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The use of steel structures in the developing countries is limited in spite of its better performance in the case of seismic events due to its high ductility. Although steel structures behave well under seismic excitation, nevertheless the use of structural steel is limiting these days. This paper aims to address various parameters related to the capacity design approach involved in the seismic design of conventional steel structures. Few cases of the early steel structures construction such as bridges in Pakistan are briefly described. Philosophies based on the capacity design approach and the importance of conventional steel lateral load resisting systems with their global mechanisms are provided. The design procedures of Eurocode 8 for Steel Moment resisting frames, Concentric cross braced frames and Eccentric braced frames are given and illustrated. It is believed that the paper will contribute and will be helpful for the designers, researchers and academicians involve in the study of lateral load resisting systems for incorporating in the design process. Since synopsis tables are provided, therefore this will allow a clear understanding of the capacity design approach for different lateral load resisting systems.

The philosophies of seismic design codes rely on the inherent capability of structures to undergo inelastic deformation. Since steel is strong, light weight, ductile and tough material hence believed to be capable of dissipating extensive energy through yielding when stressed in the inelastic range, these are exactly the properties desired for seismic resistance. In fact, other construction materials rely on these basic properties of steel to assist them in attaining adequate seismic resistance. Throughout the relatively brief history, structural steel buildings have been among the best performing structural systems. Prior to January 1994 when previously unanticipated connection failures were discovered in some buildings following the Northridge earthquake (M 6.7), many engineers mistakenly regarded such structures as nearly earthquake-proof. A year later, the Kobe earthquake (M 6.9) caused collapse of 50 steel buildings confirming the potential vulnerability of these structures. This experiences notwithstanding structural steel buildings if properly designed can provide outstanding earthquake performance. This paper introduces the general concepts of conventional steel structures that should be followed during analyzing and designing when dealing with earthquake forces. The trend of design of steel structures is highly encouraging in Pakistan as it is a high seismic region; the October 2005 earthquake is a clear example. Nevertheless, less work has been done on the seismic design of steel structures compared to other materials such as masonry, reinforce concrete and timber etc. It is to be noted here that Building Code of Pakistan (BCP) [

・ In 1935 at 05:30―Quetta, Pakistan―M 7.5 Fatalities 30,000.

・ In 1945 at 11:27―Makran Coast, Pakistan―M 8.0 Fatalities 4000.

・ In 1974 at 12:28―Northern Pakistan―M 6.2 Fatalities 5300.

・ In 2005 at 10:08―Kashmir Pakistan―M 7.6 Fatalities 86,000.

・ In 2008 at 10:28―Pakistan―M 6.4 Fatalities 166.

・ In 2011 at 01:18―Pakistan―M 7.2 Fatalities 3.

Since Pakistan is a developing Country the aforementioned earthquakes strongly influenced the infrastructure in the corresponding areas and caused huge number of casualties as collapse and high damages were depicted within the building structures. It is believed that steel structures performed well during the past earthquakes, most of these structures are bridges or structures that were constructed to serve railways such as railway stations etc. In 1947 before the

S. No | Seismic Zones | Peak Ground Acceleration | Hazard Level | Damage Intensity | Damage Effect |
---|---|---|---|---|---|

1 | 1 | 0.05 to 0.08 g | Low | Negligible | Low |

2 | 2A | 0.08 to 0.16 g | Moderate | Minor | Medium |

3 | 2B | 0.16 to 0.24 g | Moderate | ||

4 | 3 | 0.24 to 0.32 g | Large | Sever | High |

5 | 4 | >0.32 g | Sever | Collapse | Huge |

NOTE: Where “g” is the acceleration due to gravity. The acceleration values are for Medium hard rock (S_{B}) site condition with shear wave velocity (v_{s}) of 760 m/sec.

independence of Pakistan from the British steel Moment Resisting Frames achieve good performance under seismic events. After the 1931 Mach earthquake some structures (see

