# Seismic Behaviour of EC8-Compliant Moment Resisting and Concentrically Braced Frames

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Seismic design of steel frames according to EN 1998-1: Critical discussion

#### 2.1. Moment resistring frames (MRF)

_{Ed}, N

_{Ed}and V

_{Ed}are the design forces, and M

_{pl,Rd}, N

_{pl,Rd}and V

_{pl,Rd}are design resistances in accordance with EN 1993:1-1 [25].

- N
_{Ed,G}, M_{Ed,G}, V_{Ed,G}are the design forces in the column due to the non-seismic action included in the combination of actions for the seismic design situation; - N
_{Ed,E}, M_{Ed,E}, V_{Ed,E}are the seismic induced effects; - γ
_{ov}is the overstrength factor accounting for randomness of yield strength according to EC8; - Ω is minimum of ${\Omega}_{i}=\frac{{M}_{pl,Rd,i}}{{M}_{Ed,E,i}}$ of all beams where dissipative zones are located;
- M
_{pl,Rd,i}is the plastic bending resistance of the i-th beam; - M
_{Ed,E,i}is the bending moment due to the seismic loads in the i-th beam.

_{Ed}resulting from the structural analysis should satisfy the following expression:

_{r}is the design interstorey drift, h is the story height, and v is a reduction factor accounting for the lower return period of the seismic action associated with the serviceability limit state, even depending on the importance class of the building. The factor K depends on the type of infill walls and it is equal to 0.05, 0.075, and 0.01 for brittle, ductile, and non-structural elements fixed in a way so as not to interfere with (or without) non-structural elements, respectively.

_{tot}is the total gravity load, V

_{tot}is the seismic shear at the storey under consideration, d

_{r}is the interstorey drift (given by the elastic inter-storey drift by the behaviour factor), and h is the storey height. If $\theta \le 0.1$, second order effects can be disregarded; conversely if $0.1<\theta \le 0.2$, the second-order effects may approximately be taken into account by multiplying the relevant seismic action effects by a factor equal to 1/(1–θ). The value of the sensitivity coefficient θ should not exceed 0.3.

#### 2.2. Chevron concentrically braced frames (CCBF)

_{pl,br,Rd}is the plastic axial strength, χ is the buckling reduction factor calculated according to EN 1993:1-1 [25], and N

_{Ed,br}is the axial force acting on the element.

- N
_{pl,Rd}(M_{Ed}) is the design resistance to axial force of the column calculated in accordance with EN 1993:1-1 [25], taking into account the interaction with the design value of bending moment, M_{Ed}, in the seismic design situation; - N
_{Ed,G}is the axial force in the column due to the non-seismic actions included in the combination of actions for the seismic design situation; - N
_{Ed,E}is the axial force in the column due to the design seismic action; - γ
_{ov}is the material overstrength factor; - Ω is the minimum overstrength ratio Ω
_{i}= N_{pl,bRd,i}/N_{Ed,br,i};

## 3. Numerical assessment of Eurocode 8-compliant design rules

#### 3.1. Design and modelling assumptions

_{k}) and live loads (Q

_{k}) were assumed equal to 5.00 kN/m

^{2}and 3.00 kN/m

^{2}, at each storey. The inertial effects in the seismic design situation were evaluated according to EC8. A reference peak ground acceleration equal to a

_{gR}= 0.25g a type C soil, a type 1 spectral shape was assumed.

#### 3.2. Seismic performance evaluation

- the plastic redistribution parameter α
_{u}/α_{y}accounting for the system overstrength due to redundancy. The parameter α_{y}is the multiplier of the horizontal seismic design action to reach the first plastic resistance in the structure and α_{u}is the multiplier of the horizontal seismic design action necessary to form a global mechanism corresponding to the maximum shear capacity (V_{max}). - The coefficient ${\Omega}_{0}={V}_{y}/{V}_{d}$ representing the design overstrength, namely the ratio between actual capacity (V
_{y}) respect to the design shear (V_{d}).

_{max}/V

_{d}) is similar for both 3 and 6-storey frames, the larger influence of design overstrength Ω

_{0}can be recognized for the taller structure. This feature can be explained considering that the low-rise frame is less influenced by the deformation-related requirements and thus it exhibits limited design overstrength (smaller Ω

_{0}values) and better system redundancy (larger α

_{u}/α

_{1}) with respect to the taller frame.

_{max}/V

_{y}) was equal to 6.16.

