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The Earthquake can be considered as a natural phenomenon or a disaster based on the seismic response of structures during a severe earthquake that plays a vital role in the extent of structural damage and resulting injuries and losses. It is necessary to predict the performance of the existing structures and structures at the design stage when it subjected to an earthquake load. Also, it is needed to predict the repair cost required for the rehabilitation of the existing buildings that is insufficient in seismic resistance, and the construction cost and the expected repairing cost for the structures at the design stage that designed to have a ductile behavior with acceptable cracks. This study aims to propose a method for seismic performance evaluation for existing and new structures depending on the width of cracks resulted from the seismic exposure. Also, it assesses the effect of building performance during earthquakes on its life cycle cost. FEMA 356 criteria were used to predict the building responses due to seismic hazard. A case study of seven-story reinforced concrete building designed by four design app roaches and then analyzed by static nonlinear pushover analysis to predict its response and performance during earthquake events using Sap 2000 software. The first design approach is to design the building to resist gravity loads only by using ECP code. The second one is to design the building to resist gravity loads and seismic loads by using static linear analysis according to ECP code. The third one is to design the building to resist gravity loads and seismic loads by using static linear analysis according to the regulations of the Egyptian Society of Earthquake Engineering (ESEE). Finally the fourth one is to design the building as the second approach but with ground acceleration greater by five times than it or by using ductility factor R = 1. The methodology followed in this study provides initial guidelines, and steps required to assess the seismic performance and the cost associated with using a variety of design methods for reinforced concrete structures resisting eart h quakes , selecting the retrofitting strategies that would be indicated to repair the structure after an earthquake .

The last earthquake events in various world areas and the resulting harms, especially human fatalities, have shown that the structures cannot withstand the earthquake loads. The large damages caused by the earthquake happened in Cairo in 1992 showed that at the construction time, the structures were designed to sustain only vertical loads and had ineffective horizontal load resistance. That expresses that, there are low ductility elements, shear resistance, and steel confinement in the plastic hinge zone that was founded in columns and beam column connections. So it is urgent to assess the seismic performance of existing structures and to constantly refresh the seismic codes for the design of the new structures.

The design of structures for seismic load resistance forced in the Egyptian design codes that motivated the Ministry of Housing and Buildings to regularly update the Egyptian codes provisions to consider the earthquake loads effect. After October 1992, a set of Egyptian codes has been released to avoid building failure and to control significant damages in structural elements. Earthquake analysis has many considerations that have been formed using the performance assessment of existing structures that have been subjected to a severe earthquake. To get a well-engineered structure, it must satisfy the seismic performance requirements that include the careful attention in analysis, design, reinforcement detailing, and good construction. The successful integration of analysis, design, and construction achieves the safety of the structure.

Krawinkler et al. [

Maske [

To perform the performance-based design, one must develop the evaluation method of the seismic resistant performance for the reinforced concrete structural members. The performance limit states are classified into three limit states, serviceability limit state, safety limit states, and damage control limit states. Each state is defined by the damages of the structural members. The yielding of reinforcing steel bars and the width of crack are used as the index of the damages. As the result of the plastic nonlinear frame analysis based on the performance-based design process method, the crack width of each member is calculated at each step [

Igarashi [

In the preliminary design process, equivalent linear static seismic analysis is used to get the design straining actions in structural members, and then get the strength demands for the designed structural member. One can get the equivalent static seismic forces by calculating the elastic design spectrum acceleration divided by a reduction factor that depends on the structural system that named as the ductility amount response factor (R).

In accordance with (ECP-201-2012) [_{b}) resulted from the analysis of each horizontal direction of the structure to seismic loads is computed with the shown formula:

F b = γ × S d ( T 1 ) × λ × W / g (1)

where, S_{d}(T_{1}) is the design response spectrum ordinate at time period T_{1}. T_{1} is the vibration time period of the structure in the direction of the horizontal load analyzed. W is the weight magnitude of the structure considering its total elements. g is the ground acceleration. γ is an important factor for the building and its value depends on the building function. λ is the modal mass correction factor. n: is the number of floors that formed the structure.

The value of the vibration time period in seconds (T_{1}) is computed using the shown formula:

T 1 = C t × H 3 / 4 (2)

where, C_{t} is a parameter depends on the structural system of the building and the material of the structure and C_{t} = 0.075 for a concrete framed structure and H is the total height of the building in m, from the level of footing or from the top of a rigid story.

