Analysis and Design of Shear Wall Wall ANALYSIS AND DESIGN OF SHEAR WALL 1. Intr Intro odu duct ctio ion n
The accommodation of human force for the necessary use and adaptability is done by buildings. Henceforth buildings are the driving force for the people. Hence it is essential to analyse and design buildings such that they are safe, serviceable and economical. econo mical. There are many types of buildings to accommodate the needs and purpose of people. For a structural engineer a tall building can be defined as one whose structural system must be modified to make it sufficiently economical to resist lateral forces due to wind or earthquakes within the prescribed criteria for strength, drift and comfort of the occupants. High land prices, prices, limitati limitations ons of its availability availability,, transport transport problems and in-creasing in-creasing availability availability of energy, advance in technology and communications among other between them, are moving the society to grow vertical. As reinforced concrete penetrated the construction field at the turn of the century, its use in high-rise concrete structures also became more widespread. Although prior to orld orld ar ar !, high-rise structures were mostly in the domain of structural steel, the foundations and, at times, times, floor slabs were concrete. concrete. After orld orld ar ar !, reinforced reinforced concrete multistory multistory structures appeared sporadically mostly for loft buildings using flat slabs with column capitals and in a very few instances for apartment buildings up to "# - "$ stories in height. %etween "&$' and "&(' shear walls were introduced as an economical efficient bracing system for multistoried buildings. %oth of these elements-the flat plate and shear walls- became the ma)or structural system in all residential building of any height. The shear wall or diagonally braced structures seems to have good technical and economical potentials to reach heights h eights in e*cess of "'' stories.
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Analysis and Design of Shear Wall Wall
Traditionally, the primary concern of the structural engineer designing a building has been the provision of a structurally safe and adequate system to support vertical loads. +ecently there has been a considerable increase in the number of tall buildings, both residential and commercial and the modern trend is towards taller and more slender structures. Thus the effect of lateral loads like wind loads, earthquake force and blast force etc., are attaining increasing importance and almost every designer is faced with the problem of providing adequate strength and stability against lateral loads. This is a new development, as the earlier building designers usually designed for the vertical loads and as an afterthought, checked, the final design for lateral loads as well. enerally those buildings had sufficient strength against lateral loads due to numerous partitions and short span beams and cross beams and no modification in the design was needed. ow, the situation is quite different, and a clear u nderstanding of the effect of lateral loads on building and the behavior of various components under loads, is essential. ith the increa increasin sing g use of curtai curtain n walls walls dry walls walls parti partitio tions, ns, and high high stren strength gth concret concretee and steel steel reinforcement in tall buildings, the effect of wall loads have become more significant.
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Analysis and Design of Shear Wall 2. Types O Lo!d On T!"" #ui"din$s%
The buildings are sub)ected to both vertical and hori/ontal loads. At the preliminary design stage all the components of a building are designed for vertical loads only. !deally an efficient system should not require an increase in the si/es of members when the effect of lateral loads is also incorporated. 0uch designs are known as 12remium free 1 designs and may be difficult to achieve. Hori/ontal loads can be divided into the following three categories3 4i5 ind loads, 4ii5 6arthquake loads, and 4iii5 %last loads. &. L!ter!" Lo!d Resistin$ 'nits% (
!n general a shear wall building, and for that matter any other structure, is designed to satisfy certain basic structural and functional requirements. The structural requirements are3 4a5 0trength 4b5 0tiffness 4c5 0tability Thus, the designed structure should be strong enough to withstand all the lateral loads without e*cessive deformation or deflection and should be stable under the largest stipulated loads. Three types of units are commonly used for resisting the lateral loads. These are3 4a5 Frames 4b5 0hear walls 4c5 Tubes +igid frames have been used in the past for tall buildings and are still used up to certain heights. However, they are not so efficient for lateral loads and are being replaced by shear walls and cores7tubes for taller buildings. !n the present seminar, the study is concentrated on shear wall 4lateral load resisting element5 analysis and design.
