Dynamic Analysis of Setback Steel Moment Resisting Frame on Sloping Ground wi...
Evaluate Response Reduction Factor for Industrial Buildings
1. EVALUATION OF RESPONSE REDUCTION FACTOR FOR INDUSTRIAL
BUILDING HAVING STEEL TRUSSES ON RC COLUMNS
PREPARED BY:
Avi A. Patel (MS007)
GUIDED BY:
PROF. D.G. Panchal
DEPARTMENT OF CIVIL ENGINEERING
DHARMSINH DESAI UNIVERSITY
NADIAD – 387001
APRIL - 2016
2. CONTENTS
INTRODUCTION
AIM AND SCOPE OF WORK
LITERATURE REVIEW
EVALUATION OF RESPONSE REDUCTION FACTOR
SAMPLE PROBLEM
COMPARATIVE STUDY AND RESULTS
CONCLUSION
FUTURE SCOPE OF WORK
REFERENCES
2
3. INTRODUCTION
In the past, the structure were designed just for gravity loads only, seismic analysis is
a recent development.
Seismic analysis is a subset of structural analysis and is the calculation of the
response of a structure to earthquakes.
It is part of the process of structural design, earthquake engineering and retrofit in
regions where earthquakes are prevalent.
There are different method of seismic analysis.
3
4. Seismic analysis
Linear analysis
Non linear
analysis
static dynamic static dynamic
Seismic
coefficient
Response spectrum,
Time history
Pushover
analysis
IDA,
Nonlinear time
history
Vb = Ah x w Ah =
Z
2
x
I
𝐑
x
Sa
g
4
Seismic
coefficient
5. RESPONSE REDUCTION FACTOR
As per the IS 1893 definition, R factor which is used to reduce actual base shear
forces to design lateral forces, because at design basis earthquake shaking (DBE)
structure should remain in elastic response.
The response of the structure will be linear until yielding takes place, but as soon as
yielding occurs at any section the behavior of structure is inelastic.
It would be too costly to design a structure based on the elastic spectrum.
To reduce the seismic loads, IS 1893 introduced RESPONSE REDUCTION FACTOR.
This reduction can be made, only if adequate ductility is developed through proper
design and proper detailing on the elements.
5
6. R factor reflects the capability of the structure to dissipate energy through inelastic
behavior.
It is used to reduced the design forces in earthquake resisting design and account for
over strength and ductility of the structure.
Over strength is develop because the maximum lateral strength of the structure is
always exceed its design strength.
Once it enters the inelastic phase, it is capable of resisting and absorbing the large
amount of seismic energy.
Hence, seismic codes introduce a reduction in design loads, taking benefit of fact
that structure posses over strength and ductility.
6
7. Horizontal
Load
Δ
Δmax
Fu
Fy
Fdes
ΔyΔw
Fel
Due to
Over strength
Due to
Redundancy
Due to
Ductility
0
Design force
Maximum Load Capacity
Non linear
Response
First significant
yield
Linear Elastic
Response
Load at First
Yield
Maximum force if structure
remains elastic
TotalHorizontalLoad
Roof Displacement (Δ)
7
8. BACKGROUND OF DISSERTATION
Composite industrial building (steel truss on RC columns) are commonly used in
urban areas as the dominant mode of industrial construction, as RC columns costs
much less then the steel columns.
Indian standard doesn’t give any guideline regarding to response reduction factor’s
value of composite industrial building, and that motivates us to find the response
reduction factor for this kind of structure.
8
9. AIM AND SCOPE OF WORK
This dissertation aims to evaluate response reduction factor of composite industrial
building having RC column with steel trusses for single bay and multi bay.
Building will be situated in zone-5, located in Bhuj, terrain is open with well
scattered obstruction having height generally between 1.5m to 10m.
Roofing material are selected as corrugated A.C. sheets.
For the comparative study single bay truss system are selected with 15,18 and 21m
of span , and 24,30,36 and 42m of length.
For multi bay truss system, span will be twice of the single bay and rest dimensions
are same.