The design response spectrum ordinate S_{d}(T_{1}), can be computed by the shown formula:

S d ( T 1 ) = [ 2.5 R ] × a g × γ × S × η [ T c T 1 ] ≥ 0.2 × a g × γ (3)

where, a_{g} is the equivalent design ground acceleration for the ground motion of the earthquake for a specific return period. T_{c} is the peak value of the constant spectral time period acceleration. Η is a damping parameter of the horizontal elastic response spectrum, where η = 1 corresponds to a normal ratio of 5% viscous damping (in the case of reinforced concrete structures). S is the parameter depends on the soil type. γ is the important factor for the building depends on the building function. R is a reduction factor depends on the structural system of the structure used to resist seismic loads, it represents the ductility amount of the structure.

The Arab Republic of Egypt is divided into five seismic zones according to the ECP code (ECP-201-2012) [

The lateral forces F_{i} on each story with mass m_{i} shall be computed as follows:

F i = [ h i × W i ∑ j = 1 n h j × W j ] × F b (4)

where, F_{i} is the earthquake force acting horizontally on story i. F_{b} is the total base shear force due to earthquake (Equation (1)). h_{i} and h_{j} are the heights of each story with masses m_{i} and m_{j} above the foundation level, respectively. W_{i} and W_{j} are the weights of masses m_{i} and m_{j}, respectively. n is the number of floors above the foundation level.

Equation (4) computes the seismic force on each floor depending only on the story height.

Zone | Design Ground Acceleration |
---|---|

1 | 0.10 g |

2 | 0.125 g |

3 | 0.15 g |

4 | 0.20 g |

5-a | 0.25 g |

5-b | 0.30 g |

The Egyptian Society for Earthquake Engineering (ESEE 1988) [

The total base horizontal earthquake load:

Each structure shall be designed and constructed to confront and release a total horizontal earthquake load (V) in each building direction under consideration which computed by the shown formula:

V = C s × W t (5)

where, C_{s} is the seismic design coefficient and W_{t} is the total weight of the building considering dead loads and live loads.

The horizontal acceleration coefficient can be calculated using the equation mentioned below:

C s = Z × I × S × M × R × Q (6)

where, C_{s} is a coefficient of Seismic design and Z is the factor of seismic zoning determined from the shown formula:

Z = A × C × F (7)

where, A is the horizontal earthquake ground acceleration detected according to the building location on the seismic zoning map. C is the standardized response spectrum coefficient for average damping of 5%. F is the foundation soil factor. I is the important factor of the building. S is the factor depends on the type of the structural system, the value of (S) shall be determined separately for each direction of the building. M is the factor that depends on the construction material. R is the risk factor expresses the amount of risk exposure. Q is a factor that shows the quality of materials used and the quality of construction.

Pushover analysis is a method in which a series of incremental static horizontal load applied on the structure to get the load-displacement capacity curve of the building. This load still increasing until the structure reaches its maximum displacement (Hakim 2014) [

It is a design method used for assessing the response of the building to the future seismic events and deciding whether such response meets the specific performance demands. The performance levels of the buildings due to seismic loads are as (FEMA-356-2000) [

Level | Resulted damage description |
---|---|

Operational (O) | Very simple light damage, no permanent displacement, structure returns to its own strength and stiffness after load removing. |

Immediate occupancy (IO) | Light damage, no permanent displacement, structure returns to its own strength and stiffness after load removing, elevator can be restarted, fire protection operable |

Life safety (LS) | Moderate damage, some permanent displacement, some residual stiffness and strength still in the structure stories, damage to partitions, building may need large repairing cost. |

Collapse prevention (CP) | Severe damage, large displacement, little residual stiffness and strength, structure is close to collapse. |

According to design aids and examples in accordance with the (ECP-203-2007) [

W k = β ⋅ S r m ⋅ ε s m ( mm ) (8)

S r m = [ 50 + 0.25 K 1 K 2 ϕ ρ r ] ( mm ) (9)

ε s m = F s E s [ 1 − β 1 β 2 ( F s r F s ) 2 ] (10)

where, W_{k} is the crack width value in (mm). S_{rm} is the Spacing between cracks in the horizontal direction measured in (mm). ε_{sm} is the mean steel strain under a relevant combination of loads and allowing for the effect such as tension stiffening or shrinkage. β is the Coefficient that connects the average crack width to the design crack width. Φ is the Bar diameter in (mm). β_{1} is a coefficient that reflects the bond properties of the reinforcing steel bars. β_{2} is a coefficient that reflects the loading duration. K_{1} is a coefficient that reflects the type of steel bars. K_{2} is a coefficient that shows the distribution of the strain over the subjected cross section.

