Lecture 5
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Transcript of Lecture 5
Lecture 5
January 31, 2006
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 2
In this Lecture
Impulsive and convective base shear Critical direction of seismic loading
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 3
Base shear
Previous lectures have covered Procedure to find impulsive and convective
liquid masses This was done through a mechanical analog model
Procedure to obtain base shear coefficients in impulsive and convective modes
This requires time period, damping, zone factor, importance factor and response reduction factor
Now, we proceed with seismic force or base shear calculations
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 4
Base shear
Seismic force in impulsive mode (impulsive base shear)
Vi = (Ah)i x impulsive weight Seismic force in convective mode
(convective base shear) Vc = (Ah)c x convective weight (Ah)i = impulsive base shear coefficient (Ah)c = convective base shear coefficient
These are described in earlier lectures
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 5
Base shear
Now, we evaluate impulsive and convective weights Or, impulsive and convective masses Earlier we have obtained impulsive and
convective liquid mass Now, we consider structural mass also
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 6
Base shear : Ground supported tanks
Impulsive liquid mass is rigidly attached to container wall Hence, wall, roof and impulsive liquid vibrate
together In ground supported tanks, total impulsive
mass comprises of Mass of impulsive liquid Mass of wall Mass of roof
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 7
Base shear : Ground supported tanks
Hence, base shear in impulsive mode
gmmmAV twihi i
mi = mass of impulsive liquid mw = mass of container wall mt = mass of container roof g = acceleration due to gravity
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 8
Base shear : Ground supported tanks
This is base shear at the bottom of wall Base shear at the bottom of base slab is : Vi’ = Vi + (Ah)i x mb
mb is mass of base slab
Base shear at the bottom of base slab may be required to check safety against sliding
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 9
Base shear : Ground supported tanks
Base shear in convective mode
mc = mass of convective liquid
gmAV cchc
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 10
Base shear : Ground supported tanks
Total base shear, V is obtained as:
22ci VVV
Impulsive and convective base shear are combined using Square Root of Sum of Square (SRSS) rule
Except Eurocode 8, all international codes use SRSS rule Eurocode 8 uses absolute summation rule
i.e, V = Vi + Vc
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 11
Base shear : Ground supported tanks
In the latest NEHRP recommendations (FEMA 450), SRSS rule is suggested Earlier version of NEHRP recommendations
(FEMA 368) was using absolute summation rule
FEMA 450, 2003, “NEHRP recommended provisions for seismic regulations for new buildings and other structures”, Building Seismic Safety Council, National Institute of Building Sciences,, USA.
FEMA 368, 2000, “NEHRP recommended provisions for seismic regulations for new buildings and other structures”, Building Seismic Safety Council, National Institute of Building Sciences,, USA.
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 12
Bending moment:Ground supported tanks
Next, we evaluate bending or overturning effects due to base shear
Impulsive base shear comprises of three parts (Ah)i x mig (Ah)i x mwg (Ah)i x mtg
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 13
Bending moment:Ground supported tanks
mw acts at CG of wall mt acts at CG of roof mi acts at height hi from bottom of wall
If base pressure effect is not included mi acts at hi
*
If base pressure effect is included Recall hi and hi
* from Lecture 1
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 14
Bending moment:Ground supported tanks
Bending moment at the bottom of wall Due to impulsive base shear
ghmhmhmAM ttwwiiihi
hi = location of mi from bottom of wall hc = location of mc from bottom of wall hw = height of CG of wall ht = height of CG of roof
ghmAM ccchc )(
Due to convective base shear
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 15
Bending moment:Ground supported tanks
For bending moment at the bottom of wall, effect of base pressure is not included Hence, hi and hc are used
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 16
Bending moment:Ground supported tanks
Bending moment at the bottom of wall
ghmhmhmAM ttwwiiihi
ghmAM ccchc )(
Ground level
(Ah)imihi
(Ah)imw
hw
(Ah)imt
(Ah)cmc
hc
ht
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 17
Bending moment:Ground supported tanks
Total bending moment at the bottom of wall
22ci MMM
SRSS rule used to combine impulsive and convective responses
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 18
Overturning moment:Ground supported tanks
Overturning moment This is at the bottom of base slab Hence, must include effect of base pressure
hi* and hc
* will be used
Ground level
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 19
Overturning moment:Ground supported tanks
Overturning moment in impulsive mode
tb = thickness of base slab
g/tmthm
thm)th(mAM
bbbtt
bwwb*ii
ih*i
2
Overturning moment in convective mode
gthmAM bccchc )()( **
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 20
Bending moment:Ground supported tanks
Overturning moment is at the bottom of base slab Hence, lever arm is from bottom of base slab Hence, base slab thickness, tb is added to
heights measured from top of the base slab
Total overturning moment
2*2**ci MMM
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 21
Example
Example: A ground-supported circular tank is shown below along with some relevant data. Find base shear and bending moment at the bottom of wall. Also find base shear and overturning moment at the bottom of base slab.