9
10. Nonlinear analysis of each model is carried out, so that nonlinear behavior of the
industrial building is observed due to changes in the geometry.
Performance based evaluation is carried out using non linear static (pushover)
analysis.
Nonlinear models are prepared and pushover analysis is performed in SAP-2000.
Value of response reduction factor is calculated for each model.
10
11. LITERATURE REVIEW
Background of R factor
Response modification factor were first proposed by the applied technology council
in 1978.
The base shear vs roof displacement relationship were established of concentrically
braced frame by uang and bertero in 1986 and eccentrically braced frame by
whittaker in 1987.
Using this data Berkeley researchers proposed splitting R into three factor, they
account for contribution from reserved strength, ductility and viscous damping as
follows,
R = Rs x Rμ x Rξ
11
12. Much research by (ATC,1982; freeman,1990;ATC,1995) has been completed since
first formulation for R is proposed, and give new formulation of R as follows,
R = Rs x Rμ x RR
Here, RR is the redundancy factor.
This formulation with the exception of the redundancy factor is similar to those
proposed by the Berkley researchers.
A fourth factor, the viscous damping factor was included in the new formulation
primarily to account for response reduction provided by supplemental viscous
damping devices.
12
13. Minnu M M (MAY-2014) (NIT-ROURKELA)
The frames with number of story 2,4,8 and 12 with four bay is designed and details
as SMRF and OMRF as per IS:1893 (2000)
The response reduction factors obtained shows that both the SMRF and OMRF
frames failed to achieve the respected target value of response reduction factor
recommended by IS:1893 (2000) marginally.
It was also found that shorter frames exhibit higher R factor and as the height of the
frame increase R factor is decreases.
For both SMRF and OMRF frames it is found that the over strength factors exhibits a
decreasing trend as the number of story increases.
It is found that the ductility factor do not shows any trend with variation in number of
stories for both SMRF and OMRF.
13
14. IS: 875-1987(part-3)
The code is based on Design Loads For Buildings And Structures (other than
earthquake). The code provide the clauses for
Design Wind Speed (Cl-5.3)
Design Wind Pressure (Cl-5.4)
External Pressure Coefficients for walls of rectangular clad building (Table-4)
External Pressure Coefficients for pitched roof of rectangular clad building
(Table-5)
14
15. Sr.no. LATERAL LOAD RESISTING SYSTEM (R)
BUILDING FRAME SYSTEMS
1 Ordinary RC moment resisting frame 3
2 Special RC moment resisting frame 5
3 Steel frame with
concentric braces 4
eccentric braces 5
4 Steel moment resisting frame as design as per sp6 5
BUILDING WITH SHEAR WALLS
5 Load bearing masonry wall buildings
(a) unreinforced 1.5
(b)Reinforced with horizontal RC bands 2.5
(c)Reinforced with horizontal RC bands and vertical bars at corner of rooms and
jambs of opening
3
IS: 1893-PART1(2000)
15
16. EVALUATION OF RESPONSE REDUCTION
FACTOR
Evaluation of response reduction factor is carried out by force-displacement
behavior of building.
This relationship describe the response of the building frame subjected to
monotonically increasing displacements.
To achieve yield forces and yield displacement this non linear relation is often
approximated by an idealized bilinear relationship.
Two bilinear approximation methods are widely used, both the methods will
generally produce similar results.
16
17. (1) Pauley and priestley
• Elastic stiffness is based on the secant stiffness of the
frame, calculated from the force displacement curve at
the force corresponding to 0.75 Vy.
(2) Equal energy concept
• This method is assumes that the area enclosed by the
curve above the bilinear approximation is equal to the
area enclosed by the curve below the bilinear
approximation.
17
18. Pushover analysis is a static nonlinear procedure to analyze
the seismic performance of a building.
In this method, analysis is carried out under permanent
vertical loads and gradually increasing lateral loads to
estimate deformation and damage pattern of structure.
(I) Force Controlled
(II) Displacement Controlled
To obtain the exact response of the building or force-displacement behavior of
building, it is recommended to perform nonlinear analysis.