_{0}(ranging within [3.05, 4.41]), thus confirming large lateral overstrength due to the application of the codified design rules. Equipping multiple bays with chevron concentric bracing provides satisfactorily redundancy with values of plastic redistribution parameter α

_{u}/α

_{1}ranges within [1.34, 1.66].

_{y}the axial deformation corresponding to the yielding), with reference to the three limit states DL, SD, and NC. Results depicted in Figure 8a confirm the requirement devoted to control capacity-to-demand ratio is not adequate to avoid a soft-storey mechanism and to assure the uniform distribution of plastic deformation along the building height. Indeed, a cantilever-like displacement profile is recognized for both the 3 and 6-storey buildings, with severe damage concentration solely at the roof (see Figure 7b). Very poor plastic engagement of braces under tension can be recognized up to the NC limit states.

## 4. Conclusive Remarks

- Both moment resisting and concentrically braced frames designed in compliance to EC8 are characterized by large lateral overstrength due to the application of codified design requirements.
- The design process of MRFs is merely ruled by the deformation-related requirements: The need to fulfil the drift limitations at the serviceability limit state and the stability requirement (against second order effects) at the ultimate limit state forces the designer to select massive and over-resistant structural members, as shown in this study for both 3- and 6-storey frames.
- The design overstrength of CBFs is mostly derived from the interrelation and juxtaposition of the capacity-to-demand variation requirement and the maximum allowable brace slenderness ratio; to contemporarily fulfil these rules, the designer is forced to significantly oversize diagonals along the building height, as shown for both 3- and 6-storey frames.
- Results from numerical analyses confirm that the examined MRFs and CBFs behave almost elastically up to the NC limit state. Very poor plastic engagement of dissipative zones and energy dissipation capacity is recognized for both 3- and 6-storey frames.
- The overstrength variation requirement is not adequate to avoid a soft-storey mechanism in CBFs. The examined frames exhibited a cantilever displacement shape profile with severe damage concentration solely in the diagonals at upper stories.
- The obtained numerical results for both MRFs and CCBFs are consistent with what was observed in recent literature, confirming the need to amend EC8. However, a larger number of cases and parameters should be investigated to validate the rules for the next code.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**Results from IDAs for examined CBFs: (

**a**) Interstorey drift ratio; (

**b**) braces ductility demand.

Gravity Members | Concentrically Braced Bays | ||||
---|---|---|---|---|---|

Storey | Column | Beam | Column | Beam | Brace (dxt) |

S355 | S355 | S355 | S355 | S355 | |

I | HEB240 | IPE300 | HEM300 | HEB450 | 159 × 8 |

II | HEB200 | IPE300 | HEB300 | HEB450 | 159 × 8 |

III | HEB200 | IPE300 | HEB300 | HEB340 | 133 × 6.3 |

Gravity Members | Concentrically Braced Bays | ||||
---|---|---|---|---|---|

Storey | Column | Beam | Column | Beam | Brace (dxt) |

S355 | S355 | S355 | S355 | S355 | |

I | HEB300 | IPE300 | HD_400 × 551 | HEM500 | 193.7 × 12.5 |

II | HEB300 | IPE300 | HD_400 × 551 | HEM500 | 177.8 × 14.2 |

III | HEB260 | IPE300 | HD_400 × 347 | HEM500 | 177.8 × 12.5 |

IV | HEB260 | IPE300 | HD_400 × 347 | HEB550 | 168.3 × 12.5 |

V | HEB220 | IPE300 | HEB400 | HEB450 | 159 × 8 |

VI | HEB220 | IPE300 | HEB400 | HEB360 | 139.7 × 6.3 |

Storey | First Bay | Second Bay | Third Bay | |||
---|---|---|---|---|---|---|

Column | Beam | Column | Beam | Column | Beam | |

S355 | S355 | S355 | S355 | S355 | S355 | |

I | HE500B | IPE600 | HE600B | IPE600 | HE600B | IPE600 |

II | HE450B | IPE600 | HE600B | IPE600 | HE600B | IPE600 |

III | HE450B | IPE550 | HE450B | IPE550 | HE450B | IPE550 |

Storey | First Bay | Second Bay | Third Bay | |||
---|---|---|---|---|---|---|

Column | Beam | Column | Beam | Column | Beam | |

S355 | S355 | S355 | S355 | S355 | S355 | |

I | HE650M | IPE750 × 147 | HE700M | IPE750 × 147 | HE700M | IPE750 × 147 |

II | HE650M | IPE750 × 147 | HE700M | IPE750 × 147 | HE700M | IPE750 × 147 |

III | HE650B | IPE750 × 137 | HE650M | IPE750 × 137 | HE650M | IPE750 × 137 |

IV | HE650B | IPE750 × 137 | HE650M | IPE750 × 137 | HE650M | IPE750 × 137 |

V | HE450B | IPE600 | HE650B | IPE600 | HE650B | IPE600 |

VI | HE450B | IPE600 | HE650B | IPE600 | HE650B | IPE600 |

Earthquake Name | Date | Station Name | Station Country | Magnitude Mw | Fault Mechanism |
---|---|---|---|---|---|

