+06

5.00E+05 5.77E+06 3.50E+05 4.04E+06 3.40E-04 5.00E+05 5.77E+06 3.50E+05 4.04E+06

4.96E+05 5.63E+06 3.47E+05 3.94E+06 4.00E-04 4.96E+05 5.63E+06 3.47E+05 3.94E+06

4.92E+05 5.49E+06 3.44E+05 3.85E+06 4.60E-04 4.92E+05 5.49E+06 3.44E+05 3.85E+06

4.88E+05 5.36E+06 3.41E+05 3.75E+06 5.20E-04 4.88E+05 5.36E+06 3.41E+05 3.75E+06

4.83E+05 5.21E+06 3.38E+05 3.65E+06 5.80E-04 4.83E+05 5.21E+06 3.38E+05 3.65E+06

4.79E+05 5.07E+06 3.35E+05 3.55E+06 6.40E-04 4.79E+05 5.07E+06 3.35E+05 3.55E+06

4.74E+05 4.93E+06 3.32E+05 3.45E+06 7.00E-04 4.74E+05 4.93E+06 3.32E+05 3.45E+06

4.71E+05 4.83E+06 3.29E+05 3.38E+06 7.60E-04 4.71E+05 4.83E+06 3.29E+05 3.38E+06

4.67E+05 4.73E+06 3.27E+05 3.31E+06 8.20E-04 4.67E+05 4.73E+06 3.27E+05 3.31E+06

4.63E+05 4.62E+06 3.24E+05 3.24E+06 8.80E-04 4.63E+05 4.62E+06 3.24E+05 3.24E+06

4.59E+05 4.52E+06 3.22E+05 3.17E+06 9.40E-04 4.59E+05 4.52E+06 3.22E+05 3.17E+06

4.56E+05 4.43E+06 3.19E+05 3.10E+06 1.00E-03 4.56E+05 4.43E+06 3.19E+05 3.10E+06

4.53E+05 4.37E+06 3.17E+05 3.06E+06 1.06E-03 4.53E+05 4.37E+06 3.17E+05 3.06E+06

4.50E+05 4.30E+06 3.15E+05 3.01E+06 1.12E-03 4.50E+05 4.30E+06 3.15E+05 3.01E+06

4.47E+05 4.23E+06 3.13E+05 2.96E+06 1.18E-03 4.47E+05 4.23E+06 3.13E+05 2.96E+06

4.44E+05 4.16E+06 3.11E+05 2.91E+06 1.24E-03 4.44E+05 4.16E+06 3.11E+05 2.91E+06

4.39E+05 4.04E+06 3.08E+05 2.82E+06 1.30E-03 4.39E+05 4.04E+06 3.08E+05 2.82E+06

4.32E+05 3.84E+06 3.03E+05 2.69E+06 1.36E-03 4.32E+05 3.84E+06 3.03E+05 2.69E+06

4.24E+05 3.64E+06 2.97E+05 2.55E+06 1.42E-03 4.24E+05 3.64E+06 2.97E+05 2.55E+06

4.14E+05 3.41E+06 2.90E+05 2.38E+06 1.48E-03 4.14E+05 3.41E+06 2.90E+05 2.38E+06

4.05E+05 3.22E+06 2.83E+05 2.25E+06 1.54E-03 4.05E+05 3.22E+06 2.83E+05 2.25E+06

3.93E+05 3.00E+06 2.75E+05 2.10E+06 1.60E-03 3.93E+05 3.00E+06 2.75E+05 2.10E+06

3.77E+05 2.75E+06 2.64E+05 1.93E+06 1.66E-03 3.77E+05 2.75E+06 2.64E+05 1.93E+06

3.57E+05 2.45E+06 2.50E+05 1.72E+06 1.72E-03 3.57E+05 2.45E+06 2.50E+05 1.72E+06

3.35E+05 2.17E+06 2.35E+05 1.52E+06 1.78E-03 3.35E+05 2.17E+06 2.35E+05 1.52E+06

3.11E+05 1.88E+06 2.19E+05 1.32E+06 1.84E-03 3.11E+05 1.88E+06 2.19E+05 1.32E+06

2.83E+05 1.54E+06 2.09E+05 1.14E+06 1.90E-03 2.83E+05 1.54E+06 2.09E+05 1.14E+06

2.53E+05 1.17E+06 1.96E+05 9.10E+05 1.96E-03 2.53E+05 1.17E+06 1.96E+05 9.10E+05

2.19E+05 7.75E+05 1.79E+05 6.34E+05 2.02E-03 2.19E+05 7.75E+05 1.79E+05 6.34E+05

1.84E+05 3.56E+05 1.59E+05 3.07E+05 2.08E-03 1.84E+05 3.56E+05 1.59E+05 3.07E+05

1.47E+05 -7.62E+04 1.32E+05 -6.86E+04 2.14E-03 1.47E+05 -7.62E+04 1.32E+05 -6.86E+04

1.14E+05 -4.57E+05 1.03E+05 -4.11E+05 2.20E-03 1.14E+05 -4.57E+05 1.03E+05 -4.11E+05

8.42E+04 -7.94E+05 7.58E+04 -7.14E+05 2.26E-03 8.42E+04 -7.94E+05 7.58E+04 -7.14E+05

5.67E+04 -1.10E+06 5.10E+04 -9.94E+05 2.32E-03 5.67E+04 -1.10E+06 5.10E+04 -9.94E+05

3.33E+04 -1.37E+06 3.00E+04 -1.23E+06 2.38E-03 3.33E+04 -1.37E+06 3.00E+04 -1.23E+06

2.05E+04 -1.52E+06 1.85E+04 -1.37E+06 2.44E-03 2.05E+04 -1.52E+06 1.85E+04 -1.37E+06

1.70E+04 -1.58E+06 1.53E+04 -1.42E+06 2.50E-03 1.70E+04 -1.58E+06 1.53E+04 -1.42E+06

1.35E+04 -1.64E+06 1.22E+04 -1.48E+06 2.56E-03 1.35E+04 -1.64E+06 1.22E+04 -1.48E+06

1.00E+04 -1.70E+06 9006 -1.53E+06 2.62E-03 1.00E+04 -1.70E+06 9.01E+03 -1.53E+06

6503 -1.77E+06 5852 -1.59E+06 2.68E-03 6.50E+03 -1.77E+06 5.85E+03 -1.59E+06

2998 -1.83E+06 2698 -1.64E+06 2.74E-03 3.00E+03 -1.83E+06 2.70E+03 -1.64E+06