K 2 = ε 1 + ε 2 / 2 ε 2 (11)

where, ε_{2} and ε_{1} are the minimum and maximum strain values on the subjected section, and shall be calculated according to the analysis of a cracked section.

ρ r = A s A c e f (12)

where, A_{s} is the area of longitudinal tension steel within the effective tension area. A_{cef} is the area of effective concrete section in tension = width of the section × t_{cef}. t_{cef} = 2.5 × concrete cover. F_{s} is the stress in longitudinal steel bars at the tension zone calculated based on the analysis of cracked section under permanent loads. F_{sr} is the stress in longitudinal steel bars located in the tension zone calculated according to the analysis of cracked section due to the loads that causing first crack.

The moment M_{t} and M_{b} values describe the damage level and its suitable repairing method, the normal force values in beams is small and can be neglected. By taking the average moment at the top and bottom (reversible moment). According to ECP code [_{k}), the horizontal distance between the cracks (S_{rm}), and the vertical distance between the neutral axis and the maximum tensile stress. From the value of (S_{rm}) and the vertical distance between the neutral axis and the maximum tensile stress, the whole length of cracks that will be injected with epoxy can be calculated.

Description of the Case Study Building

The prototype building consists of 7-story framed reinforced concrete structure, with a story height of 3.0 m, the overall plan is 12 m × 12 m (144 m^{2}).

The structural system was designed using a design practice that considers gravity loads and linear static seismic loads according to ECP code (ECP-201-2012) [

Material | |
---|---|

Concrete | 25 N/mm^{2 }(MPa) |

Steel | 360/520 for main bars & 240/350 for confinement bars |

Loads | |

Own weight | Calculated by the program |

Dead load | 5 KN/m^{2} |

Live load | 2 KN/m^{2} |

Wind load | Not Considered |

Seismic load | As mentioned below |

Modeling | |

Elements | Non Linear frame element for beam and column Shell element for slab |

P-delta effect | Not considered |

Diaphragm | Rigid diaphragm for slab |

Support type | Fixed |

The building designed to resist vertical loads only which are the dead loads and live loads. By using AutoCAD program (Autodesk 2014) [

1) Construction bill of quantities for the designed structure

The cost of the structural works needed for construction is shown in

2) Performance based analysis for the designed structure

The performance based analysis is performed by nonlinear static pushover analysis that is implemented using the SAP2000 software (Computer and Structures 2014) [

The load-displacement capacity curve resulted is shown in

At each pushover analysis step obtain the location of hinges in the structural elements, plastic hinges rotation and hinges reached to the FEMA provisions, which are IO, LS, and CP identified by using colored plastic hinges as shown in

For columns at step 5 as shown in

For beams at step 5 as shown in

Axial for cein(t) for columns at step 5 is shown in

By using equation of the (ECP-203) [

Red color means that the steel is yielded and Green color means that the steel is not yielded.

By using the ECP-203 code [

• Spacing between cracks in beams for calculation of the length of cracks needed to be injected with epoxy = 20 cm.

By using an excel sheet that constructed for calculation of section’s moment capacity:

Moment capacity for beam B1 = 10.1 t∙m and for beam B2 = 16.6 t∙m.

• Neutral axis height for calculation of the length of cracks needed to be injected by epoxy = 36 cm.

EAM MARK | SIZE (BXD) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | LINKS | ||||||
---|---|---|---|---|---|---|---|---|---|---|

LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | ||

B1 | 250 × 600 | 3T16 | 3T16 | 3T16 | 3T16 | 2T16 | 3T16 | 5ø8/m | 5ø8/m | 5ø8/m |

B2 | 250 × 600 | 5T16 | 5T16 | 5T16 | 8T16 | 4T12 | 8T16 | 8ø10/m | 5ø8/m | 8ø10/m |

SCHEDULE OF ISOLATED FOOTINGS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

FOOTING MARK | P.C. FOOTING DIM.(mm) | R.C. FOOTING DIM.(mm) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | ||||||

