Report POA and IDA_final

EAS 664: PRINCIPAL OF STRUCTURAL DESIGN ASSIGNMENT (DR. FADZLI)

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1.0 Introduction

i. Static Analysis

SAP2000 can perform both linear static and multi-step static analysis. The

linear static analysis of a structure involves the solution of the system of

linear equations represented by K u = r. Various types of load patterns

are multi-stepped, which mean that they actually represent many

separate spatial loading patterns applied in sequence. These include the

vehicle, live, and wave types of load patterns.

ii. Dynamic Static Analysis

SAP2000 dynamic analysis capabilities include the calculation of vibration

modes using Ritz or Eigen vectors, response-spectrum analysis, and time-

history analysis for both linear and nonlinear behavior.

2.0 Pushover analysis

Pushover analysis features in SAP2000 include the implementation of FEMA

356 and the hinge and fiber hinge option based on stress-strain. The

nonlinear layered shell element enables users to consider plastic behavior of

concrete shear walls, slabs, steel plates, and other area finite elements in the

pushover analysis. Force-Deformation relations are defined for steel and

concrete hinges.

3.0 Time-history analysis

Time-history analysis captures the step-by-step response of structures to

seismic ground motion and other types of loading such as blast, machinery,

wind, waves, etc. Analysis can use modal superposition or direct-integration

methods, and both can be linear or nonlinear. The nonlinear modal method,

also called FNA for Fast Nonlinear Analysis, is extremely efficient and

accurate for a wide class of problems. The direct-integration method is even

more general, and can handle large deformations and other highly nonlinear

behavior. Nonlinear time-history analyses can be chained together with other


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nonlinear cases (including staged construction) addressing a wide range of

applications.

Incremental Dynamic Analysis (IDA) is a computational analysis method

of Seismic Engineering to perform a comprehensive assessment of the

behavior of structures under seismic loads. IDA involves performing

multiple non-linear analysis of a structural model under a suite of ground

motion record, each scaled to several levels of seismic intensity.

4.0 Design

i. Steel Frame

Fully integrated steel frame design includes member size optimization

and implementation of design codes. SAP2000 allows users to

interactively view design results at any frame member, change the

parameters or section properties, and display the updated member

results.

ii. Concrete Frame

Fully integrated concrete frame design in SAP2000 includes: required

area of steel calculations, auto selection lists for new member sizing,

implementation of design codes, interactive design and review, and

comprehensive overwrite capabilities.

5.0 Modelling

Studied Models:

There are two models, model A and model B, derived in this report intended to

compare one model to another. These model have same plan view and frame size,

but model A is a concrete frame structure and model B is a steel frame structure.

Modelling Steps and Assumptions:

The modelling is done by SAP2000. The step in modelling the structures is proceed in

the following steps :


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1. The unit is changed into the same unit which is used in the building model,

kN,m,C.

2. New model 2D frames is chosen.

3. The number of stories is 3, number of bays in x direction is 3. Story height is 3.3

m, and bay width is 6 m.

4. The material that is used for model A is G30 concrete with concrete cover of

0.025m, weight per unit volume of 25 Kn/m3, fc = 30000kN/m2 and E = 30000000

kN/m2.

5. The material for model B are S275 steel, fy = 275000 kN/m2 and E = 21000000

kN/m2.

6. Beam and column dimensions are 300 x 700 mm (beam) and 500 x 500 mm

(column). The number of bars along x and y direction is 6, bar size is N32. The

confine bar is N12, the spacing is 15 cm, and number of bars x and y direction is

3. All the properties is used G40 concrete.

7. The support is fixed.

8. Hinge properties were defined, deformation controlled, set M3 for beam, and set

interaction P-M3 for column.

9. For POA analysis :

a. The loading from the third, second, and first story are 239.04 kN, 159.36

kN, 79.68 kN for triangular loading, and 239.04 kN for each floor for

rectangular loading.

b. Hinge for the beam and column were set for 0 and 1.

c. Three different diaphragm constrain were defined and assigned to each

story level.

d. Three load pattern were defined, dead load, live load and lateral

pushover. Load case type was static and analysis type was nonlinear.


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e. For load application, displacement control was used with 2m monitored

displacement, and results were saved in multiple states with minimum 10

steps and maximum 100 steps.

f. Distributed load for dead load, 23.4 kN/m and live load 7.5 kN/m were

assigned on the beam.

g. Run the analysis.

10. For IDA analysis :

a. Hinge for the beam and column is 1.

b. Time history were define for 3 tipes of ground motion NGA0477,

NGA0545, and NGA2399 taken from

http://peer.berkeley.edu/nga/search.html

c. Non-linear analysis and direct integration time history is defined in the

load case.

d. Scale factor is define by increasing the ag from 0.05g until 0.50g.

e. Time integration newmark is used.

f. Run the analysis


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The following figures show the models as appeared in SAP2000.