Pushover analysis
18
19. Apply gravity loads and conduct static analysis:
DL+(0.25 OR 0.3)LL
BaseShear,V
Roof Displacement, d
19
Apply lateral loads to the structure in proportion to the selected load pattern:
BaseShear,V Roof Displacement, d
d
V
Moment
Curvature
Calculate member forces under the applied lateral load and gravity load combination
– check for yielding in the members:
BaseShear,V Roof Displacement, d
d
V
Moment
Curvature
Record the base shear V and roof displacement d:
BaseShear,V Roof Displacement, d
d
V
Moment
Curvature
Repeat Steps to for increments of lateral load:
BaseShear,V Roof Displacement, d
d
Moment
Curvature
⑥ Repeat Steps to for increments of lateral load:
BaseShear,V Roof Displacement, d
d
Moment
Curvature
⑦ Repeat Steps to for increments of lateral load:
BaseShear,V Roof Displacement, d
d
Moment
Curvature
⑧ Repeat Steps to for increments of lateral load:
BaseShear,V Roof Displacement, d
d
Moment
Curvature
20. PERFORMANCE CRITERIA
Structural performance level
Immediate Occupancy Nonstructural components with minor crack
Life Safety Significant Damage to the non structural
member and crack will be generated in
structural member.
Collapse prevention Structural components are significantly
damaged
Collapse Structure losses stability
Force-deformation Relationship
as per FEMA-356
20
21. KEY COMPONENTS OF ‘R’
Rs is a reserved strength of the building to resist lateral forces within the elastic
range upto the yield takes place.
Using nonlinear static analysis, construct the base shear vs roof displacement
relationship of the structure, calculate maximum capacity of the structure (Vo).
The reserve strength of the building is equal to the ratio of Vo to Vd.
Rs =
𝑉𝑜
𝑉𝑑
Over Strength Factor :-
Over strength factor, ductility factor and redundancy factor are key components of
response reduction factor.
R = Rs x Rμ x RR
21
22. The ability of the building frame to be displaced beyond the elastic limit, while
resisting significant load and absorbing energy by inelastic behavior is termed as
ductility.
Displacement ductility is defined as the ratio of ∆m to ∆y.
μ =
∆𝑚
∆𝑦
Newmark and hall (1982)
The relationship derived for Rμ as a function of μ, for short, intermediate and long
period structures is presented below:
Ductility Factor :-
22
23. Miranda and bertero (1994)
Miranda and Bertero (1994) summarized and reworked the Rμ - μ - T relationships
developed by a number of researchers including Newmark and Hall (1982), Riddell
and Newmark (1979), and Krawinkler and Nassar (1992), in addition to developing
general Rμ - μ - T equations for rock, alluvium, and soft soil sites.
The equation was obtained from a study of 124 ground motions recorded on a wide
range of soil conditions.
The expressions for the period-dependent force reduction factors Rμ are given by:
23
24. 24
Where Φ is calculated from different equations for rock, alluvium and soft sites as
shown below:
where, Tg is the predominant time period of the ground motion.
25. The function of this factor is to quantify the improve reliability of seismic framing
system that use multiple lines of vertical seismic framing in each principle direction
of building.