Pakistan located in Southeast Asia; composed of number of rivers therefore bridges represent a sort of common connection for different regions and presents a vital role in the transportation such as railways, highways as well for pedestrians. Before the independence many bridges that are constructed in the British Era are constructed of steel using riveted trusses having built-up members (mostly back to back channels). For examples the Jhelum Bridge (

single-span cantilever bridge completed in 1889. It was one of the great engineering feats of its time because the Indus River was too large to divert its waters to install piers therefore large beams cantilevered from the river side and was supported by the land on the other side. These cantilevers from both sides were joined in the middle by a system of trusses. Just 30 m away from this bridge the Ayub Arch stands which is an arch-pan bridge built to divert railway traffic away from the aging Lansdowne Bridge Rohri. The Attock railway bridge (

In Pakistan, almost all the railway station are ancient such as the one of Lahore (see

In more recent times steel structures are available in the form of telecommunication towers, electric poles, sign boards, petrol pumps etc. and rarely some industrial buildings (See

Since steel frames are generally highly flexible, therefore they are characterized by relatively high fundamental period. Further, as it is revealed in [

medium and long period, the “equal displacement rule” implies. Therefore the main factors affecting the structural behavior under seismic excitation can be obtained from pushover analysis using the “equal displacement rules”, as shown in

Ductility reduction factor: It is the ratio of V_{e} to V_{y} as shown in Equation (1), it can also be termed as expected behaviour factor.

q μ , ρ = V e V y (1)

Redundancy factor: It is the over-strength given by the redistribution of the plastic hinges and termed as redundancy factor; it is the ratio of V_{u} obtained from pushover analysis to V_{y} defined by Equation (2). Redundancy exists when multiple elements must yield or fail before a complete collapse mechanism forms. Structures possessing low inherent redundancy are required to be stronger and more resistant to damage and therefore seismic design forces are amplified. Therefore, normally it is assumed that structures having larger global ductility exhibits high redundancy and vice versa.

Ω ρ = V u V y (2)

Elastic overstrength factor: It is the allowable stress reduction factor and is given by the ratio of V_{y} to V_{d} given by Equation (3). As an ideal scenario in the design Ω_{E} might be unity. Since the structural capacity must not be less than the design forces, Ω_{E} is always at least 1.

Ω E = V y V d (3)

Global overstrength factor: It is given by the ratio of V_{u} to V_{d}; it corresponds to the product of redundancy factor and elastic overstrength, evaluated from Eq. (4).

Ω E , ρ = Ω E × Ω ρ = ( V y V d ) × ( V u V y ) = V u V d (4)

Reserve ductility: It is the ratio of V_{e} to V_{u} as given in Equation (5) as well from Equation (7) and Equation (8).

q μ = ( V e V u ) (5)

Behaviour factor: It is given by the ratio of V_{e} to V_{d}. it is simply the product of elastic overstrength, redundancy factor and reserve ductility defined by Eq. (6).

q d = Ω E × Ω ρ × q μ = ( V y V d ) × ( V u V y ) × ( V e V u ) = V e V d or q d = ( Δ u Δ y ) (6)

q μ = V e V u = q d Ω E , ρ (7)

q μ , ρ = V e V y = q u × Ω ρ (8)

Seismic design necessitates the combinations of deformability, strength and most importantly the ductility characteristics of a structural system. Although steel structures have the capability to resist the lateral actions by means of different Lateral Load Resisting Systems (LLRS). Nevertheless the impairing of strength with the ductility and deformability is a big challenge for the designer. Several types of earthquake resistant steel structures (some LLRS can be combined with the others) which depend on the selected load carrying mechanism can be conceived. These LLRSs have pros and cons on each other due to their characteristics such as high deformability (like MRFs), architectural constraints (like cross bracing that may restrict the opening) and geotechnical issues (for example concentration of forces on the footings). The most conventional types of earthquake resistant steel structures are: a) Rigid Frames, b) Concentric Braced Frames and c) Eccentric Braced Frames.

