Analysis and Design of Shear WallANALYSIS AND DESIGN OF SHEAR WALL 1. Introduction 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. 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, limitations of its availability, transport problems and in-creasing 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 World War I, high-rise structures were mostly in the domain of structural steel, the foundations and, at times, floor slabs were concrete. After World War I, reinforced concrete 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 12 - 14 stories in height. Between 1940 and 1950 shear walls were introduced as an economical efficient bracing system for multistoried buildings. Both of these elements-the flat plate and shear walls- became the major 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 in excess of 100 stories. CADS, PESCE, Mandya Page 1 Analysis and Design of Shear 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. Recently 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. Generally 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. Now, the situation is quite different, and a clear understanding of the effect of lateral loads on building and the behavior of various components under loads, is essential. With the increasing use of curtain walls dry walls partitions, and high strength concrete and steel reinforcement in tall buildings, the effect of wall loads have become more significant. CADS, PESCE, Mandya Page 2 These are: (a) Frames (b) Shear walls (c) Tubes Rigid frames have been used in the past for tall buildings and are still used up to certain heights. The structural requirements are: (a) Strength (b) Stiffness (c) Stability Thus. and (iii) Blast loads.Analysis and Design of Shear Wall 2. Or Shear walls are vertical walls that are designed to receive lateral forces from diaphragms and transmit them CADS. Horizontal loads can be divided into the following three categories: (i) Wind loads. Such designs are known as 'Premium free ' designs and may be difficult to achieve. they are not so efficient for lateral loads and are being replaced by shear walls and cores/tubes for taller buildings. the designed structure should be strong enough to withstand all the lateral loads without excessive deformation or deflection and should be stable under the largest stipulated loads. is designed to satisfy certain basic structural and functional requirements. Lateral Load Resisting Units: In general a shear wall building. (ii) Earthquake loads. Ideally an efficient system should not require an increase in the sizes of members when the effect of lateral loads is also incorporated. the study is concentrated on shear wall (lateral load resisting element) analysis and design. Three types of units are commonly used for resisting the lateral loads. and for that matter any other structure. At the preliminary design stage all the components of a building are designed for vertical loads only. In the present seminar. PESCE. 4. Types Of Load On Tall Buildings: The buildings are subjected to both vertical and horizontal loads. However. Mandya Page 3 . 3. SHEAR WALLS: Reinforced concrete (RC) buildings often have vertical plate-like RC walls called Shear Walls. Shear walls are vertical elements of the horizontal force resisting system. Shear walls should be provided along preferably both length and width. Mandya Page 4 . CADS. a proper grid of beams and columns in the vertical plane (called a moment-resistant frame) must be provided along the other direction to resist strong earthquake effects. Special design checks are required to ensure that the net cross-sectional area of a wall at an opening is sufficient to carry the horizontal earthquake force. PESCE. Door or window openings can be provided in shear walls. The forces in these walls are predominantly shear forces in which the fibers within the wall try to slide past one another (Fig . However. but their size must be small to ensure least interruption to force flow through walls. which significantly reduces lateral sway of the building and thereby reduces damage to structure and its contents.1 Further. openings should be symmetrically located.. They could be placed symmetrically along one or both directions in plan. those due to self-weight and contents of building). Shear walls provide large strength and stiffness to buildings in the direction of their orientation. Moreover. Shear walls are more effective when located along exterior perimeter of the building – such a layout increases resistance of the building to twisting. 2).Analysis and Design of Shear Wall to the ground. Shear walls in buildings must be symmetrically located in plan to reduce ill-effects of twist in buildings (Fig. Thus.e. Fig. Since shear walls carry large horizontal earthquake forces. if they are provided along only one direction. the overturning effects on them are large. most RC buildings with shear walls also have columns.1). these columns primarily carry gravity loads (i. design of their foundations requires special attention. Mandya Page 5 . PESCE. The strength of the concrete. steel and anchorage between them must resist these shear forces or the wall will tear or “shear” apart.2 Behavior Of Shear Walls During Earth Quake: Shear walls resist two types of forces: shear forces and uplift forces. This transfer creates shear forces throughout the height of the wall between the top and bottom shear wall connections.Analysis and Design of Shear Wall 4. (Fig 3) CADS. Connections to the structure above transfer horizontal forces to the shear wall.1 Classification Of Shear Walls (Varghese 2001) Simple rectangular types and flanged walls(bar bell type) Coupled shear walls Rigid frame shear walls Framed walls with in filled frames Column supported shear walls Core type shear walls 4. 