739.8 -1.87E+06 665.9 -1.68E+06 2.80E-03 7.40E+02 -1.87E+06 6.66E+02 -1.68E+06

34.46 -1.88E+06 31.02 -1.69E+06 2.86E-03 3.45E+01 -1.88E+06 3.10E+01 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 2.92E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 2.98E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.04E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.10E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.16E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.22E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.28E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.34E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.40E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.46E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.52E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.58E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.64E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.70E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.76E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.82E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.88E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.94E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 4.00E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.94E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.88E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.82E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.76E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.70E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.64E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.58E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.52E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.46E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.40E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.34E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.28E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.22E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.16E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.10E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 3.04E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 2.98E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

2.36E-12 -1.88E+06 2.13E-12 -1.69E+06 2.92E-03 2.36E-12 -1.88E+06 2.13E-12 -1.69E+06

-34.46 -1.88E+06 -31.02 -1.69E+06 2.86E-03

OBTAINED FROM XTRACT

-5.00E+06

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

-6.00E+05 -4.00E+05 -2.00E+05 0.00E+00 2.00E+05 4.00E+05 6.00E+05


-5.00E+06

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

- 1 . 0 0 E + 0 5 0 . 0 0 E + 0 0 1 . 0 0 E + 0 5 2 . 0 0 E + 0 5 3 . 0 0 E + 0 5 4 . 0 0 E + 0 5 5 . 0 0 E + 0 5 6 . 0 0 E + 0 5 7 . 0 0 E + 0 5 8 . 0 0 E + 0 5 9 . 0 0 E + 0 5

AX

IAL

FOR

CE,

P (

N)

MOMENT, M (N-M)


Mn, Pn

ΦPn, ΦMn

Mu, Pu



RC Model

Wall Shear APPENDIX

AD, AS, QW

hw 19950 mm Conversions

lw 1800 mm 1 mm 0.0393701 in

bw 230 mm 1 mm2 0.00155 in2

f'c 42 MPa 6.091583 ksi 1 MPa 0.1450377 ksi

fyt 295 MPa 42.78612 ksi 1 K 4.4482 kN

hw/lw 11.08333 Slender

ρl 0.004617

ρt 0.00455

Acw 414000 mm2 641.7 in2

α 2

φ 0.75

Vn,max 400.6703 K 1782.27 kN

Vn 225.0917 K 1001.258 kN

φVn 168.8188 K 750.9433 kN

φo 1.25

Vu,SAP 675 kN

Vu/φVn 0.90 OK

Documents

Linear Dynamic Analysis and Seismic Evaluation of RC Building