$. SHEAR WALLS3 +einforced concrete 4+85 buildings often have vertical plate-like +8 walls called 0hear alls. 0hear walls are vertical elements of the hori/ontal force resisting system. 9r 0hear walls are vertical walls that are designed to receive lateral forces from diaphragms and transmit them CADS, PESCE, Mandya
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Analysis and Design of Shear Wall to the ground. The forces in these walls are predominantly shear forces in which the fibers within the wall try to slide past one another 4Fig ."5.
Fi$.1
Further, most +8 buildings with shear walls also have columns these columns primarily carry gravity loads 4i.e., those due to self-weight and contents of building5. 0hear walls provide large strength and stiffness to buildings in the direction of their orientation, which significantly reduces lateral sway of the building and thereby reduces damage to structure and its contents. 0ince shear walls carry large hori/ontal earthquake forces, the overturning effects on them are large. Thus, design of their foundations requires special attention. 0hear walls should be provided along preferably both length and width. However, if they are provided along only one direction, a proper grid of beams and columns in the vertical plane 4called a moment-resistant frame5 must be provided along the other direction to resist strong earthquake effects. :oor or window openings can be provided in shear walls, but their si/e must be small to ensure least interruption to force flow through walls. ;oreover, openings should be symmetrically located. 0pecial design checks are required to ensure that the net cross-sectional area of a wall at an opening is sufficient to carry the hori/ontal earthquake force. 0hear walls in buildings must be symmetrically located in plan to reduce ill-effects of twist in buildings 4Fig. #5. They could be placed symmetrically along one or both directions in plan. 0hear walls are more effective when located along e*terior perimeter of the building < such a layout increases resistance of the building to twisting.
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Analysis and Design of Shear Wall
).1 *"!ssiic!tion O S+e!r W!""s ,-!r$+ese 21/ • • • • • •
0imple rectangular types and flanged walls4bar bell type5 8oupled shear walls +igid frame shear walls Framed walls with in filled frames 8olumn supported shear walls 8ore type shear walls
).2 #e+!0ior O S+e!r W!""s Durin$ E!rt+ u!e%
0hear walls resist two types of forces3 shear forces and uplift forces. 8onnections to the structure above transfer hori/ontal forces to the shear wall. This transfer creates shear forces throughout the height of the wall between the top and bottom shear wall connections. The strength of the concrete, steel and anchorage between them must resist these shear forces or the wall will tear or =shear> apart. 4Fig ?5
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Analysis and Design of Shear Wall @plift forces e*ist on shear walls because the hori/ontal forces are applied to the top of the wall. These uplift forces try to lift up one end of the wall and push the other end down. !n some cases, the uplift force is large enough to tip the wall over. @plift forces are greater on tall short walls and less on long walls. %earing walls have less uplift than non-bearing walls because gravity loads on shear walls help them resist uplift. 0hear walls need hold own devices at each end when the gravity loads cannot resist all of the uplift. The holds own device then provides the necessary uplift resistance.
Earthquake STIFFNESS
Force
STRENGTH
Connection for Uplift Connection for Resistance
Sliding
Fi$. & T3o unctions o ! S+e!r W!""
).& Function!" Re4uire5ent O A S+e!r W!""
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Analysis and Design of Shear Wall The philosophy of earthquake design for structures other than essential facilities has been well established and proposed as follows3 •
To
prevent
non-structural
damage
in
frequent
minor
ground
shaking
•
To prevent structural damage and minimi/e non-structural damage in occasional moderate ground shaking
•
To avoid collapse or serious damage in rare ma)or ground shaking
0hear walls function by working as a large vertical cantilever which has the ability to resist large seismic forces. They can be very efficient in resisting hori/ontal loads and generally provide strength much more economically than a frame structure. The reason for this e*tra strength is because they can be designed to have some ductility. To have this ductility they are designed with internal steel frames, this allows them to survive even after ma)or damage has been inflicted. 0hear walls must provide the necessary lateral strength to resist hori/ontal earthquake forces. hen shear walls are strong enough, they will transfer these hori/ontal forces to the ne*t element in the load path below them. These other components in the load path may be other shear walls, slabs or footings. 0hear walls also provide lateral stiffness to prevent the roof or floor above from e*cessive side-sway. hen shear walls are stiff enough, they will prevent floor and roof framing member from moving off their supports. Also, buildings that are sufficiently stiff will usually suffer less nonstructural damage. ).) Stren$t+ O S+e!r W!""s%
0hear walls, in particular, must be strong in themselves and also strongly connected to each other and to the hori/ontal diaphragms. !n a simple building with shear walls at each end, ground motion enters the building and creates inertial forces that move the floor diaphragms. This movement is resisted by the shear walls and the forces are transmitted back down to the foundation. As shear walls act primarily as cantilevers they have three basic failure modes, shown in 4Fig.$5. hile designing the walls a balance must be found in the ratio of vertical load and
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Analysis and Design of Shear Wall ductility. The possibility of any of the modes of failure occurring can be minimi/ed by increasing the vertical load on the wall. This is generally done by increasing the dead load, however as the dead load is increased the ductility is reduced. A compromise must be found where the increase in strength, from the increase in dead load, is not offset by the reduction in ductility.