3 Two functions of a Shear Wall 4. Earthquake STIFFNESS Force STRENGTH Connection for Uplift Connection for Resistance Sliding Fig. PESCE. The holds own device then provides the necessary uplift resistance. the uplift force is large enough to tip the wall over. Bearing walls have less uplift than non-bearing walls because gravity loads on shear walls help them resist uplift. Mandya Page 6 . These uplift forces try to lift up one end of the wall and push the other end down. In some cases.3 Functional Requirement Of A Shear Wall CADS.Analysis and Design of Shear Wall Uplift forces exist on shear walls because the horizontal forces are applied to the top of the wall. Uplift forces are greater on tall short walls and less on long walls. Shear walls need hold own devices at each end when the gravity loads cannot resist all of the uplift. Analysis and Design of Shear Wall The philosophy of earthquake design for structures other than essential facilities has been well established and proposed as follows: To To prevent structural damage and minimize non-structural damage in occasional moderate ground shaking To avoid collapse or serious damage in rare major ground shaking prevent non-structural damage in frequent minor ground shaking Shear walls function by working as a large vertical cantilever which has the ability to resist large seismic forces. The reason for this extra strength is because they can be designed to have some ductility. This movement is resisted by the shear walls and the forces are transmitted back down to the foundation. They can be very efficient in resisting horizontal loads and generally provide strength much more economically than a frame structure. To have this ductility they are designed with internal steel frames. 4. When shear walls are stiff enough. they will transfer these horizontal forces to the next element in the load path below them. shown in (Fig. Also. Shear walls also provide lateral stiffness to prevent the roof or floor above from excessive side-sway. When shear walls are strong enough. These other components in the load path may be other shear walls. buildings that are sufficiently stiff will usually suffer less nonstructural damage.4). PESCE. While designing the walls a balance must be found in the ratio of vertical load and CADS.4 Strength Of Shear Walls: Shear walls. in particular. As shear walls act primarily as cantilevers they have three basic failure modes. In a simple building with shear walls at each end. Mandya Page 7 . Shear walls must provide the necessary lateral strength to resist horizontal earthquake forces. must be strong in themselves and also strongly connected to each other and to the horizontal diaphragms. this allows them to survive even after major damage has been inflicted. slabs or footings. they will prevent floor and roof framing member from moving off their supports. ground motion enters the building and creates inertial forces that move the floor diaphragms. Long short walls are stiffer than tall narrow ones. just like its strength. For a wall of constant height.6 Advantages Of Shear Walls In Rc Buildings: CADS. This special confining transverse reinforcement in boundary elements is similar to that provided in columns of RC frames. RC walls with boundary elements have substantially higher bending strength and horizontal shear force carrying capacity.5 Shear Wall As Stiffeners: The stiffness of the shear wall. and are therefore less susceptible to earthquake damage than walls without boundary elements. This is generally done by increasing the dead load. A compromise must be found where the increase in strength. the stiffness will grow exponentially as the wall length increases. Fig. To ensure that shear walls behave in a ductile way. the thickness of the shear wall in these boundary elements is also increased. is not offset by the reduction in ductility. Mandya Page 8 .Analysis and Design of Shear Wall ductility. End regions of a wall with increased confinement are called boundary elements. 4. Sometimes. concrete in the wall end regions must be reinforced in a special manner to sustain these load reversals without loosing strength. Shear walls provide stiffness in large part by the ratio of their height to width. however as the dead load is increased the ductility is reduced. depends on the combined stiffness of its components: concrete and steel. 