The value of redundancy factor is given in ATC-19 (table 4.3)
Redundancy Factor :-
Lines of vertical seismic framing Draft redundancy factor
2 0.71
3 0.86
4 1
25
26. SAMPLE PROBLEM
BUILDING PLAN DIMENSION (15X24)m
EAVES HEIGHT 6m
RIDGE HEIGHT 9m
SPACING OF TRUSS 6m
LOCATION OF BUILDING BHUJ
EXPECTED LIFE OF THE STRUCTURE 50 year
TERREIN TYPE Open with well scattered
obstructions having
height generally
between 1.5 to 10 m
TOPOGRAPHY FACTOR (K3) 1
SECTIONS TO BE USE FOR TRUSS
AND PURLINS
INDIAN STANDARD
CHANNEL SECTIONS
TYPE OF ROOFING A.C. sheets
PERMIABILITY Low
26
15m
6m
12m
12m
12m
12m
3m
28. Desiding geometry of truss: (Howe Pitched Truss)
Height of truss 3m
Truss angle 21.80˚
Property of A.C. sheet
thickness 6 mm
weight 0.130 KN/m2
width 1.4 m
28
29. LOAD CALCULATIONS
DEAD LOAD CALCULATION
Considering weight of roofing material=0.130kN/m2
spacing of purlin =1.4 m
Spacing of truss =6 m
A.C. sheet roofing load = 0.13 kN/m2
= 0.13 kN/m2 X 1.4 m X 6 m
= 1.092 kN
Weight of purlin = 0.162 kN/m
= 0.162kN/m2 X 6 m
= 0.972 kN
Self weight of the truss = {(span/3)+5} kg/m2
= {(15/3)+5} X(10/1000) kN/m2
= 0.1 kN/m2
= 0.1 kN/m2 X 1.299 m X 6 m
= 0.7794 kN
29
30. Additional weight = 0.012 kN/m2 X 1.299 m X 6 m
= 0.0935 kN
DL on typical purlin = 1.092 + 0.972 + 0.779 + 0.0935
= 2.936 kN
DL on purlin at eaves level = (2.936/2) kN
= 1.46 kN
same as,
DL on purlin at ridge level = 1.48 kN
DL on purlin at before ridge level = 2.758 kN
For Middle frame of structure For outer frame of structure
30
31. LIVE LOAD CALCULATIONS
Live load on purlin = 750-20(Φ-10)
= 750-20(21.80-10)
= 0.514 kN/m2
So, take live load on roof truss = (2/3) X 0.514
= 0.343 kN/m2
Live load on typical purlin = 0.343 kN/m2 X 1.4 m X 6m
= 2.88 kN
same as,
Live load on purlin at eaves level = 1.44 kN
Live load on purlin at ridge level = 1.21 kN
Live load on purlin at before ridge level = 2.55 kN
For middle frame of structure For outer frame of structure
31
32. Vb (basic wind speed)
50m/s
[for bhuj, Appendix A, Cl.-5.2 ,IS:875(part:3)-1983]
K1 (risk coefficient factor)
1
[for all general buildings and structure,table-1, IS:875(part:3)-1983]
K2 (terrain height and structure
size factor)
0.98
[for class B , terrain category 2, table – 2, IS:875 (part:3)-1983]
K3 (topography factor)
1
[for wind slope less than 3˚ , cl. 5.3.3.1, IS:875 (part:3)-1983]
WIND LOAD CALCULATION
Design wind speed (Vz) = Vb X K1 X K2 X K3
= 50 X 1 X 0.98 X 1
= 49
Design wind pressure (Pz) = 0.6 X (Vz)^2
= 1440.6 N/m2
= 1.44 KN/m2
32
33. External Pressure Coefficient for Pitched Roof of Rectangular Clad Building
ROOF ANGLE WIND ANGLE θ WIND ANGLE θ
0˚ 90˚
θ EF GH EG EH
20˚ -0.4 -0.4 -0.7 -0.6
21.80˚ -0.328 -0.4 -0.7 -0.6
30˚ 0 -0.4 -0.7 -0.6
Force at each nodal point is given By: F = (Cpe ± Cpi) x A x Pz
Here Cpi = internal pressure coefficient
= ± 0.2 (for low permeability)
33
34. Wind ward
side
coefficient
Cpe+Cpi
lee ward
side
coefficient
Cpe+Cpi
A X Pz Force at
wind ward
coefficient
Force at lee
ward
coefficient
Typical purlin -0.528 -0.6 8.4 X 1.44 -6.39 -7.26
At eves level -0.528 -0.6 4.2 X 1.44 -3.19 -3.63
At ridge level -0.528 -0.6 6.46 X 1.44 -2.46 -2.79
At before ridge level -0.528 -0.6 7.43 X 1.44 -5.65 -6.42