B | L | THICK. | B | L | THICK. | SHORT DIR. | LONG DIR. | SHORT DIR. | LONG DIR. | |

F1 | 2600 | 2600 | 300 | 2000 | 2000 | 700 | 6T16/m | 6T16/m | --- | --- |

F2 | 3500 | 3500 | 300 | 2900 | 2900 | 700 | 8T16/m | 8T16/m | --- | --- |

F3 | 5000 | 5000 | 300 | 4400 | 4400 | 800 | 10T18/m | 10T18/m | --- | --- |

TYPE | DIMENSIONS b × t (mm) | REINFORCEMENT | |||
---|---|---|---|---|---|

BOTTOM | TOP | SIDE | STIRRUPS | ||

TB1 | 250 × 700 | 4T16 | 4T16 | --- | 5ø8/m |

Item | Volume (m^{3}) | Contractor fees (Pounds) | Material cost (Pounds) | Supervision percentage (%) | Losses percentage (%) |
---|---|---|---|---|---|

Plain Concrete | 30.32 | 130 | 690 | 10 | 3 |

Reinforced Concrete | 312.12 | 330 | 690 | 10 | 3 |

Total construction cost = 890529 L∙E, Total construction cost/m^{2} of floor = 883.46 L∙E/m^{2}.

Floor | hi (m) | Fi (t) | Shear (t) | Moment (t∙m) = hi × Fi |
---|---|---|---|---|

7 | 21 | 11.57 | 11.571 | 243 |

6 | 18 | 9.918 | 21.489 | 178.524 |

5 | 15 | 8.265 | 29.754 | 123.975 |

4 | 12 | 6.612 | 36.366 | 79.344 |

3 | 9 | 4.959 | 41.325 | 44.631 |

2 | 6 | 3.306 | 44.631 | 19.836 |

1 | 3 | 1.653 | 46.284 | 4.959 |

The building is designed to resist vertical loads and static linear seismic loads in accordance with ECP-201 [_{g} = 0.15 g, and the response spectrum shape is type 1, the building facility is a residential building, its importance factor γ = 1, the soil type under the building is considered to be stiff soil, which presents soil class C and the soil factor S = 1.5. The ductility reduction factor R, is taken as R = 5 considering that the vertical loads and the total base shear force a re totally resisted by the non-ductile frame structural system. The beams dimensions and reinforcement are shown in (

Earthquake loads according to ECP (2012)

A residential building located in Cairo, Egypt, soil class c, zone 3, h floor =3 m, n floors = 7, response spectrum type 1.

For soil class C

S = 1.5 , T B = 0.1 , T C = 0.25 , T D = 1.2 , C t = 0.075 (R.C. Structure)

T = C t × H 3 4 = 0.075 × 21 × 3 4 = 0.7357 seconds < 4 T C = 4 × 0.25 = 1 sec .

For concrete framed structure (residential)

γ = 1 , η = 1 , For T C ≤ T ≤ T D → S d ( T ) = [ 2.5 R ] × a g × γ , R = 5 × S × η [ T c T ] ≥ 0.2 × a g × γ

S d ( T ) = [ 2.5 5 ] × ( 0.15 × 9.81 ) 1 × 1.5 × 1 × [ 0.25 0.7357 ] = 0.375 ≥ 0.2 × a g × γ = 0.2943

Calculation of weight for all floors

W slab + beams = 1.04 × 12 × 12 × 7 = 1048.32 t ,

W columns = [ ( 4 × 0.4 × 0.4 ) + ( 4 × 0.5 × 0.5 ) + ( 0.7 × 0.7 ) ] × 2.5 × 21 = 111.825 t ,

W dead = 1048.32 + 111.825 = 1160.145 t , W live = 0.2 × 12 × 12 × 7 = 201.6 t ,

W total = W D + 0.25 W L = 1210.55 t , W floor = 172.94 t

Calculation of total base shear force and the horizontal force on each floor

F b = γ × S d ( T ) × λ × W / g = 0.375 × 1 × ( 1210.55 / 9.81 ) = 46.275 t

∑ W i h i = 172.94 ( 3 + 6 + 9 + 12 + 15 + 18 + 21 ) = 14526.96 t ⋅ m ,

F i = [ h i × W i ∑ j = 1 n h j × W j ] × F b = 46.275 × [ h i × 172.94 14526.96 ] = 0.551 h i