4: Principle modes of failure of R C shear wall Under the large overturning effects caused by horizontal earthquake forces. from the increase in dead load. 4. PESCE. The possibility of any of the modes of failure occurring can be minimized by increasing the vertical load on the wall. edges of shear walls experience high compressive and tensile stresses. in past earthquakes. Shear walls are easy to construct. CADS. Shear wall buildings are a popular choice in many earthquake prone countries.Analysis and Design of Shear Wall Properly designed and detailed buildings with shear walls have shown very good performance in past earthquakes. Shear walls are efficient. even buildings with sufficient amount of walls that were not specially detailed for seismic performance (but had enough well-distributed reinforcement) were saved from collapse. New Zealand and USA. PESCE. Chile. However. Mandya Page 9 . both in terms of construction cost and effectiveness in minimizing earthquake damage in structural and nonstructural elements (like glass windows and building contents). like Japan. Shear walls in high seismic regions require special detailing. because reinforcement detailing of walls is relatively straight-forward and therefore easily implemented at site. The maximum spacing should not exceed L/5. 2. 3. 3t or 450 mm. is to be lesser of a) ½ distance to an adjacent shear wall web b) 1/10th of the total wall height c) Actual width. This reinforcement is uniformly distributed in the wall. the effective extension of the flange width beyond the face of the web to be considered in design. If the factored shear stress (v) exceeds 0. The minimum steel ratios for each of horizontal and vertical directions should be 0. If it is flanged wall. PESCE.Analysis and Design of Shear Wall 5. where L and t are length and thickness of the wall respectively.2fck boundary elements are to be provided along the vertical boundaries of the walls. The diameter of the bars should not exceed 1/10th of the thickness of the part of the wall.25 or if the thickness of wall exceeds 200 mm the bars should be provided as two mats in the plane of the wall one on each face. 2. 3. 5. Mandya Page 10 . 1. Walls are to be provided with reinforcement in two orthogonal directions in the plane of the wall. The thickness of the wall should not be less than 150 mm. DESIGN OF RECTANGULAR AND FLANGED SHEAR WALLS General Dimensions The following factors determine the general dimensional requirement of the walls.15fck. Vertical steel provided in the wall for shear should not be less than horizontal steel Reinforcements for Shear CADS. Where the extreme fiber compressive stresses in the wall due to all loads (the gravity and lateral loads) exceed 0. These elements can be discontinued when the compressive stresses are less than 0. Reinforcements The following rules are to be observed for detailing of steel 1.0025. 4. [but not more than 1. Mandya Page 11 . (assuming 0.Analysis and Design of Shear Wall The nominal shear is calculated by the formula Where d= effective width (=0. The shear taken by concrete is given by the same value as in beam shear.25% steel) and if necessary its value can be increased by multiplying factor due to axial load (δ) as per IS 456 clause 40.5] Where Pu =total axial load And the resultant shear stress is τc then the shear capacity of concrete is given by Vc=τctd With Vs=Vu-Vc The steel required for shear force resistance is determined using the relation Adequacy of boundary elements CADS.2. PESCE.8 for rectangular sections) Vu=factored shear The nominal shear should not exceed the maximum allowable shear τmax as given by IS 456-2000.2. This can be determined by interaction curve or formal give in IS 13920:1993 (Annex A). Splicing of vertical flexural reinforcement should be avoided as far as possible in the regions of flexural yielding which can be taken to extend of for a distance of the length of wall (L) above the base of the wall or 1/6th the wall height. CADS. The boundary elements when provided will have greater thickness than web. Required splice and anchorage Horizontal steel which acts as web steel shall be anchored near edges of the wall or confined to the core of the boundary elements. Muv=moment of resistance provided by the rectangular section with distributed vertical reinforcement across this wall section only (excluding boundary elements) C= c/c distance between the boundary elements. PESCE. If the gravity loads tend to add the strength of the wall the load factor for this is taken as only 0. Flexural Strength The wall should be safe under the action of combined bending and axial load.8% and not greater than 4%. and splicing length should not be more than 150 mm. not more than 1/3rd of steel should be spliced at such a section and pitch of splicing should be staggered minimum of 600 mm.these elements should be provided with special confining steel throughout their height. if spliced. Mandya Page 12 .Analysis and Design of Shear Wall The boundary elements should be able to carry all the vertical loads.8. The maximum axial load on the boundary elements due to effects of vertical load and moments is P=sum of factored gravity loads + Where Mu= factored moment on the whole wall. The boundary elements are designed as vertical columns with the vertical steel not les than 0. Mandya Page 13 .5 and neglecting small quantities we get CADS.Analysis and Design of Shear Wall Lateral ties are provided in