Figure 5.1 : Model of Frame

6.0 POA Analysis Results:

Graph 6.1: Pushover Analysis (Concrete Frame, 3 Stories)


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Graph 6.2: Pushover Analysis (Steel Frame, 3 Stories)


Result of Push Over Analysis (Uniform Load)

CONCRETE FRAME

Step Displacement BaseForce AtoB BtoIO IOtoLS LStoCP CPtoC CtoD DtoE BeyondE Total

m KN

0 2.29E-17 0 28 14 0 0 0 0 0 0 42

1 0.000956 28.058 27 15 0 0 0 0 0 0 42

2 0.026869 631.913 25 11 6 0 0 0 0 0 42

3 0.032322 713.82 25 11 6 0 0 0 0 0 42

4 0.058459 933.058 24 3 15 0 0 0 0 0 42

5 0.130036 1213.451 21 3 6 7 0 5 0 0 42

6 0.131796 1216.262 20 4 6 5 0 7 0 0 42

7 0.139593 1216.423 20 4 6 3 0 9 0 0 42

8 0.154081 1213.832 20 4 0 6 0 12 0 0 42

9 0.178775 1201.284 20 0 4 0 0 18 0 0 42

STEEL FRAME


m KN

0 6.07E-17 0 42 0 0 0 0 0 0 0 42

1 0.062319 1697.003 41 1 0 0 0 0 0 0 42

2 0.076634 1985.06 36 6 0 0 0 0 0 0 42

3 0.077622 1997.242 35 6 1 0 0 0 0 0 42

4 0.118632 2272.859 30 8 4 0 0 0 0 0 42

5 0.123683 2288.092 25 13 4 0 0 0 0 0 42


6 0.212985 2414.455 23 11 4 0 4 0 0 0 42

7 0.223493 2423.319 22 12 4 0 4 0 0 0 42

8 0.423493 2426.468 22 12 2 0 6 0 0 0 42

9 0.623493 2429.617 22 12 2 0 6 0 0 0 42

10 0.823493 2432.716 22 11 3 0 6 0 0 0 42

11 1.023493 2435.815 22 11 3 0 6 0 0 0 42

12 1.223493 2438.915 22 11 3 0 6 0 0 0 42

13 1.423493 2442.014 22 11 3 0 6 0 0 0 42

14 1.623493 2445.114 22 11 3 0 6 0 0 0 42

15 1.823493 2448.214 22 11 3 0 6 0 0 0 42

16 2 2450.917 22 11 3 0 6 0 0 0 42

Result of Push Over Analysis (Triangular Load)

CONCRETE FRAME


m KN

0 2.40E-17 0 28 14 0 0 0 0 0 0 42

1 0.001026 24.809 27 15 0 0 0 0 0 0 42

2 0.028578 554.091 25 11 6 0 0 0 0 0 42

3 0.030107 572.833 25 11 6 0 0 0 0 0 42

4 0.052159 724.269 24 9 9 0 0 0 0 0 42

5 0.145479 999.867 24 0 3 3 0 12 0 0 42

6 0.158069 1019.734 21 3 2 1 0 15 0 0 42

7 0.16176 1020.341 20 4 0 3 0 15 0 0 42


STEEL FRAME


m KN

0 6.08E-17 0 42 0 0 0 0 0 0 0 42

1 0.066546 1519.719 41 1 0 0 0 0 0 0 42

2 0.081362 1797.886 36 6 0 0 0 0 0 0 42

3 0.090248 1904.455 33 7 2 0 0 0 0 0 42

4 0.125552 2075.799 27 10 5 0 0 0 0 0 42

5 0.208834 2190.822 25 7 6 0 4 0 0 0 42

6 0.218627 2199.085 24 8 3 3 4 0 0 0 42

7 0.418627 2201.947 24 8 3 1 6 0 0 0 42

8 0.618627 2204.808 24 8 3 1 6 0 0 0 42

9 0.818627 2207.67 24 8 3 1 6 0 0 0 42

10 1.018627 2210.533 24 8 3 1 6 0 0 0 42

11 1.218627 2213.395 24 8 3 1 6 0 0 0 42

12 1.567709 2218.337 22 10 3 1 6 0 0 0 42

13 1.767709 2221.109 21 11 3 1 6 0 0 0 42

14 1.967709 2223.868 21 11 3 0 7 0 0 0 42

15 2 2224.313 21 11 3 0 7 0 0 0 42


7.0 IDA Analysis Result

CONCRETE FRAME

Scale Factor (g)