The main features for these systems with the design criteria with respect to Eurocode 8 [

In this section rigid steel frames are discussed which remain elastical or in-elastical depending on the loading conditions. In the case of a low earthquake according to the performance criteria MRFs should be remain in the elastic state. On the other hand for any strong motion earthquake rigid frames might behave in elastically with the condition that it dissipates the seismic energy. Stiffness is affected if MRFs goes into the plastic state. The plastic state of rigid frames in the case of seismic event can be controlled by applying the capacity design rules [

As moment resisting frames are realized by rigid connections (See

In Eurocode 8 the design elastic response spectrum is normally reduced by a behavior factor (q) that equals to 4 for DCM and 6.5 for DCH. Furthermore in order to have a global ductile behavior of the MRFs, beams should be verified in order to have sufficient resistance against lateral torsion buckling in accordance with EN 1993. Beam ends are the fuses in rigid frames and if these are designed properly they perform well. For assuring plastic hinges in the beams, Code gives some supplementary checks for the beams of MRF where demand to capacity due to moment is 100%, due to shear it is 50% whereas due to axial it is only 15% as brittle failure is more related to shear and axial. Column are assumed to be elastic as more vulnerable to axial forces specially the compressive

Description | EC8-DCH | ASCE-SMF |
---|---|---|

Restrictions on the use of Cross section | For q higher than four only class 1 sections are permitted to be used | Sections must be compact |

Seismic load reduction factor | q equal to 5α_{u}/α_{1} | R equal to 8 |

Energy dissipation philosophy (significant inelastic deformation) | Given by ductility class high | Given by special moment resisting frames, and are anticipated to undergo |

Overstrength factor | Obtained from ratio of plastic moment of columns to beams | Restricted to 3 |

Local ductility | Plastic hinge rotation is restricted to 35 mrad | Plastic hinge rotation is restricted to 30 mrad with inter-storey drifts to 0.04 radians |

Strength checks for Beams | M E , d M p l , R d ≤ 1.0 , N E , d N p l , R d ≤ 0.15 , V E , d V p l , R d ≤ 0.5 | Only strength checks as per AISC/LRFD are required |

Ratio | q Ω = ? | R Ω = 8 3 = 2.67 |

Strong column weak beam (SCWB) philosophy | ∑ M R c ≥ 1.3 ∑ M R b | ∑ M p c * ∑ M b c * ≥ 1.0 , Columns should have sufficient flexural strength |

Non-dissipative members such as columns | N E d = N E d , G + 1.1 γ o v Ω N E d , E Math_33##Math_34# | Verification of strength with loads computed from special load combinations having Ωo |

Connections | full strength | full strength |

ones, therefore the actual seismic forces are increased by overstrength factor. Columns shall be verified in compression considering the most unfavorable combination of the axial force and bending moments. More generally, global ductility is achieved by the implementation of Strong Column Weak Beam “SCWB” philosophy. In this context, Eurocode 8 suggests the condition shown in Equation (9) must be fulfilled at all seismic beam-to-column joints:

∑ M R c ≥ 1.3 ∑ M R b (9)

The factor 1.3 takes into account the strain hardening and the material overstrength which is obtained generally by the multiplication of 1.1 with γ_{ov} and as a general rule is considered as 1.3. Generally this check is often satisfied at the joint when capacity design is employed in the design.

Eccentrically braced frames as shown in

In this way the stiffness and ductility properties can be in principle adequately calibrated, so leading towards optimal structural solutions. The performances of the structure are strongly dependent on the behavior of the links, require particular care in the design phase [

link (dissipation is guaranteed by yielding in shear), the long link (link dissipate energy by yielding in flexure, see

W v = V p , l i n k × θ p × e (10)

The limit between long and short links corresponds to the situation in which yielding could equally take place in shear or bending, therefore Equation (11) explains the case.