lapped splices of diameter larger than 16 mm dia of ties =1/4 diameter of bar or 6 mm. Formula for Moment of resistance of Rectangular Shear walls( IS 13920) IS 13920 (1993) Appendix A gives the expression for moment of resistances of slender rectangular walls with uniformly distributed reinforcement and subjected to moment and axial load. PESCE. For particular case of x/L < 0. PESCE. Mandya Page 14 .Analysis and Design of Shear Wall CADS. 640 kN Moment =1. Mandya Page 15 .Seismic load Axial force(kN) 1950 250 Moment (kNm) 600 4800 Shear(kN) 20 700 Solution Step1 Determination of design loads P1= (0. t=250 mm CADS. PESCE.16m and thickness 250 mm is subjected to the following forces assume Fck=20Mpa and fy=415Mpa and the wall is high wall with following loading loading 1. L=4160 mm. Design Example (Varghese 2001) Design a shear wall of length 4.Analysis and Design of Shear Wall 6.2 (700+20) = 864 kN Step2 check for requirement of boundary elements Assuming uniform thickness.860 kN P2= 1.2 (4800+600) = 6480 kNm Shear=1.8x1950) + (1.2x250) =1.2 (1950+250) = 2.DL+LL 2. Also there is tension at one end of the wall due to B. PESCE.2fck=0.M .25 CADS.52 and -6.Analysis and Design of Shear Wall I= ^12 = mm4 A=bd=4160x250=1. Mandya =0.25 b) The thickness of the section is more than 200 mm depth of section = c/c boundary elements=3400+380 =3780 mm = 0.25 N/mm2 Page 16 . Step3 Adopt the dimension of boundary elements Adopt a bar bell type wall with a central 3400 mm portion and two ends 380 x 760 mm giving a total length of 3400 + 380 =4160mm. boundary elements are needed.2x25=5N/mm2 As extreme stresses are high. Step4 Check for requirement of two layers of steel Two layers of steel required if a) Shear stress is more than 0.25 = 0.04x106 mm2 fc= = =11.45N/mm2 0.92 N/mm =1. d=3780 mm required considering Sv=1m height CADS.0025 and check for safety of wall. As =0.92 N/mm2 τc=0.also τmax=3. PESCE.Analysis and Design of Shear Wall Also thickness of wall is more than 200 mm so use two layers of steel with suitable cover.36Mpa for 0.1 Mpa.56 x 250 x 3780 = 529. Mandya Page 17 . Designed steel is required for Vs = (0. Step5 Steel determination Let us put minimum required steel of 0.92 -0.36) bd =0. τV =0.0025 x 250 x 1000 = 625 mm2 in two layers Provide 10dia @ 250 mm < 450mm (max) Astp=314mm2/m Provide same steel in both vertical and horizontal Step6 Calculation of Vs taken by steel. Therefore.25% steel and fck 25. 2kN Step7 Shear reinforcement As the wall is high horizontal steel is more effective. Mandya Page 18 .595 = 1107 kN Step 9 To calculate the parameters λ Φ and x/L λ = Φ= = β= 0. PESCE. Step 8 To find flexural strength of web part of wall Vertical load on wall (with factor of 0.628 nominal steel provided will satisfy shear requirements.Analysis and Design of Shear Wall horizontal shear steel area =628 mm2 =Asv available = = 0.2(250) = 1860 kN Assuming it as UDL over the area the axial load for the central part beams=Pw Pw = 1860 = 1860 x 0.8) P= 0.5 CADS.8 (1950) +1.516 ( we know) < 0. 86 m (=c) Axial load = kN This load acts as tension at one end and compression at other end Step 12 Calculate the compression due to axial loads at these ends Fraction of area at each end = Factored compression at compression end taking worst case P2=(0. Mandya Page 19 .2025x2640) =535kN Factored compression at tension end (taking P1) =0. PESCE.041 x 25 x 250 x 34002 =2370 kNm < 6480 kNm (required) Step 10 To calculate moment carried by boundary elements M1 M1=6480-2370 =4110 kNm Step 11 Calculation of compression and tension in boundary elements due to M1 Distance between boundary elements =3480 +380 =3.Analysis and Design of Shear Wall = = 0.2025 x 1860 = 377kN Compression at compression end=1065+535=1600kN Tension at tension end= -1065+377=-688kN Step13 Design of boundary elements for compression CADS.041 Mu=0. 16 mm . Step15 Design of reinforcement around the openings. on all the sides of the hole to compensate for the steel cut off by the hole. check laterals for confinement and check for anchorage and splice length. Assume opening size of 1200 x 1200 Area of reinforcement cut off by opening = 1200(thickness) =1200 x 250 x 0. CADS. PESCE.0025 =750mm2 Provide 4 nos. Step14 Design of tension side of shear wall Provide the same steel as in compression side check also for tension (earthquake forces can act in both directions). one on each face of the wall. 16 mm bar =804 mm2 Provide 2 nos.Analysis and Design of Shear Wall Design one end as column. Mandya Page 20 . Openings are provided in the main body of the wall. PESCE.Analysis and Design of Shear Wall CADS. Mandya Page 21 . Mandya Page 22 . CADS.Analysis and Design of Shear Wall Enlarged view of Boundary Element. PESCE. Mandya Page 23 .Analysis and Design of Shear Wall Detailing as per IS 13920:1993 CADS. PESCE. BIS. P.Analysis and Design of Shear Wall REFERENCES: IS 1893(Part 1) : 2002.C. Prentice-Hall of India Private Limited. New Delhi. Mandya Page 24 . “Advanced Reinforced Concrete Design”. 2001 .Varghese. CADS. New Delhi IS 13920: 1993 code of practice for Ductile detailing of reinforced concrete structures subjected to seismic forces. Criteria for Earthquake Resistant Design of Structures. PESCE.