Fi$. )% 2rinciple modes of failure of + 8 shear wall
@nder the large overturning effects caused by hori/ontal earthquake forces, edges of shear walls e*perience high compressive and tensile stresses. To ensure that shear walls behave in a ductile way, concrete in the wall end regions must be reinforced in a special manner to sustain these load reversals without loosing strength. 6nd regions of a wall with increased confinement are called boundary elements. This special confining transverse reinforcement in boundary elements is similar to that provided in columns of +8 frames. 0ometimes, the thickness of the shear wall in these boundary elements is also increased. +8 walls with boundary elements have substantially higher bending strength and hori/ontal shear force carrying capacity, and are therefore less susceptible to earthquake da mage than walls without boundary elements. ).6 S+e!r W!"" As Stieners%
The stiffness of the shear wall, )ust like its strength, depends on the combined stiffness of its components3 concrete and steel. 0hear walls provide stiffness in large part by the ratio of their height to width. ong short walls are stiffer than tall narrow ones. For a wall of constant height, the stiffness will grow e*ponentially as the wall length increases. ).7 Ad0!nt!$es O S+e!r W!""s In Rc #ui"din$s%
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Analysis and Design of Shear Wall 2roperly designed and detailed buildings with shear walls have shown very good performance in past earthquakes. 0hear walls in high seismic regions require special detailing. However, in past earthquakes, even buildings with sufficient amount of walls that were not specially detailed for seismic performance 4but had enough well-distributed reinforcement5 were saved from collapse. 0hear wall buildings are a popular choice in many earthquake prone countries, like Bapan, 8hile, ew Cealand and @0A. 0hear walls are easy to construct, because reinforcement detailing of walls is relatively straight-forward and therefore easily implemented at site. 0hear walls are efficient, both in terms of construction cost and effectiveness in minimi/ing earthquake damage in structural and nonstructural elements 4like glass windows and building contents5.
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Analysis and Design of Shear Wall 6. DESIGN OF RE*TANG'LAR AND FLANGED SHEAR WALLS Gener!" Di5ensions
The following factors determine the general dimensional requirement of the walls. ". The thickness of the wall should not be less than "(' mm. #. !f it is flanged wall, the effective e*tension of the flange width beyond the face of the web to be considered in design, is to be lesser of a5 D distance to an ad)acent shear wall web b5 "7"'th of the total wall height c5 Actual width. ?. here the e*treme fiber compressive stresses in the wall due to all loads 4the gravity and lateral loads5 e*ceed '.#f ck boundary elements are to be provided along the vertical boundaries of the walls. These elements can be discontinued when the compressive stresses are less than '."(f ck . Reinorce5ents
The following rules are to be observed for detailing of steel 1. alls are to be provided with reinforcement in two orthogonal directions in the plane of
the wall. The minimum steel ratios for each of hori/ontal and vertical directions should be '.''#(.
