Sabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in


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1 Sabah Shawkat Cabinet of Structural Engineering Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are a few differences. A wall is distinguished from a column by having a length that is more than five times the thickness. Plain concrete walls should have a minimum thickness of 1 mm. Where the load on the wall is eccentric, the wall must have centrally placed reinforcement of at least. percent of the crosssection area if the eccentricity ratio exceeds.. This reinforcement may not be included in the loadcarrying capacity of the wall. Shear walls should be designed as vertical cantilevers, and the reinforcement arrangement should be checked as for a beam. Where the shear walls have returns at the compression end, they should be treated as flanged beams. If the walls contains openings, the assumption for beams that plane sections remain plane is no longer valid. Shear walls connected by beams or floor slabs. The stability of shearwall structure is often provided by several walls connected together by beams or floors. Where the walls are of uniform section throughout the height and are connected by regularly spaced uniform beams. Many shear walls contain one or more rows of openings. Figure 3.61: Building with shear walls When walls are used to brace a framed structure, it may be acceptable to disregard the lateral stiffness of the frame and assume the horizontal load carried entirely by the walls. The equilibrium and compatibility equations at each level produces a set of simultaneous equations which are solved to give the lateral deflection and rotation at each level.
2 Sabah Shawkat Cabinet of Structural Engineering 17 Figure 3.6: Shear walls subjected to bending moment and vertical load If a tall building has an asymmetrical structural plan and is subjected to horizontal loading, torsional as well as bending displacements will occur, and hence a full threedimensional analysis is required. In many tall building shear wall provide most, if not all, of the required strength for lateral loading resulting from gravity, wind, and earthquake effects. Figure 3.63
3 Sabah Shawkat Cabinet of Structural Engineering 17 The system (Hull  Core Structures) has been used for very tall buildings in both steel and concrete. Lateral loads are resisted by both the hull and the core, their mode of interaction depending on the design of the floor system. Figure 3.64: Shear walls subjected to horizontal load and vertical load A floor slabs of multistory buildings, when effectively connected to the wall, acting as stiffeners, provide adequate lateral strength. As essential prerequisites, adequate foundations and sufficient connection to all floors, to transmit horizontal loads, must be assured. Figure 3.65: side view of shearing wall shows the thickness of bearing wall in accordance with boundary conditions of the members Normally, for wind loading, the governing design criterion or limit state will be deflection. Shear walls, when carefully designed and detailed, hold the promise of giving the
4 Sabah Shawkat Cabinet of Structural Engineering 17 greatest degree of protection against nonstructural damage in moderate earthquakes, while assuring survival in case of catastrophic seismic disturbances, on account of their ductility. Yielding of the flexural bars will also affect the width of diagonal cracks. The shear strength of tall shear walls may also be controlled by combined moment and shear failure at the base of the wall. Door and service openings in shear walls introduce weaknesses that are not confined merely to the consequential reduction in crosssection. Stress concentrations are developed at the corners, and adequate reinforcement needs to be provided to cater for these concentrations. This reinforcement should take the form of diagonal bars positioned at the corners of the openings. The reinforcement will generally be adequate if it is designed to resist a tensile force equal to twice the shear force in the vertical components of the wall as shown, but should not be less than two 16mm diameter bars across each corner of the opening. Figure 3.66: Diagonal reinforcement in coupling beams, beam crosssection and possible mechanisms involving openings A single cantilever shear wall, such as the one shown in figure 3.67, can be expected to behave in the same way as a reinforced concrete beam. The shear walls will be subjected to bending moments and shear forces originating from lateral loads, and to axial compression induced by gravity. At the base of the wall, where yielding of the flexural reinforcement in both faces of the section can occur, the contribution of the concrete towards shear strength should be disregarded where the axial compression on the gross section is less than 1% of the cylinder crushing