1). Construction bill of quantities for the designed structure

The cost of the structural works needed for construction is shown in (

2) Performance based analysis for the designed structure

The performance based analysis is performed by nonlinear static pushover analysis that is implemented using the SAP2000 software (Computer and Structures 2014) [

The load-displacement capacity curve resulted is shown in

At each pushover analysis step obtain the location of hinges in the structural elements, plastic hinges rotation and hinges reached to the FEMA provisions, which are IO, LS, and CP identified by using colored plastic hinges as shown in

For columns at step 5 as shown in

For beams at step 5 as shown in

Axial force in (t) for columns at step 5 as shown in

By using equations of the (ECP-203) [

Red color means that the steel is yielded Green color means that the steel is not yielded.

By using the ECP-203 code [

• Spacing between cracks in beams for calculation of the length of cracks needed to be injected with epoxy = 12 cm.

By using an excel sheet that constructed for calculation of section’s moment capacity:

• Moment capacity for beam B1 = 10.06 t∙m and for beam B2 = 16.6 t∙m.

• Neutral axis height for calculation of the length of cracks needed to be injected by epoxy = 28 cm.

Floor | hi (m) | Fi (t) | Shear (t) | Moment (t∙m) = hi × Fi |
---|---|---|---|---|

7 | 21 | 11.57 | 11.571 | 243 |

6 | 18 | 9.918 | 21.489 | 178.524 |

5 | 15 | 8.265 | 29.754 | 123.975 |

4 | 12 | 6.612 | 36.366 | 79.344 |

3 | 9 | 4.959 | 41.325 | 44.631 |

2 | 6 | 3.306 | 44.631 | 19.836 |

1 | 3 | 1.653 | 46.284 | 4.959 |

BEAM MARK | SIZE (BXD) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | LINKS | ||||||
---|---|---|---|---|---|---|---|---|---|---|

LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | ||

B1 | 250X600 | 3T16 | 3T16 | 3T16 | 5T16 | 3T16 | 5T16 | 5ø8/m | 5ø8/m | 5ø8/m |

B2 | 250X600 | 5T16 | 5T16 | 5T16 | 8T16 | 4T12 | 8T16 | 8ø12/m | 8ø8/m | 8ø12/m |

SCHEDULE OF ISOLATED FOOTINGS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

FOOTING MARK | P.C. FOOTING DIM.(mm) | R.C. FOOTING DIM.(mm) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | ||||||

B | L | THICK. | B | L | THICK. | SHORT DIR. | LONG DIR. | SHORT DIR. | LONG DIR. | |

F1 | 2800 | 2800 | 300 | 2200 | 2200 | 700 | 7T16/m | 7T16/m | --- | --- |

F2 | 3700 | 3700 | 300 | 3100 | 3100 | 700 | 9T16/m | 9T16/m | --- | --- |

F3 | 5000 | 5000 | 300 | 4400 | 4400 | 800 | 10T18/m | 10T18/m | --- | --- |

Item | Volume (m^{3}) | Contractor fees (Pounds) | Material cost (Pounds) | Supervision percentage (%) | Losses percentage (%) |
---|---|---|---|---|---|

Plain Concrete | 33.34 | 130 | 690 | 10 | 3 |

Reinforced Concrete | 329.05 | 330 | 690 | 10 | 3 |

Total construction cost = 957737 L∙E, Total construction cost/m^{2 }of floor = 950.14 L∙E/m^{2}.

Floor | hi (m) | Fi (t) | Shear (t) | Moment (t∙m) = hi × Fi |
---|---|---|---|---|

7 | 21 | 57.855 | 57.855 | 1215 |

6 | 18 | 49.59 | 107.445 | 892.62 |

5 | 15 | 41.325 | 148.77 | 619.875 |

4 | 12 | 33.06 | 181.83 | 396.72 |

3 | 9 | 24.795 | 206.625 | 223.155 |

2 | 6 | 16.53 | 223.155 | 99.18 |

1 | 3 | 8.265 | 231.42 | 24.795 |

Base shear force = 231.42 t, Overturning moment = 3471.35 t∙m.