This reinforcement is uniformly distributed in the wall. 2. !f the factored shear stress 4v5 e*ceeds '.#(
or if the thickness of wall e*ceeds #''
mm the bars should be provided as two mats in the plane of the wall one on each face. &. The diameter of the bars should not e*ceed "7"'th of the thickness of the part of the wall. ). The ma*imum spacing should not e*ceed 7(, ?t or $(' mm, where and t are length and thickness of the wall respectively. 6. Eertical steel provided in the wall for shear should not be less than hori/ontal steel Reinorce5ents or S+e!r CADS, PESCE, Mandya
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Analysis and Design of Shear Wall The nominal shear is calculated by the formula
here d effective width 4'.G for rectangular sections5 Eufactored shear The nominal shear should not e*ceed the ma*imum allowable shear ma* as given by !0 $(I-#'''. The shear taken by concrete is given by the same value as in beam shear. 4assuming '.#(J steel5 and if necessary its value can be increased by multiplying factor due to a*ial load 4K5 as per !0 $(I clause $'.#.#.
Lbut not more than ".(M
here 2u total a*ial load And the resultant shear stress is c then the shear capacity of concrete is given by
Ecctd
ith EsEu-Ec The steel required for shear force resistance is determined using the relation
Ade4u!cy o 8ound!ry e"e5ents
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Analysis and Design of Shear Wall The boundary elements should be able to carry all the vertical loads. The boundary elements when provided will have greater thickness than web. The ma*imum a*ial load on the boundary elements due to effects of vertical load and moments is
2sum of factored gravity loads N
here ;u factored moment on the whole wall. ;uvmoment of resistance provided by the rectangular section with distributed vertical reinforcement across this wall section only 4e*cluding boundary elements5 8 c7c distance between the boundary elements. !f the gravity loads tend to add the strength of the wall the load factor for this is taken as only '.G. The boundary elements are designed as vertical columns with the vertical steel not les than '.GJ and not greater than $J.these elements should be provided with special confining steel throughout their height. F"e9ur!" Stren$t+
The wall should be safe under the action of combined bending and a*ial load. This can be determined by interaction curve or formal give in !0 "?&#'3"&&? 4Anne* A5. Re4uired sp"ice !nd !nc+or!$e
Hori/ontal steel which acts as web steel shall be anchored near edges of the wall or confined to the core of the boundary elements. 0plicing of vertical fle*ural reinforcement should be avoided as far as possible in the regions of fle*ural yielding which can be taken to e*tend of for a distance of the length of wall 45 above the base of the wall or "7Ith the wall height. if spliced, not more than "7? rd of steel should be spliced at such a section and pitch of splicing should be staggered minimum of I'' mm. and splicing length should not be more than "(' mm. CADS, PESCE, Mandya
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Analysis and Design of Shear Wall ateral ties are provided in lapped splices of diameter larger than "I mm dia of ties "7$ diameter of bar or I mm. For5u"! or :o5ent o resist!nce o Rect!n$u"!r S+e!r 3!""s, IS 1&;2/
!0 "?&#' 4"&&?5 Appendi* A gives the e*pression for moment of resistances of slender rectangular walls with uniformly distributed reinforcement and sub)ected to moment and a*ial load.
For particular case of *7 O '.( and neglecting small quantities we get
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Analysis and Design of Shear Wall
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Analysis and Design of Shear Wall 7. Desi$n E9!5p"e ,-!r$+ese 21/
:esign a shear wall of length $."Im and thickness #(' mm is sub)ected to the following forces assume Fck#';pa and fy$"(;pa and the wall is high wall with following loading loading ".:N #.0eismic load
A*ial force4k5 "&(' #('
;oment 4km5 I'' $G''
0hear4k5 #' P''
So"ution Step1 :etermination of design loads
2" 4'.G*"&('5 N 4".#*#('5 ",GI' k 2# ".# 4"&('N#('5 #,I$' k ;oment ".# 4$G''NI''5 I$G' km 0hear".# 4P''N#'5 GI$ k Step2 check for requirement of boundary elements
Assuming uniform thickness, $"I' mm t#(' mm CADS, PESCE, Mandya
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Analysis and Design of Shear Wall
!
mm$
<12
Abd$"I'*#('".'$*"'I mm#
f#$
$
"".(# and -I.$(7mm# '.#f ck '.#*#((7mm# As e*treme stresses are high, boundary elements are needed. Also there is tension at one end of the wall due to %.; . Step& Adopt the dimension of boundary elements
Adopt a bar bell type wall with a central ?$'' mm portion and two ends ?G' * PI' mm giving a total length of ?$'' N ?G' $"I'mm. Step) 8heck for requirement of two layers of steel
Two layers of steel required if a5 0hear stress is more than '.#( b5 The thickness of the section is more than #'' mm depth of section c7c boundary elements?$''N?G' ?PG' mm
'.#(
'.#(
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'.&# 7mm
".#( 7mm#
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Analysis and Design of Shear Wall Also thickness of wall is more than #'' mm so use two layers of steel with suitable cover.