W v = W M ⇒ V p , l i n k × θ p × e = 2 M p , l i n k × θ p ⇒ e = 2 × ( M p , l i n k V p , l i n k ) (11)

For values of e around this limit, significant bending moments and shear forces exist simultaneously and their interaction has to be considered. In Eurocode 8, the value of e for considering a plastic mechanism in shear (short links) is given by Equation (12).

e < e s = 1.6 × ( M p , l i n k V p , l i n k ) (12)

The value of e for considering only a plastic mechanism in bending (long links) is calculated using Equation (13).

e < e L = 3 × ( M p , l i n k V p , l i n k ) (13)

Between these two values e_{s} and e_{L}, links are said to be “intermediate” and the interaction between shear and bending has to be considered. If the typology of the structure is such that the shear and bending moment diagrams are not symmetrical, only one plastic hinge will form if the link is long, therefore Equation (14) takes place.

Description | Eurocodes (EC3/EC8) | AISC/ASCE | Remarks |
---|---|---|---|

Energy dissipation philosophy | EBFs shall be designed so that specific elements or parts of elements called seismic links are able to dissipate energy by the formation of plastic bending and/or plastic shear mechanisms. | EBFs are expected to withstand significant inelastic deformations in the links when subjected to the forces resulting from the motions of the design earthquake. | An almost same criterion is considered |

Rotation capacity (local ductility concept) | Plastic hinge rotation is limited to 35 mrad for structures of DCH and 25 mrad for structures of DCM | Link rotation angle shall not exceed (a) 0.08 radians for links of length 1.6 M_{p}/V_{p} or less and (b) 0.02 radians for links of length 2.6 M_{p}/V_{p} or greater. | For high seismicity it is recommended by both codes to apply ductility concept |

Dissipative members | Plastic Hinges should take place in links prior to yielding or failure elsewhere. | EBFs are expected to withstand significant in-elastic deformations in the links when subjected to forces resulting from the motions of the design earthquake. | Links can be short, long and Intermediate. Which fail due to Shear, bending and bending & Shear respectively. |

If N E D / N p l , R d ≤ 0.15 then Check for Design Resistance of Link is | V E D ≤ V p , l i n k _{ } M E D ≤ M p , l i n k | Effect of axial force on the link, available shear strength need not be considered if P u ≤ 0.15 P y _{ }(LRFD) or P a ≤ 0.15 / 1.5 P y _{ }(ASD) | N_{ED}, M_{ED}& V_{ED} respectively are the design axial force, design bending moment and design shear at both ends of the link. |

Check to achieve global dissipative behaviour of the structure | The maximum overstrength Ω_{i} should not differ from the minimum value Ω by more than 25% | The required strength of each lateral brace at the ends of the link shall be P b = 0.06 M r / h 0 , where h_{0} is the distance flange centroids | Ω i = 1.5 V p , l i n k , i / V E D , i _{}among all short links and minimum value of Ω i = 1.5 M p , l i n k , i / M E D , i _{ }among all intermediate and long links. |

Seismic load reduction factor | A behaviour factor (q) equal to 4 for DCM and 5α_{u}/α_{1} for DCH is provided. | A response modification factor (R) equal to 8.0 for EBFs is given | An almost same criterion is considered |

Overstrength factor | the minimum value of Ω i = 1.5 V p , l i n k , i / V E D , i among all short links, whereas the minimum value of Ω i = 1.5 M p , l i n k , i / M E D , i among all intermediate and long links; | Ω_{o} equal to 2 for EBFs is given | Ω_{o} in EC8 is (1.1γ_{ov}Ω) |

W M = M p , l i n k × θ p (14)

In this case, the limiting length between long and short links corresponds to Equation (15).

⇒ e = ( M p , l i n k V p , l i n k ) (15)

The following rules are allowed by Eurocode 8:

1) The reduction of the elastic design spectrum through a behavior factor (q) equals to 4 for DCM and 6.5 for DCH; 2) The web of the link should not be reinforced with plate, 3) In cases, when Equation (16) holds.