The building is designed to resist vertical loads and static linear seismic loads in accordance with ECP-201 [_{g} = 0.15 g, and the shape of the response spectrum is type 1, the building facility is a residential building with an importance factor γ = 1, the soil type under the building is considered to be stiff soil, which presents soil class C and a soil factor S = 1.5. The ductility reduction factor R, is taken R = 1 considering that the vertical loads and the total base shear force are totally resisted by the non-ductile frame structure. The beams dimensions and reinforcement are shown in (

1) Construction bill of quantities for the designed structure

The cost of the structural works needed for construction is shown in

2) Performance based analysis for the designed structure

The performance based analysis is performed by nonlinear static pushover analysis that is implemented using the SAP2000 software (Computer and Structures 2014). The force on each floor used for pushover analysis is shown in

The load-displacement capacity curve resulted is shown in

At each pushover analysis step obtain the location of hinges in the structural elements, plastic hinges rotation and hinges reached to the FEMA provisions, which are IO, LS, and CP identified by using colored plastic hinges as shown in

For columns at step 5 as shown in

For beams at step 5 as shown in

Axial force in (t) for columns at step 5 as shown in

By using equations of the (ECP-203) [

Red color means that the steel element is yielded Green color means that the steel is not yielded.

By using the ECP-203 code [

• Spacing between cracks in beams for calculation of the length of cracks needed to be injected with epoxy = 37 cm.

By using an excel sheet that constructed for calculation of section’s moment capacity:

• Moment capacity for beam B1= 41.69 t∙m and for beam B2 = 62.31 t∙m.

• Neutral axis height for calculation of the length of cracks needed to be injected by epoxy = 63 cm.

BEAM MARK | SIZE (BXD) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | LINKS | ||||||
---|---|---|---|---|---|---|---|---|---|---|

LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | ||

B1 | 400X900 | 8T16 | 8T16 | 8T16 | 10T16 | 4T16 | 10T16 | 6ø10/m | 5ø10/m | 6ø10/m |

B2 | 400X900 | 12T18 | 12T18 | 12T18 | 15T18 | 5T18 | 15T18 | 8ø14/m | 8ø12/m | 8ø14/m |

SCHEDULE OF ISOLATED FOOTINGS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

FOOTING MARK | P.C. FOOTING DIM.(mm) | R.C. FOOTING DIM.(mm) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | ||||||

B | L | THICK. | B | L | THICK. | SHORT DIR. | LONG DIR. | SHORT DIR. | LONG DIR. | |

F1 | 3000 | 3000 | 300 | 2400 | 2400 | 700 | 8T18/m | 8T18/m | --- | --- |

F2 | 3900 | 3900 | 300 | 3300 | 3300 | 700 | 9T18/m | 9T18/m | --- | --- |

F3 | 5200 | 5200 | 300 | 4600 | 4600 | 800 | 10T18/m | 10T18/m | --- | --- |

Item | Volume (m^{3}) | Contractor fees (Pounds) | Material cost (Pounds) | Supervision percentage (%) | Losses percentage (%) |
---|---|---|---|---|---|

Plain Concrete | 37.64 | 130 | 690 | 10 | 3 |

Reinforced Concrete | 463.6 | 330 | 690 | 10 | 3 |

Total construction cost = 1323868.4 L∙E, Total construction cost/m^{2 }of floor = 1313.37 L∙E/m^{2}.

The prototype concrete building designed to sustain vertical loads and linear static seismic loads determined from the regulations of the Egyptian Society for Earthquake Engineering (ESEE).

Earthquake loads according to the Egyptian Society for Earthquake Engineering (ESEE) Regulations.

A residential building located in Cairo, Egypt, the floor height = 3 m, floors number = 7.

Total horizontal seismic force (V) = C_{s} × W_{total}, C s = Z I S M R Q

Importance factor (I) = 1 for Residential Building

Structural system type factor (S) = 1 for Moment-Resisting Frames

Material factor (M) = 1 for Reinforced Concrete

Risk factor (R) = 1 for No Risk

Quality control factor (Q) = 1 for Good Quality Control

The seismic zoning factor (Z) = ACF

Horizontal acceleration ratio (A) = 0.04 g for Cairo, Egypt

Foundation soil factor (F) = 1.3 for fine grained soil

Timeperiod ( T ) = 0.09 H d = 0.09 × 21 12 = 0. 5456 second

Coefficient of standardized response spectrum for average damping of 5% (C) = 0.89.

According to the value of (T) determined from

Z = 0.04 × 0.89 × 1.3 = 0.0463, C_{s} = Z I S M R Q = 0.0463 × 1 × 1 × 1 × 1 × 1 = 0.0463.