NGA0477 NGA0545 NGA2399

Displacement (x-direction)

Base Reaction Displacement (x-

direction) Base Reaction


Base Reaction

(m) (kN) (m) (kN) (m) (kN)

0.00 0 0 0 0 0 0

0.05 0.002459 17.821 0.004226 24.129 0.076688 49.718

0.10 0.004918 35.643 0.008452 48.257 0.153375 99.435

0.15 0.007377 53.464 0.012678 72.386 0.230063 149.153

0.20 0.009836 71.285 0.016904 96.514 0.30675 198.81

0.25 0.012295 89.107 0.02113 120.643 0.383436 248.587

0.30 0.014754 106.928 0.025356 144.771 0.460124 298.305

0.35 0.017213 124.749 0.029582 168.9 0.536812 348.022

0.40 0.019672 142.571 0.033809 193.028 0.6135 397.731

0.45 0.022131 160.392 0.038035 217.157 0.690664 447.448

0.50 0.02459 178.212 0.042261 241.286 0.766792 497.166

STEEL FRAME

Scale Factor (g)

NGA0477 NGA0545 NGA2399


Base Reaction Displacement (x-

direction) Base Reaction


Base Reaction

(m) (kN) (m) (kN) (m) (kN)

0.00 0 0 0 0 0 0

0.05 0.002093 2.632 0.00327 9.447 0.060192 10.56

0.10 0.004186 5.263 0.00654 18.894 0.120383 21.12


0.15 0.006279 7.895 0.00981 28.34 0.180576 31.68

0.20 0.008373 10.526 0.01308 37.787 0.240767 42.24

0.25 0.010466 13.158 0.016341 47.206 0.300959 52.8

0.30 0.012559 15.789 0.01962 56.68 0.361151 63.36

0.35 0.014652 18.421 0.02289 66.127 0.421343 73.92

0.40 0.016745 21.053 0.02616 75.574 0.481535 84.48

0.45 0.018838 23.684 0.03597 85.02 0.541726 95.04

0.50 0.020932 26.316 0.0327 94.467 0.601918 105.601


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8.0 Discussion

a. POA Analysis

Graph 8.1: Displacement vs Base Force for rectangular loading

Graph 8.2: Displacement vs Base Force for triangular loading


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The 8.1 graph shows the steel frame has bigger displacement and also

bigger base reaction. Based on this result, it can be conclude that steel

frame could deflect larger, which mean that it is more ductile than the

concrete frame. This phenomenon also can be notice from the elastis

limit of the steel frame is until 1985.96 kN which is longer than the

concrete frame 713.82 kN.

Loading distribution has effect on the value of the maximum base

reaction. It can be seen by comparing graph 8.1 and 8.2. When the

loading is distributed uniformly, the base shear become larger than if the

loading distributed in triangular way. For comparison, concrete frame

with unifom loading has ultimate force 2423.219 kN and the frame with

triangular loading, the ultimate force is 2199.085 kN.

Different height of building stories has effect on base force value. The

frame with seven stories got higher base reaction than three stories

frame. But in this case, from graph 8.3, five stories frame got the higher

value of base force compared to seven stories and three stories. It

supposed that five stories frame base force value should lies between

seven stories and three stories. This is could happend because the

different assignment and different assumption made during the design

and analysis process.

Graph 8.3: Displacement vs Base Force for 3 different kind of stories


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b. IDA Analysis

Graph 8.4 : IDA Analysis (Concrete Frame_3 Stories)

Graph 8.4 and 8.5 show comparison of three kind of ground motion, NGA 0477,

NGA 0545, and NGA 2399, for concrete frame and steel frame. The maximum

displacement of the frame is reached when the frame subjected to NGA2399

ground motion. Its value is 0.766792 m for concrete frame and 0.722302 m for

steel frame. The value difference only between both frame is only 5.8% which

considered small difference. The maximum value is reached due to magnitude

of the NGA2399 ground motion is the highest among the other two ground

motion. NGA 2399 has magnitude 5.90 while other two magnitude is 5.77 in

NGA 0545 and 5.80 in NGA 0477.

Graph 8.5: IDA Analysis (Steel Frame_3 Stories)


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The effect of story level on the frame can be seen in graph 8.6. The maximum

value of base reaction is belongs to seven stories frame which value is 35.481

kN. And the lowest base reaction is 11.947 kN belongs to five stories frame. But

the higest deflection is obtain from three level stories which maximum

displacement 0.20932 m. This evidence shows that the three level stories frame

deflect larger than the the seven stories and five stories frame.

Graph 8.6 : Comparison various heigt of steel frame with same ground motion

Report POA and IDA_final

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