4.2 Ground Motion (Horizontal and Vertical)
The horizontal ground motions in longitudinal and transverse directions of bridge cause most damaging effects in earthquakes. The vertical motion in bridge can arise due to vertical ground motion and vertical motion in cantilever spans arising due to horizontal motion of piers. The effect of vertical ground motions is important in bridges with long spans, prestressed concrete spans, bridges with long horizontal cantilevers and where stability is the criteria of design. The vertical ground motions can be quite significant in near field earthquakes.
4.2.1
4.2.1 Components Components of of Ground Ground MotionMotion
The characteristics of seismic ground motion expected at any location depend upon the magnitude of earthquake, depth of focus, distance of epicenter and characteristics of the path through which the seismic wave travels. The random ground motion can be resolved in three mutually perpendicular directions. The components are considered to act simultaneously, but independently and their method of combination is described in Section 4.1.2
Section 4.1.2
In zones IV and V the effects of vertical components shall be considered for all elements of the bridge. However, the effect of vertical component may be omitted for all elements in zone II and III, except for the following cases:
(a) prestressed concrete s upers tructure (b) bearings and linkages
(c) horizontal cantilever structural elements (d) for stability checks and
(e) bridges located in the near field regions 4.2.2 Combination of Component Motions
Guidelines For Seismic Design of Bridges
The seismic forces shall be assumed to come from any horizontal direction. For this purpose two separate analyses shall be performed for design seismic forces acting along two orthogonal horizontal directions. The design seismic force resultants (i.e. axial force, bending moments, shear forces, and torsion) at any cross-section of a bridge component resulting from the analyses in the two orthogonal horizontal directions (x,z) shall be combined as below:
a) ±r 1±0.3r 2
b) ±0.3r 1±r 2
Where,
r 1= Force resultant due to full design seismic force along x direction.
r 2 = Force resultant due to full design seismic force along z direction. When vertical seismic forces are also considered, the design seismic force resultants at any cross section of a bridge component shall be combined as below:
a) ±r 1±0.3r 2 ±0.3r 3
b) ±0.3r 1±r 2 ±0.3r 3
c) ±0.3r 1± 0.3r 2 ±r 3
Where,
r 1and r 2 are as defined above and r 3is the force resultant due to full design
seismic force along the vertical direction.
Note: The earthquake motion have been combined for all cases irrespective of whether structure is orthogonal/skew/curved/irregular.
4.2.3 Vertical component of Seismic action 4.2.3 Vertical component of Seismic action
Analysis for vertical seismic action requires time period of superstructure in vertical direction. Time period for the superstructure has to be worked out separately using the property of the superstructure, in order to estimate the seismic acceleration coefficient (Sa/g) for vertical acceleration. It can be obtained by free vibration analysis of superstructure using standard structural analysis software. However, for simply supported superstructure with nearly uniform flexural rigidity, the fundamental time period Tv, for vertical motion can be estimated using the expression:
Eq. 4.1
Where,
l is the span metres, m is the mass per unit length (N-m), and EI is the flexural rigidity of the superstructure in N-m2 .
EI may be estimated for simply supported span as (l 3 /48 ▲), where ▲is
Guidelines For Seismic Design of Bridges
The seismic zone factor for vertical ground motions may be taken as two-thirds of that for horizontal motions.
4.2.4
4.2.4 Design Forces Design Forces for for elements of elements of Structures and Structures and use use of of response reduction response reduction factorfactor
The forces on various members obtained from the elastic analysis of bridge structure are to be divided by Response Reduction Factor given inTable 4.1Table 4.1 before combining with other forces as per load combinations given inTable 1 & Table B.1 to B.4Table 1 & Table B.1 to B.4 of IRC: 6 - 2017 for working stress approach and limit state design respectively.
Table 4.1 Response Reduction Factors (R) Table 4.1 Response Reduction Factors (R)
BRIDGE COMPONENT BRIDGE COMPONENT 'R' WITH 'R' WITH DUCTILE DUCTILE DETAILING DETAILING 'R' WITHOUT 'R' WITHOUT DUCTILE DUCTILE DETAILING DETAILING (for Bridges in (for Bridges in Zone II only) Zone II only) Substructure Substructure
(i) Masonry / PCC Piers, Abutments 1.0 1.0 1.01.0
(ii) RCC Wall piers and abutments transverse
direction (where plastic hinge cannot develop) 1.0 1.0 1.01.0
(iii) RCC Wall piers and abutments in longitudinal
direction (where hinges can develop) 3.0 3.0 2.52.5
(iv) RCC Single Column 3.0 3.0 2.52.5
(v) RCC/PSC Frame ( Refer Note VI) 3.0 3.0 2.52.5
(vi) Steel Framed 3.0 3.0 2.52.5
(vii) Steel Cantilever Pier 1.5 1.5 1.01.0
Bearings and Connections (see note(V) also) 1.0 1.0 1.01.0
Stoppers (Reaction Blocks)
Those restraining dislodgement or drifting away of bridge elements.
1.0 1.0
1.0 1.0
Notes: Notes:
i. Bracing and bracing connection primarily carrying horizontal seismic force for steel and steel composite superstructure, R factor shall be taken as 3 where ductile detailing is adopted.
ii. Response reduction factor is not to be applied for calculation of displacements of elements of bridge as a whole.
Guidelines For Seismic Design of Bridges
iii. When elastomeric bearings are used to transmit horizontal seismic forces, the response reduction factor (R) shall be taken as1.0 for all substructurefor all substructure. In case substructure and foundation will remain in elastic state, no ductile detailing is required.
iv. Ductile detailing is mandatory for piers of bridges located in seismic zones III, IV and V where plastic hinges are likely to form and when adopted for bridges in seismic zone II, for which “R value with ductile detailing” as given inTable 4.1Table 4.1 shall be used.
v. Bearings and connections shall be designed to resist the lesser of the following forces, i.e., (a) design seismic forces obtained by using the response reduction factors given in Table 4.1
Table 4.1 and (b) forces developed due to over strength moment when hinge is formed in the substructure. For calculation of overstrength moments, (Mo) shall be considered as Mo=γo MRd γo = Overstrength factor & MRD is plastic moment of section, for detail refer
Chapter 7
Chapter 7 . Over-strength factors forConcrete members: γo= 1.35 & for Steel members: γo = 1.25
vi.
vi. The shear force for over strength moments in case of cantilever piers shall be calculated as MRD/h, “h” is height shown in Fig 7.1 in Chapter 7in Fig 7.1 in Chapter 7. In case of portal type pier capacity
of all possible hinges need to be considered..
vii. Capacity Design should be carried out where plastic hinges are likely to form.