Calculation of weight for all floors

W slab + beams = 1.04 × 12 × 12 × 7 = 1048.32 t ,

W columns = [ ( 4 × 0.4 × 0.4 ) + ( 4 × 0.5 × 0.5 ) + ( 0.7 × 0.7 ) ] × 2.5 × 21 = 111.825 t ,

W dead = 1048.32 + 111.825 = 1160.145 t , W live = 0.2 × 12 × 12 × 7 = 201.6 t ,

W total = W D + 0.25 W L = 1210.55 t , W floor = 172.94 t

Calculation of total base shear force and the horizontal force on each floor (

V = C s × W t o t a l = 0.0463 × 1210.55 = 56 t ,

∑ W i h i = 172.94 ( 3 + 6 + 9 + 12 + 15 + 18 + 21 ) = 14526.96 t ⋅ m

F i = [ h i × W i ∑ j = 1 n h j × W j ] × V = 56 × [ h i × 172.94 14526.96 ] = 0.667 h i

1) Construction bill of quantities for the designed structure

The cost of the structural works needed for construction is shown in

2) Performance based analysis for the designed structure

The performance based analysis is performed by nonlinear static pushover analysis that is implemented using the SAP2000 software (Computer and Structures 2014) [

The load-displacement capacity curve resulted is shown in

At each pushover analysis step obtain the location of hinges in the structural elements, plastic hinges rotation and hinges reached to the FEMA provisions, which are IO, LS, and CP identified by using colored plastic hinges as shown in

For columns at step 5 as shown in

For beams at step 5 as shown in

Axial force in (t) for columns at step 5 as shown in

By using equations of the (ECP-203) [

Red color means that the steel is yielded Green color means that the steel is not yielded.

By using the ECP-203 [

• Spacing between cracks in beams for calculation of the length of cracks needed to be injected with epoxy = 18 cm.

By using an excel sheet that constructed for calculation of section’s moment capacity:

• Moment capacity for beam B1 = 10.1 t∙m and for beam B2 = 26.6 t∙m.

• Average Neutral axis height for calculation of the length of cracks needed to be injected by epoxy = 32 cm.

Floor | hi (m) | Fi (t) | Shear (t) | Moment (t∙m) = hi × Fi |
---|---|---|---|---|

7 | 21 | 14 | 14 | 294 |

6 | 18 | 12 | 26 | 216 |

5 | 15 | 10 | 36 | 150 |

4 | 12 | 8 | 44 | 96 |

3 | 9 | 6 | 50 | 54 |

2 | 6 | 4 | 54 | 24 |

1 | 3 | 2 | 56 | 6 |

BEAM MARK | SIZE (BXD) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | LINKS | ||||||
---|---|---|---|---|---|---|---|---|---|---|

LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | LEFT | MID SPAN | RIGHT | ||

B1 | 250X600 | 3T16 | 3T16 | 3T16 | 5T16 | 3T12 | 5T16 | 5ø8/m | 5ø8/m | 5ø8/m |

B2 | 250X600 | 5T16 | 5T16 | 5T16 | 8T18 | 4T16 | 8T18 | 8ø12/m | 8ø8/m | 8ø12/m |

SCHEDULE OF ISOLATED FOOTINGS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

FOOTING MARK | P.C. FOOTING DIM.(mm) | R.C. FOOTING DIM.(mm) | BOTTOM REINFORCEMENT | TOP REINFORCEMENT | ||||||

B | L | THICK. | B | L | THICK. | SHORT DIR. | LONG DIR. | SHORT DIR. | LONG DIR. | |

F1 | 2800 | 2800 | 300 | 2200 | 2200 | 700 | 7T16/m | 7T16/m | --- | --- |

F2 | 3700 | 3700 | 300 | 3100 | 3100 | 700 | 9T16/m | 9T16/m | --- | --- |

F3 | 5000 | 5000 | 300 | 4400 | 4400 | 800 | 10T18/m | 10T18/m | --- | --- |

Item | Volume (m^{3}) | Contractor fees (Pounds) | Material cost (Pounds) | Supervision percentage (%) | Losses percentage (%) |
---|---|---|---|---|---|

Plain Concrete | 33.34 | 130 | 690 | 10 | 3 |

Reinforced Concrete | 329.05 | 330 | 690 | 10 | 3 |

Total construction cost = 996450 L∙E, Total construction cost/m^{2} of floor = 988.55 L∙E/m^{2}.