Step6 0teel determination
et us put minimum required steel of '.''#( and check for safety of wall. As '.''#( * #(' * "''' I#( mm# in two layers 2rovide "'dia Q #(' mm O $('mm 4ma*5 Astp?"$mm#7m 2rovide same steel in both vertical and hori/ontal Step7 8alculation of Es taken by steel.
E '.&# 7mm# c'.?I;pa for '.#(J steel and fck #(.also ma*?." ;pa. :esigned steel is required for Es 4'.&# -'.?I5 bd '.(I * #(' * ?PG' (#&. #k
Step= 0hear reinforcement
As the wall is high hori/ontal steel is more effective. Therefore,
d?PG' mm
required
considering 0v"m height CADS, PESCE, Mandya
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Analysis and Design of Shear Wall hori/ontal shear steel area I#G mm# Asv
available
'.I#G
nominal steel provided will satisfy shear requirements.
Step > To find fle*ural strength of web part of wall
Eertical load on wall 4with factor of '.G5 2 '.G 4"&('5 N".#4#('5 "GI' k Assuming it as @: over the area the a*ial load for the central part beams2w
2w "GI'
"GI' * '.(&( ""'P k
Step ; To calculate the parameters R S and *7
R
S
'.("I 4 we know5
O '.(
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Analysis and Design of Shear Wall
'.'$" ;u'.'$" * #( * #(' * ?$''# #?P' km O I$G' km 4required5
Step 1 To calculate moment carried by boundary elements ;"
;"I$G'-#?P' $""' km Step 11 8alculation of compression and tension in boundary elements due to ;"
:istance between boundary elements ?$G' N?G' ?.GI m 4c5
A*ial load
k
This load acts as tension at one end and compression at other end Step 12 8alculate the compression due to a*ial loads at these ends
Fraction of area at each end
Factored compression at compression end taking worst case 2#4'.#'#(*#I$'5 (?(k Factored compression at tension end 4taking 2"5 '.#'#( * "GI' ?PPk 8ompression at compression end"'I(N(?("I''k Tension at tension end -"'I(N?PP-IGGk Step1& :esign of boundary elements for compression CADS, PESCE, Mandya
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Analysis and Design of Shear Wall :esign one end as column, check laterals for confinement and check for anchorage and splice length. Step1) :esign of tension side of shear wall
2rovide the same steel as in compression side check also for tension 4earthquake forces can act in both directions5. Step16 :esign of reinforcement around the openings.
9penings are provided in the main body of the wall. Assume opening si/e of "#'' * "#''
Area of reinforcement cut off by opening "#''4thickness5
"#'' * #(' * '.''#(
P('mm#
2rovide $ nos. "I mm bar G'$ mm# 2rovide # nos. "I mm , one on each face of the wall, on all the sides of the hole to compensate for the steel cut off by the hole.
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Analysis and Design of Shear Wall
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Analysis and Design of Shear Wall
En"!r$ed 0ie3 o #ound!ry E"e5ent.
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Analysis and Design of Shear Wall
Det!i"in$ !s per IS 1&;2%1;;&
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Analysis and Design of Shear Wall
REFEREN*ES%
!0 "G&?42art "5 3 #''#, 8riteria for 6arthquake +esistant :esign of 0tructures, %!0, ew :elhi
!0 "?&#'3 "&&? code of practice for :uctile detailing of reinforced concrete structures sub)ected to seismic forces.
2.8.Earghese, =Advanced +einforced 8oncrete :esign>, 2rentice-Hall of !ndia 2rivate imited, ew :elhi, #''" .
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