N E d N P l , R d ≤ 0.15 (16)

In cases, when Equation (17) is satisfied.

N E d N P l , R d > 0.15 (17)

Then plastic shear and moment should be reduced by the effect of axial forces in the bracings.

The recommended inelastic rotation limits for different link lengths without restriction on the configuration of the link are; 0.08 radians or 4.6 for Short links, 0.02 radians or 1.15˚ for Long links and for Intermediate links the value is determined by linear interpolation. The criteria that must be satisfied in order to form a global plastic mechanism are similar in frames with eccentric or concentric braces, because they correspond to the same concept. Further, there should be homogenization of the dissipative connections overstrength Ω_{i} over the height of the building for short and long links is calculated using Equation (18) and Equation (19), respectively:

Short links: Ω i = 1.5 ( V p l , R d , i V E d , i ) (18)

Long links: Ω i = 1.5 ( M p l , R d , i M E d , i ) (19)

The minimum value of Ω_{i} should be used in the design, further the maximum value of Ω_{i} should not differ from the minimum by more than 25%. Ω_{i} will ensure that yielding occurs simultaneously at several places over the height of the building, and a global mechanism is formed. The beams, columns, and connections are “capacity designed” relative to the real strengths of the seismic links.

One of the main concern of steel MRFs is their high susceptibility to large lateral displacements (lateral stiffness) during severe earthquakes, therefore needs special attention while designing. In order to limit interstorey drift, the issues due to geometric nonlinearities and brittle fracture of beam-to-column connections are mitigated and therefore excessive damage to non-structural elements is avoided. Therefore as an alternative, to many practical and economic issues involved, engineers are increasingly turning to the use of concentrically braced steel frames as a structure’s lateral load resisting system. Steel concentrically braced frames are assumed and recommended to be strong, stiff and ductile. The quality of the seismic response of these frames is determined by the performance of the brace. For achieving a good performance in cross bracing system the brace must behave as a structural fuse thus should fail prior to any other component of the frame. This is important because although the frame may sustain significant damage during an earthquake, it is expected to remain stable and the building must be capable of resisting gravity loads and withstanding aftershocks without collapse.

Concentrically braced frames as shown in

A similar approach like the one for MRFs is defined by Eurocode 8 for concentric braced frames. In this case it is aimed to obtain a ductile behavior by imposing that the yielding of diagonal members occurs before premature failure of beams, columns and connections (capacity design approach) [

λ ¯ ≤ 2.0 is used to ensure satisfactory behavior under cyclic loading, where λ ¯ is defined as the square root of the ratio between the plastic resistance N p l , R d and the Eulerian buckling load N c r of the diagonal.

d) A minimum allowable value for the non-dimensional slenderness λ ¯ of diagonals is given by λ ¯ > 1.3.

e) In the case of cross bracing configurations (X-CBFs), devoted to avoid overloading of columns in the pre-buckling stage of compressed diagonal, i.e. when the actual structural scheme is the Tension/Compression one; where Ω_{i} is the diagonal overstrength coefficient for the i^{th} diagonal members of the considered braced frame, defined as the axial strength capacity to demand ratio, given by Equation (20).

Ω i = ( N p l , R d , i N E d , i ) (20)

A maximum allowable value for the difference between the maximum (Ω_{max}) and the minimum (Ω_{min}) values of the diagonal overstrength coefficients Ω_{i}, according to Equation (21).

Ω max Ω min ≤ 1.25 (21)

Equation (21) is devoted to obtain a uniform distribution of plastic demand along the building height, thus reducing the potential for damage concentration and eventual soft-storey mechanisms;

f) The amplification of design axial forces in beam and columns (non-dissipative elements) through the system overstrength factor Ω.