Repairing of the structure after an earthquake event is determined mainly by its level of damage that determined by the width of cracks in concrete members and the reinforcing steel bars condition (yielded or not). We can detect the damage levels and the most appropriate repairing technique as mentioned below in

The cost assessment results are summarized in

Design Case | Construction cost (L∙E/m^{2}) | Repair cost^{ } (L∙E/m^{2})^{ } | Base Shear (t)^{ } Resistance | Life cycle cost (L∙E/m^{2}) | Construction Cost Ratio |
---|---|---|---|---|---|

Case 1 (D + L) | 883.46 | 426.6^{ } | 184.87 | 1310.05 | 1 (The reference value) |

Case 2 (R = 5) | 950.14^{ } | 391.87^{ } | 246.25 | 1342 | 1.0755 |

Case 3 (R = 1) | 1313.37^{ } | 277.8^{ } | 431.29 | 1591.14 | 1.487 |

Case 4 (ESEE) | 988.55 | 377 | 246.58 | 1356.53 | 1.12 |

The nonlinear analysis of structures designed to resist earthquakes is very important to assess the response of the structure under earthquake effect and to know the state of the building after seismic load. The ductility of building is very important but one should be careful since the large displacement will be accompanied with damage that can make the structural members irreparable and the building may lose its function. One should perform a cost assessment for each seismic mitigation design to visualize the life cycle cost of the structure to get a cost effective design, which consists of the construction cost and the repairing cost after earthquake damage. The paper presented a proposed method for seismic performance evaluation for existing and new structures depending on the width of cracks resulted from the seismic exposure. Also it helps engineers to perform a cost assessment for the reinforced concrete buildings designed to resist earthquakes to get its life cycle cost.

The steps and methodology required for structural evaluation and cost assessment mentioned in this study are summarized as follows:

1) Construct a 3-D model for structure to be analyzed by using sap 2000 software.

2) Calculate the construction cost of the designed structure by (L∙E/m^{2}) as shown in

3) Perform a nonlinear static pushover analysis by using SAP2000 software to locate the weakness points in the structure that appears as cracks in the structural members, if this structure is constructed and exposed to the designed seismic ground acceleration and story shear as shown in

4) Get the plastic moment on each member as shown in

Item | Volume (m^{3}) | Contractor fees (Pounds) | Material cost (Pounds) | Supervision percentage (%) | Losses percentage (%) |
---|---|---|---|---|---|

Plain Concrete (P.C) | …. | …. | …. | …. | …. |

Reinforced Concrete (R.C) | …. | …. | …. | …. | …. |

Cost of P.C = volume × (contractor fees + material cost) × % of losses and Supervision cost; Cost of R.C = volume × (contractor fees + material cost) × % of losses and Supervision cost; Cost of Reinforcement = steel weight × unit cost × % of losses and Supervision cost.

Floor | hi (m) | Fi (t) |
---|---|---|

7 | 21 | 11.571 |

6 | 18 | 9.918 |

5 | 15 | 8.265 |

4 | 12 | 6.612 |

3 | 9 | 4.959 |

2 | 6 | 3.306 |

1 | 3 | 1.653 |

5) Select the suitable repairing method for each member according to the crack width value as shown in

6) Calculate the repairing cost of the structure for each design approach by (L∙E/m^{2}) as shown in

Damage | Unit | Repair cost (L∙E/unit) |
---|---|---|

Slight | m | 65 |

Minor | m | 135 |

Moderate | m^{2} | 430 |

Severe | … | 2800 + Steel bars cost |

7) Perform a cost analysis for assessment of the cost-efficiency of seismic mitigation design based on the long term performance of the structure subjected to seismic hazard, a life-cycle cost due to the initial construction cost should be included to assess the impact of potential earthquakes that occurred during the expected life-cycle of the structure. Generally, a more resistant design with higher initial construction cost will have a lower life-cycle cost.

The authors declare no conflict of interest, financial or otherwise.

Fayed, Y., Sobaih, M.E. and El Hakem, Y. (2019) Proposed Method for Cost Assessment of Seismic Mitigation Designs for Reinforced Concrete Buildings According to ECP Code. Open Journal of Civil Engineering, 9, 319-355. https://doi.org/10.4236/ojce.2019.94023