Wind ward
side
coefficient
Cpe+Cpi
lee ward
side
coefficient
Cpe+Cpi
A X Pz Force at
wind ward
coefficient
Force at lee
ward
coefficient
Typical purlin 0.128 -0.2 8.4 X 1.44 -1.54 -2.42
At eves level 0.128 -0.2 4.2 X 1.44 -0.77 -1.20
At ridge level 0.128 -0.2 6.46 X 1.44 -0.59 -0.93
At before ridge level 0.128 -0.2 7.43 X 1.44 -1.36 -2.14
Case 1 for Cpi = +0.2 at θ = 0˚
Case 2 for Cpi = -0.2 at θ = 0˚
34
35. Wind ward side
coefficient
Cpe+Cpi
lee ward side
coefficient
Cpe+Cpi
A X Pz Force at wind
ward coefficient
Force at lee
ward
coefficient
Typical purlin -0.5 -0.4 8.4 X 1.44 -6.05 -4.84
At eves level -0.5 -0.4 4.2 X 1.44 -3.02 -2.42
At ridge level -0.5 -0.4 6.46 X 1.44 -2.33 -1.86
At before ridge level -0.5 -0.4 7.43 X 1.44 -5.35 -4.28
Wind ward
side coefficient
Cpe+Cpi
lee ward side
coefficient
Cpe+Cpi
A X Pz Force at wind
ward
coefficient
Force at lee
ward
coefficient
Typical purlin -0.9 -0.8 8.4 X 1.44 -10.89 -9.68
At eves level -0.9 -0.8 4.2 X 1.44 -5.44 -4.84
At ridge level -0.9 -0.8 6.46 X 1.44 -4.18 -3.72
At before ridge level -0.9 -0.8 7.43 X 1.44 -9.63 -8.56
Case 3 for Cpi = +0.2 at θ = 90˚
Case 4 for Cpi = -0.2 at θ = 90˚
35
36. External Pressure Coefficient (Cpe) for Walls of Rectangular Clad Building
Wind Angle A B C D
0˚ +0.7 -0.25 -0.6 -0.6
90˚ -0.5 -0.5 +0.7 -0.1
A
C
D
B
Wind force at last columns Wind force at intermediate columns
A 0.5 x 3 x 1.44 = 2.16 0.5 x 6 x 1.44 = 4.32
B -0.45 x 3 x 1.44 = -1.94 -0.45 x 6 x 1.44 = -3.89
C -0.8 x 3 x 1.44 = -3.46 -------------------------
D -0.8 x 3 x 1.44 = -3.46 -------------------------
Case 1 for Cpi = +0.2 at θ = 0˚
36
Case 2 for Cpi = -0.2 at θ = 0˚
Wind force at last columns Wind force at intermediate columns
A 0.9 x 3 x 1.44 = 3.89 0.9 x 6 x 1.44 = 7.78
B -0.05 x 3 x 1.44 = -0.22 -0.05 x 6 x 1.44 = -0.43
C -0.4 x 3 x 1.44 = -1.73 -------------------------
D -0.4 x 3 x 1.44 = -1.73 -------------------------
Case 3 for Cpi = +0.2 at θ = 90˚
Wind force at last columns Wind force at intermediate columns
A -0.7 x 3 x 1.44 = -3.02 -0.7 x 6 x 1.44 = -6.48
B -0.7 x 3 x 1.44 = -3.02 -0.7 x 6 x 1.44 = -6.48
C 0.5 x 3 x 1.44 = 2.16 -------------------------
D -0.3 x 3 x -1.44 = 1.29 -------------------------
Wind force at last columns Wind force at intermediate columns
A -0.3 x 3 x 1.44 = -1.29 -0.3 x 6 x 1.44 = -2.59
B -0.3 x 3 x 1.44 = -1.29 -0.3 x 6 x 1.44 = -2.59
C 0.9 x 3 x 1.44 = 3.89 -------------------------
D 0.1 x 3 x 1.44 = 0.43 -------------------------
Case 4 for Cpi = -0.2 at θ = 90˚
37. Section properties
37
Sr.No. member Section
1 Top chord 2 ISA 85x85x12
2 Bottom chord 2 ISA 55x55x8
3 Vertical member ISA 75x75x6
4 Diagonal ember ISA 100x100x8
5 Bottom runner 2 ISA 110x110x10
6 Bracing 2 ISA 110x110x10
7 Purlin ISMC 150
8 column 375x375
38. Base shear Calculation
Vb = Ah x W
Design horizontal acceleration spectrum calculation (Ah)
Ah=
𝑍
2
x
𝐼
𝑅
x
𝑆𝑎
𝑔
here,
Ah =
0.36
2
x
1
5
x 2.5
= 0.09
Vb = 0.09 x 525.4
Vb = 47.28
Z = 0.36
I = 1
R = 5
Sa/g = 2.5
38
42. 42
4.93
5.23 5.15 5.09
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
15 m span
R factor
Linear ( R factor)
5.01
4 3.94 3.9
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
18 m span
R factor
Linear ( R factor)