The paper has dealt initially with the importance of seismic codes in general and particularly in Pakistan. From past earthquakes for example Quetta 1935, it is revealed that steel structures performed well within the limited use of steel frame structures; nevertheless their trend is still not so common in Pakistan. Useful and important steel structures have been constructed before the independence of Pakistan as mentioned in this paper. Furthermore, the use of most advance code such as Eurocode 8 is convenient to be used in the country as the defined spectrum of the code is based on the seismic zonation which is presently available for all the regions of the country. Common parameters that are normally adopted by seismic codes are given and the importance of over-strength factor especially the elastic one that was highlighted gives a clear understanding for the designer involved in the seismic design of structures. In addition, conventional seismic load resisting systems were illustrated and their design criteria according to Eurocode 8 were provided with synoptic tables for the counterpart US code. The procedure of Eurocode 8 is explained through the use of capacity design approach in which it is evident that the calculation of overstrength required some steps and iterations whereas in the US codes this factor is generally fixed for all the lateral load resisting systems. In addition, the behavior factor in Eurocode is less compared to the suggested value of response modification factor in the US codes. Furthermore, it is to be underline that the capacity design rule of Eurocode 8 requires some iteration as calculation of overstrength factor is involved and this becomes more complex when the deformability needs to be satisfied. It is believed and concluded that the lateral load resisting systems that dissipate more seismic energy are of prime importance and therefore need attention to be incorporated in the plastic design.

Naqash, M.T. and Alluqmani, A. (2018) Codal Requirements Using Capacity Design Philosophy, and Their Applications in the Design of Steel Structures in Seismic Zones. Open Journal of Earthquake Research, 7, 88-107. https://doi.org/10.4236/ojer.2018.72006

q_{m}_{,}_{r}: Ductility reduction factor

V_{e}: Elastic base shear

V_{y}: Base shear obtained at the arrival of first plastic hinge_{ }

W_{r}: Redundancy factor

V_{u}: Ultimate base shear

W_{E}: Elastic overstrength factor

V_{d}: Design base shear calculated from the prescribed Code

W_{E}_{,}_{r}: Global overstrength factor

q_{m}: Reserve ductility

R: Response modification factor

q: Behaviour factor

α_{u}: Multiplier of horizontal seismic design action at formation of global plastic

mechanism

α_{1}: Multiplier of horizontal design seismic action at formation of first plastic hinge in the system

γ_{c}: Partial factor for concrete

γ_{Rd}: Model uncertainty factor on design value of resistances in the estimation of capacity design action effects, accounting for various sources of overstrength

γ_{s}: Partial factor for steel

M_{Ed}: Design bending moment from the analysis for the seismic design situation

M_{pl}_{,}_{RdA}: Design value of plastic moment resistance at end A of a member

M_{pl}_{,}_{RdB}: Design value of plastic moment resistance at end B of a member

V_{Ed}_{,i}, M_{Ed}_{,i}: Design values of the shear force and of the bending moment in Link i in the seismic design situation

V_{p}_{,link,i}M_{p}_{,link,i}: Shear and bending plastic design resistances of link i

ΣM_{Rc} and M_{Rb}: Sum of the design values of the moments of resistance framing the joint of the columns and beams respectively

N_{Ed}: Design axial force from the analysis for the seismic design situation

V_{Ed}: Design shear force from the analysis for the seismic design situation

N_{Ed}_{,E}: Axial force from the analysis due to the design seismic action alone

N_{Ed}_{,G}: Axial force due to the non-seismic actions included in the combination of actions for the seismic design situation

N_{pl}_{,Rd}: design value of yield resistance in tension of the gross cross-section of a member

V_{pl}_{,Rd}: Design value of shear resistance of a member

N_{Rd}(M_{Ed},V_{Ed}): Design value of axial resistance of column or diagonal taking into account the interaction with the bending moment M_{Ed} and the shear V_{Ed} in the seismic situation

Ω: Multiplicative factor on axial force N_{Ed}_{,E} from the analysis due to the design seismic action, for the design of the non-dissipative members in concentric or eccentric braced frames