Alkion | 24.02.1981 | Xylokastro-O.T.E. | Greece | 6.6 | Normal |

Montenegro | 24.05.1979 | Bar-Skupstina Opstine | Montenegro | 6.2 | Reverse |

Izmit | 13.09.1999 | Yarimca (Eri) | Turkey | 5.8 | Strike–Slip |

Izmit | 13.09.1999 | Usgs Golden Station Kor | Turkey | 5.8 | Strike–Slip |

Faial | 09.07.1998 | Horta | Portugal | 6.1 | Strike–Slip |

L’Aquila | 06.04.2009 | L’Aquila - V. Aterno-Aquila Park In | Italy | 6.3 | Normal |

Aigion | 15.06.1995 | Aigio-OTE | Greece | 6.5 | Normal |

Alkion | 24.02.1981 | Korinthos-OTE Building | Greece | 6.6 | Normal |

Umbria-Marche | 26.09.1997 | Castelnuovo-Assisi | Italy | 6.0 | Normal |

Izmit | 17.08.1999 | Heybeliada-Senatoryum | Turkey | 7.4 | Strike–Slip |

Izmit | 17.08.1999 | Istanbul-Zeytinburnu | Turkey | 7.4 | Strike–Slip |

Ishakli | 03.02.2002 | Afyon-Bayindirlik ve Iskan | Turkey | 5.8 | Normal |

Olfus | 29.05.2008 | Ljosafoss-Hydroelectric Power | Iceland | 6.3 | Strike–Slip |

Olfus | 29.05.2008 | Selfoss-City Hall | Iceland | 6.3 | Strike–Slip |

Structures | V_{d} | V_{y} | V_{max} | α_{u}/α_{y} | Ω_{0} | V_{max}/V_{d} | |
---|---|---|---|---|---|---|---|

kN | kN | kN | - | - | - | ||

3-storey | First mode | 995.58 | 3950.00 | 6136.66 | 1.55 | 3.97 | 6.16 |

Masses | 995.58 | 4200.00 | 6743.97 | 1.61 | 4.22 | 6.77 | |

6-Storey | First mode | 1361.79 | 7450.00 | 9247.89 | 1.24 | 5.47 | 6.79 |

Masses | 1361.79 | 8150.00 | 10406.35 | 1.28 | 5.98 | 7.64 |

Structures | V_{d} | V_{y} | V_{max} | α_{u}/α_{1} | Ω_{0} | V_{max}/V_{d} | |
---|---|---|---|---|---|---|---|

kN | kN | kN | - | - | - | ||

3-storey | First mode | 1484.99 | 4530.00 | 7510.00 | 1.66 | 3.05 | 5.06 |

Masses | 1484.99 | 5570.00 | 7640.00 | 1.37 | 3.75 | 5.14 | |

6-Storey | First mode | 2945.86 | 12800.00 | 17100.00 | 1.34 | 4.35 | 5.80 |

Masses | 2945.86 | 13000.00 | 19500.00 | 1.50 | 4.41 | 7.64 |

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**MDPI and ACS Style**

Costanzo, S.; Tartaglia, R.; Di Lorenzo, G.; De Martino, A.
Seismic Behaviour of EC8-Compliant Moment Resisting and Concentrically Braced Frames. *Buildings* **2019**, *9*, 196.
https://doi.org/10.3390/buildings9090196

**AMA Style**

Costanzo S, Tartaglia R, Di Lorenzo G, De Martino A.
Seismic Behaviour of EC8-Compliant Moment Resisting and Concentrically Braced Frames. *Buildings*. 2019; 9(9):196.
https://doi.org/10.3390/buildings9090196

**Chicago/Turabian Style**

Costanzo, Silvia, Roberto Tartaglia, Gianmaria Di Lorenzo, and Attilio De Martino.
2019. "Seismic Behaviour of EC8-Compliant Moment Resisting and Concentrically Braced Frames" *Buildings* 9, no. 9: 196.
https://doi.org/10.3390/buildings9090196