5.08
4.34 4.29 4.25
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
21 m span
R factor
Linear ( R factor)
4.57
4.47 4.4
4.25
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
2(15) m span
R factor
Linear ( R factor)
5.03
4.3
4.2
4.68
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
2(18) m span
R factor
Linear ( R factor)
3.28
2.97 2.96 2.98
0
1
2
3
4
5
6
20 25 30 35 40 45
RESPONSEREDUCTIONFACTOR
LENGTH OF BUILDING (m)
2(21) m span
R factor
Linear ( R factor)
43. CONCLUSION
A study of the variation of Response Reduction Factor with different span sizes and
number of bays in length for both single bay and multi bay is conducted.
In both single bay truss system and multi bay truss system it is observed that as the
number of bays increases the R factor tends to decrease.
Lateral dimension of building normal to the applied lateral forces influences the
Response Reduction Factor.
Multibay frames exhibit lower response reduction factor as compare to singlebay
frames.
The shorter frames exhibits higher R values compared to longer frame.
The R factor for single bay truss system is varies from 3.9 to 5.23 and for multi bay
truss system it is varies from 2.96 to 5.03.
43
44. FUTURE SCOPE OF STUDY
Performance Evaluation of the structure can be done by dynamic nonlinear method.
The present study has not considered the effect of soil structure interaction.
In the elements of structure, hinge modeling can be done as fiber modeling.
The present study can be extended to frame with different height of building.
44
45. REFERENCES
N. SUBRAMANIAN, Design of Steel Structure, Oxford University Publication.
H.J.Shah (2009), Design of Reinforced Concrete Structure Vol.1, Charotar Publication.
IS 456 (2000) Indian Standard for Plain and Reinforced Concrete - Code of Practice, Bureau
of Indian Standards, New Delhi. 2000.
IS: 800-2007, “Code of Practice for General Construction in Steel”.
IS: 875-1987(part-3),Code of Practice for Design Wind Loads For Buildings And Structures.
Design Aids for Reinforced Concrete to IS 456-1978, Bureau of Indian Standards, New
Delhi. 2000.
1988 NEHRP
45
46. ATC 40 (1996) Seismic Evaluation and Retrofit of Concrete Buildings: Vol. 1.Applied
Technology Council. USA.
ATC 19 (1995) structural standards modification factor by applied technology of council,
(redwood city california)
Krawinkler, H. and Nassar, A. (1992) Seismic design based on ductility and cumulative
damage demands and capacities. In: Nonlinear seismic analysis of reinforced concrete
buildings, New York, USA. p. 27–47.
Park, R. 1988. Ductility evaluation from laboratory and analytical testing. Proceedings of the
9th World Conference on earthquake Engineering, Tokyo, Japan Vol.VIII, pp.605-616.
Minnu M M (MAY-2014), Evaluation of Response Reduction Factors for Moment Resisting
RC Frames , M.Tech Thesis, NIT Rourkela.
Adeel Zafar (2009) Response Modification Factor Of Reinforced Concrete Moment Resisting
Frames In Developing Countries, Master of Science in Civil Engineering Thesis, University
of Illinois at Urbana-Champaign.
IS 1893 Part 1 (2002) Indian Standard Criteria for Earthquake Resistant Design of Structures.
Bureau of Indian Standards. New Delhi. 2002.
46