5 Sabah Shawkat Cabinet of Structural Engineering 17 strength of the concrete. Sectional area of the concrete and should be equally divided between the two faces of the wall. The maximum area of vertical reinforcement should not exceed 4% of the gross crosssectional area of the concrete. Horizontal reinforcement equal to not less than half the area of vertical reinforcement should be provided between the vertical reinforcement and the wall surface on both faces. The spacing of the vertical bars should not exceed the lesser of 3mm or twice the wall thickness. The spacing of horizontal bars should not exceed 3mm and the diameter should not be less than onequarter of the vertical bars. Figure 3.67: Geometry and reinforcement of typical shear wall The prime function of the vertical reinforcement, passing across a construction joint, is to supply the necessary clamping force and to enable friction forces to be transferred. Figure 3.68: Geometry and reinforcement of shear wall in tall building
6 Sabah Shawkat Cabinet of Structural Engineering 17 Figure 3.69: Precast reinforced concrete walls Figure 3.61: Shear subjected to lateral load Figure : Shear walls with flexible coupling beams
7 Sabah Shawkat Cabinet of Structural Engineering 17 Figure 3.61
8 Sabah Shawkat Cabinet of Structural Engineering 17 Figure
9 Sabah Shawkat Cabinet of Structural Engineering 17 Calculation of sectional forces and moments of structures Example 3.61: Reinforced concrete wall subjected to horizontal load H o or W o Construction height Storey height H = 7.5 m l =.75 m Sectional area of the first pillar 1 and A1 or 1 = m Sectional area of the second pillar and A or = 1.6 m Moment of inertia of the first pillar I1 = 4 m 4 Moment of inertia of the first pillar I = m 4 Moment of inertia of the crosssectional area Structures weakened openings I = 39 M 4 Moment of inertia of girders IPR =.6 m 4 Modulus of elasticity of pillars E = 1 GPa Modulus of elasticity of girder E = GPa Static moment of sectional area Walls weakened with openings S = 5.4 m 3 Shear force applied in base Construction Ho = 354 kn The distance between the center of gravity of the pillars c = 6.1 m Width of the window type openings a = m
10 Sabah Shawkat Cabinet of Structural Engineering 17 Figure : Shear walls contains openings Data: Figure : Geometry calculated reinforcing walls subjected to horizontal loading Ho E 1 MPa E MPa 1 m I 1 4 m m I m 4 S 5.4 m 3 I 39 m 4 i.6 m 4 l.75 m S c c 3.49m Z 1 l H o 354 kn a 1 m 3 E i I c E I 1 I.48m.19m 1 S a 3 l Z 6.16 H o l S I 135.9kN Determination the value of 6.16 d T( ) d T( ) ( 1 ) T ( ) T' ( 1) Odesolve ( 1)
11 Sabah Shawkat Cabinet of Structural Engineering 17 Diagram () vs ( ) where the value of the function can read from the graf, based on the coefficient for paying the relationship H ( ) Diagram () vs ( ) d.1 1 ( ) v 1 3 tonne v l tonne e l 1.5 m e 1 m Solving the values of K and J S I 1 I 1 I 1 I 1 K v I e v c 1 e 1 K m 1 kg c 1
12 Sabah Shawkat Cabinet of Structural Engineering 17 S I 1 I 1 I 1 I 1 J v I e v c 1 e 1 J m 1 kg c 1 i 1 j i i1 ( ) H o l S I ( ) Determination the values of M1 and M M 1 ( ) I 1 I 1 I H o Z ( 1 ) c S I ( ) M ( ) I I 1 I H o Z ( 1 ) c S I ( ) j j j kn ( 1 ) j j
13 Sabah Shawkat Cabinet of Structural Engineering 17 c S 1 I j.14 j c S 1 I j q j kn ( 1 ) c I m ( ) H o l S I ( ) q( ) ( ( 1 )) c I m M 1 j M j j j External load w acting on the structure induces in the individual pillars bending moments. M 1 1 j M 1 j kn m kn m
14 Sabah Shawkat Cabinet of Structural Engineering 17 Example 3.6: Solution of reinforcing concrete walls with openings subjected to vertical load The reinforcing walls, as mentioned in the introduction, other than the horizontal load and the vertical load are transmitted as well. This chapter is about solving the stiffening of reinforced walls in terms of a vertical load defined the basic assumptions that in dealing with all three types of reinforcing walls. L  floor height H  total height of the wall A1A  crosssectional area of each pillar c  distance between pillars  width of openings N  normal force acting in the pillar shear force applied in the girders E  modulus of elasticity of the walls E' modulus of girders V1  vertical loads on pillar 1 at level each floor v  vertical loads on the Pillar at the level of each floor E1  eccentricity at which the load acts v1 e  eccentricity at which the load applied v
15 Sabah Shawkat Cabinet of Structural Engineering 17 Data: Figure: E 1 MPa E MPa 1 m I 1 4 m m I m 4 S 5.4 m 3 I 39 m 4 i.6 m 4 l.75 m Z 1 l H o 354 kn a 1 m S c c 3.49m v 1 3 kn v kn e 1.5 m e 1 m H o l S I 135.9kN K S I I 1 I 1 I 1 I v e v c 1 e 1 c E i I c E I 1 I.48m K 5.6kN.19m 1 S a 3 l Z 6.16 i 1 j i i1 ( ) K ( ) Diagram () vs 6.16 Odesolve ( 1) d T( ) d T( ) ( 1 ) T ( ) T' ( 1)
16 Sabah Shawkat Cabinet of Structural Engineering 17 ( ) Diagram () vs Figure: ( ) 1 ( ) d.1 1 ( ) Figure: M 1 ( ) I 1 I 1 I Z ( 1 ) v l 1 e 1 v e c K ( ) M ( ) I I 1 I Z ( 1 ) v l 1 e 1 v e c K ( )
17 Sabah Shawkat Cabinet of Structural Engineering 17 N 1 ( ) N ( ) Z l Z l v 1 ( 1 ) K ( ) v ( 1 ) K ( ) Diagram () vs 1 ( ) ( ) d ( ) Figure: Diagram () vs K 1 d T( ) d T( ) K T ( ) T' ( 1) Odesolve ( 1)
18 Sabah Shawkat Cabinet of Structural Engineering ( ) (.4).91 (.5).95 Figure: j j ( 1 ) j kn j M 1 j M j j j Figure
19 Sabah Shawkat Cabinet of Structural Engineering 17 M 1 1 j M 1 j N 1 1 j kn m kn m N 1 j kn kn Diagram vs
20 Sabah Shawkat Cabinet of Structural Engineering 17 Figure:
21 Sabah Shawkat Cabinet of Structural Engineering 17 Diagram vs Figure: Diagram vs
22 Sabah Shawkat Cabinet of Structural Engineering 17 Figure: Diagram vs
23 Sabah Shawkat Cabinet of Structural Engineering 17 1,9,8,7,6,5,4,3,,1,1,,3,4 Figure:
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