mi = 141.4 t; mc = 163.4 t
mw = 65.3 t, mt =33.1 t,
mb = 55.2 t,
hi =1.5 m, hi* = 3.95 m,
hc = 2.3 m, hc* = 3.63 m
(Ah)i = 0.225, (Ah)c = 0.08
Roof slab 150 mm thick
Base slab 250 mm thick
4 m
10 m
Wall 200 mm thick
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 22
Example
Solution:Impulsive base shear at the bottom of wall is Vi = (Ah)i (mi + mw + mt) g
= 0.225 x (141.4 + 65.3 + 33.1) x 9.81 = 529.3 kN
Convective base shear at the bottom of wall is Vc = (Ah)c mc g
= 0.08 x 163.4 x 9.81 = 128.2 kN Total base shear at the bottom of wall is
544.6kN128.2529.3VVV 222c
2i
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 23
Example
For obtaining bending moment, we need height of CG of roof slab from bottom of wall, ht.
ht = 4.0 + 0.075 = 4.075 m
Impulsive bending moment at the bottom of wall is
Mi = (Ah)i (mihi + mwhw + mtht) g = 0.225 x (141.4 x 1.5 + 65.3 x 2.0 + 33.1 x 4.075) x
9.81 = 1054 kN-m
Convective bending moment at the bottom of wall is Mc = (Ah)c mc hc g = 0.08 x 163.4 x 2.3 x 9.81 = 295 kN-m
Total bending moment at bottom of wall is m-1095kN2951054MMM 222
c2i
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 24
Example
Now, we obtain base shear at the bottom of base slab
Impulsive base shear at the bottom of base slab is Vi = (Ah)i (mi + mw + mt + mb) g = 0.225 x (141.4 + 65.3 + 33.1 + 55.2) x 9.81 = 651.1 kN Convective base shear at the bottom of base slab is Vc = (Ah)c mc g = 0.08 x 163.4 x 9.81 = 128.2 kN Total base shear at the bottom of base slab is
663.6kN128.2651.1VVV 222c
2i
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 25
Example
Impulsive overturning moment at the bottom of base slab Mi
* = (Ah)i [mi (hi* + tb) + mw(hw + tb) + mt(ht +tb) + mb
tb/2]g = 0.225 x [141.4(3.95 + 0.25) + 65.3(2.0 + 0.25) + 33.1(4.075 + 0.25) + 55.2 x 0.25/2] x 9.81 = 1966 kN-mConvective overturning moment at the bottom of base slab Mc
* = (Ah)c mc (hc* + tb) g
= 0.08 x 163.4 x (3.63 + 0.25) x 9.81 = 498 kN-m
Total overturning moment at bottom of base slab
Notice that this value is substantially larger that the value at the
bottom of wall (85%)
m-kN 20284981966MMM 22*c
*i
* 22
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 26
Base shear : Elevated tanks
In elevated tanks, base shear at the bottom of staging is of interest
Ms is structural mass Base shear in impulsive mode
gmmAV siihi
Base shear in convective mode
gmAV cchc
Total base shear22ci VVV
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 27
Bending moment:Elevated tanks
Bending moment at the bottom of staging Bottom of staging refers to footing top
Impulsive base shear comprises of two parts (Ah)i x mig Ah)i x msg
Convective base shear has only one part (Ah)c x mcg
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 28
Bending moment:Elevated tanks
mi acts at hi*
mc acts at hc*
Bending moment at bottom of staging is being obtained
Hence, effect of base pressure included and hi*
and hc* are used
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 29
Bending moment:Elevated tanks
Structural mass, ms comprises of mass of empty container and 1/3rd mass of staging ms is assumed to act at CG of empty container CG of empty container shall be obtained by
considering roof, wall, floor slab and floor beams
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 30
Bending moment:Elevated tanks
Bending moment at the bottom of staging
ghmhhmAM cgss*iiih
*i
ghhmAM s*ccch
*c
hs = staging height Measured from top of footing to bottom of wall
hcg = distance of CG of empty container from bottom of staging
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 31
Bending moment:Elevated tanks
Bending moment at the bottom of staging
Top of footing
(Ah)i msg
hs
hcg
hi*
hs
hc*
ghhmAM s*ccch
*c ghmhhmAM cgss
*iiih
*i
(Ah)i mig
(Ah)c mcg
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 32
Bending moment:Elevated tanks
Total bending moment
22c*
i** MMM
For shaft supported tanks, M* will be the design moment for shaft
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 33
Bending moment:Elevated tanks
For analysis of frame staging, two approaches are possible
Approach 1: Perform analysis in two steps Step 1:
Analyze frame for (Ah)imig + (Ah)imsg Obtain forces in columns and braces
Step 2: Analyze the frame for (Ah)cmcg Obtain forces in columns and braces
Use SRSS rule to combine the member forces obtained in Step 1 and Step 2
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 34
Bending moment:Elevated tanks
Approach 2: Apply horizontal force V at height h1 such
that V x h1 = M* V and M* are obtained using SRSS rule as
described in slide nos. 26 and 32 In this approach, analysis is done in single step
Simpler and faster than Approach 1
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 35
Example
Example: An elevated tank on frame staging is shown below along with some relevant data. Find base shear and bending moment at the bottom of staging.
AA is CG of empty container
mi = 100t; mc = 180 t
Mass of container = 160 t
Mass of staging = 120 t
hi* = 3 m, hc
* = 4.2 m
(Ah)i = 0.08, (Ah)c = 0.04
GL
hs = 15 m
2.8 m
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 36
Example
Structural mass, ms = mass of container + 1/3rd mass of staging = 160 + 1/3 x 120 = 200 t
Base shear in impulsive mode
gmmAV sihi i
819x200100x080 ..
Base shear in convective mode gmAV cchc
819x180x040 .. kN6.70
= 78.5 + 157 = 235.5 kN
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 37
Example
Total base shear
22ci VVV
22 6705235 .. kN8.245
Now, we proceed to obtain bending moment at the bottom staging
Distance of CG of empty container from bottom of staging, hcg = 2.8 + 15 = 17.8 m
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 38
Example
Base moment in impulsive mode
ghmhhmAM cgss*iiih
*i
819x817x2001503x100080 ....
= 78.5 x 18 + 157 x 17.8
= 4207 kNm
Note: 78.5 kN of force will act at 18.0m and 157 kN of force will act at
17.8 m from top of footing.
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 39
Example
Base moment in convective mode
ghhmAM s*ccch
*c
819x1524x180x040 ...
Total base moment22c*
i** MMM
22 13564207 kNm4420
= 70.6 x 19.2= 1356 kNm
Note: 70.6 kN of force will act at 19.2 m from top of footing.
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 40
Example
Now, for staging analysis, seismic forces are to be applied at suitable heights
There are two approaches Refer slide no 33
Approach 1: Step 1: Apply force of 78.5 kN at 18 m and 157 kN at
17.8 m from top of footing and analyze the frame Step 2: Apply 70.6 kN at 19.2 m from top of footing and
analyze the frame Member forces (i.e., BM, SF etc. in columns and braces)
of Steps 1 and 2 shall be combined using SRSS
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 41
Example
Approach 2: Total base shear, V = 245.8 kN will be applied at height
h1, such that
V x h1 = M*
245.8 x h1 = 4420
h1 = 17.98 m Thus, apply force of 245.8 kN at 17.98 m from top of
footing and get member forces (i.e., BM, SF in columns and braces).
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 42
Elevated tanks:Empty condition
Elevated tanks shall be analysed for tank full as well as tank empty conditions Design shall be done for the critical condition
In empty condition, no convective liquid mass Hence, tank will be modeled using single
degree of freedom system Mass of empty container and 1/3rd staging
mass shall be considered
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 43
Elevated tanks:Empty condition
Lateral stiffness of staging, Ks will remain same in full and empty conditions
In full condition, mass is more In empty condition mass is less
Hence, time period of empty tank will be less Recall, T = Hence, Sa/g will be more
Usually, tank full condition is critical However, for tanks of low capacity, empty
condition may become critical
K
M2Π
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 44
Direction of seismic force
Let us a consider a vertical cantilever with rectangular cross section
Horizontal load P is applied First in X-Direction Then in Y-direction (see Figure below) More deflection, when force in Y-direction Hence, direction of lateral loading is important !!
P
P
X
Y
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 45
Direction of seismic force
On the other hand, if cantilever is circular Direction is not of concern Same deflection for any direction of loading
Hence, it is important to ascertain the most critical direction of lateral seismic force Direction of force, which will produce maximum
response is the most critical direction In the rectangular cantilever problem, Y-direction is the
most critical direction for deflection
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 46
Direction of seismic force
For frame stagings consisting of columns and braces, IS 11682:1985 suggests that horizontal seismic loads shall be applied in the critical direction
IS 11682:1985, “Criteria for Design of RCC Staging for Overhead Water Tanks”, Bureau of Indian Standards, New Delhi
Clause 7.1.1.2 Horizontal forces – Actual forces and moments resulting from horizontal forces may be calculated for critical direction and used in the design of the structures. Analysis may be done by any of the accepted methods including considering as space frame.
Clause 7.2.2 Bending moments in horizontal braces due to horizontal loads shall be calculated when horizontal forces act in a critical direction. The moments in braces shall be the sum of moments in the upper and lower columns at the joint resolved in the direction of horizontal braces.
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 47
Direction of seismic force
Section 4.8 of IITK-GSDMA Guidelines contains provisions on critical direction of seismic force for tanks
Ground-supported circular tanks need to be analyzed for only one direction of seismic loads These are axisymmetric Hence, analysis in any one direction is sufficient
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 48
Direction of seismic force
Ground-supported rectangular tanks shall be analyzed for two directions Parallel to length of the tank Parallel to width of the tank Stresses in a particular wall shall
be obtained for seismic loads perpendicular to that wall
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 49
Direction of seismic force
RC circular shafts of elevated tanks are also axisymmetric Hence, analysis in one direction is sufficient
If circular shaft supports rectangular container Then, analysis in two directions will be
necessary
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 50
Direction of seismic force
For elevated tanks on frame staging Critical direction of seismic loading for columns
and braces shall be properly ascertained Braces and columns may have different
critical directions of loading For example, in a 4 - column staging
Seismic loading along the length of the brace is critical for braces
Seismic loading in diagonal direction gives maximum axial force in columns
See next slide
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 51
Direction of seismic force
Critical directions for 4 - column staging
Critical direction for shear force in brace
Critical direction for axial force in column
Bending Axis
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 52
Direction of seismic force
For 6 – column and 8 – column staging, critical directions are given in Figure C-6 of the Guideline
See next two slides More information available in Sameer
and Jain (1994) Sameer, S. U., and Jain, S. K., 1994, “Lateral load
analysis of frame staging for elevated water tanks”, Journal of Structural Engineering, ASCE, Vol.120, No.5, 1375-1393. (http://www.nicee.org/ecourse/Tank_ASCE.pdf)
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 53
Direction of seismic force
Critical directions for 6 - column staging
Critical direction for shear force and bending moment in columns
Critical direction for shear force and bending moment in braces and axial force in columns
Bending Axis
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 54
Direction of seismic force
Critical directions for 8 - column staging
Critical direction for shear force and bending moment in braces
Critical direction for shear force, bending moment and axial force in columns
Bending Axis
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 55
Direction of seismic force
As an alternative to analysis in the critical directions, following two load combinations can be used
100 % + 30% rule Also used in IS 1893(Part 1) for buildings
SRSS rule
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 56
Direction of seismic force
100%+30% rule implies following combinations
ELx + 0.3 ELY
ELY + 0.3 ELx
ELx is response quantity when seismic loads are applied in X-direction
ELY is response quantity when seismic loads are applied in Y-direction
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 57
Direction of seismic force
100%+30% rule requires Analyze tank with seismic force in X-direction;
obtain response quantity, ELX
Response quantity means BM in column, SF in brace, etc.
Analyze tank with seismic force in Y-direction; obtain response quantity, ELY
Combine response quantity as per 100%+30% rule
Combination is on response quantity and not on seismic loads
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 58
Direction of seismic force
Important to note that the earthquake directions are reversible
Hence, in 100%+30% rule, there are total eight load combinations
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 59
Direction of seismic force
SRSS rule implies following combination
22yx ELEL
Note: ELx is response quantity when seismic loads
are applied in X-direction ELY is response quantity when seismic loads
are applied in Y-direction Hence, analyze tank in two directions and
use SRSS combination of response quantity
Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 5/ Slide 60
At the end of Lecture 5
This completes seismic force evaluation on tanks
There are two main steps Evaluation of impulsive and convective masses Evaluation of base shear coefficients for
impulsive and convective modes SRSS rule is used to combine impulsive
and convective responses Critical direction of seismic loading shall
be properly ascertained Else, 100%+30% or SRSS rule be used