Civil - Design Of Reinforced Concrete And Brick Masonry Structures- Design Of Brick Masonry
1. Design an interior crosswall for a two storeyed building to carry 100mm thick RC slab with 3m storeyheight. The wall is unstiffened and supports 2.65m wide slab. Loading on theslab is given as below: i) Liveload on floor slab = 2 kN/m2 ii) Liveload on roof slab = 1.5 kN/m2 iii) Floorfinish = 0.2 kN/m2 iv) Rooffinish = 1.96 kN/m2 Assume the compressive strength of brick as 10N/mm2and mortar type as M1. The loading on the wallincludes the load from slab (LL + DL) and self weight of the wall. Assuming thewall thickness as 100mm and size of each masonry unit as 200 x 100 x 90mm, Loading on slab: Live load: on floor slab = 2 kN/m2 on roof slab = 1.5kN/m2 Dead load: Floor finish = 0.2 kN/m2 Roof finish = 1.96kN/m2 Self weight of slabs = 2 x 0.1 x 25 = 5 kN/m2Load from slab = 10.66 kN/m2 For 2.65m length of slab, Load from slab = 10.66 x 2.658 = 28.36 kN/m Self weight of masonry = 2 x 0.1 x 20 x 3 = 12 kN/m Total = 40.36 kN/m Permissible stress of masonry for M1 mortar and masonryunit of compressive strength 10N/mm2 is taken from Table 8, IS 1905 -1987. Permissible stress = 0.96 N/mm2 Stress reduction factor, Area reduction factor, Shapemodification factor are applied as per Cl.5.4. Stress reduction factor (Kst) Slenderness ratio (Least of le/t & he/t) From Table 4, he= 0.75 H = 0.75 x 3 = 2.25m [Both endsfixed] he/t= 2.25 / 0.1 = 22.5 < 27 Therefore,the stress reduction factor from T condition is, For22 -> 0.56 (e = 0) For24 -> 0.51 For22.5 -> 0.55 Kst = 0.55 Areareduction factor (KA) [Cl.5.4.1.2,IS1905-1987] A =0.1 x 1 = 0.1m2 < 0.2 m2 KA =0.7 + (1.5 x 0.1) = 0.85 Shape modification factor (Ksh) [Cl. 5.4.1.3, IS1905-1987] Kshfor block of size 200 x 100 x 90 mm laid along 100mm side, from Table 10 forHeight to Width ratio of 90 x 100, Height/ Width = 90/100 = 0.9 For 0.75xo à 1 For 1xo à 1.1 For 0.9xo à1.06 Ksh =1.06 ?permodified = Kst.KA.Ksh.?per =0.55 x 0.85 x 1.06 x 0.96 = 0.48 N/mm2 ?act/m = 40.36x103 / 100x1000 = 0.4036 N/mm2 <? per [0.48 N/mm2] Hence the adopted thickness of 100mm with M1 mortar andmasonry unit with compressive strength 10N/mm2 is safe in carryingthe load from slab. 1. 2.Inthe above problem, design the wall if it is continuous and stiffened by crosswall of 100mm thickness and length of the wall being 3.6m. Loadingon the masonry wall = 40.36 kN/m Actual stress = 40.36x1000 / 100x1000 =0.4036 N/mm2 ?per for M1 mortar and masonry unit ofcompressive strength 10 N/mm2 with 100mm thickness, Permissible stress = 0.96 N/mm2 [From Table 8, IS1905 -1987] SlendernessàLeastratio,ofHe/t&Le/t? He = 0.75 H = 0.75 x 3 = 2.25m Le = 0.8L = 0.8 x 3.7 = 2.96m [From Table 5, IS1905 -1987] For the cross walls provided, stiffening coefficients arefound from Table 6, IS1905 -1987. tp à Thickness of pier Se = 1 Thickness of wall = 1 x 0.1 = 0.1m [Consideringstiffness] ?=2.25 / 0.1= 22.5 <27 The stress reduction factor (Kst) for Tableno.10 for ? = 22. condition, For ? =220.56 For ? = 240.51 For ? = 220.55.5 Kst = 0.55 Area reduction factor for area = 0.1 x 1 = 0.1m2 <0.2m2, KA = 0.7 + (1.5 x 0.1) = 0.85 Shape modification factor: [Cl.5.4.1.3] Ksh for block size of 200 x 100 x 90mm laid along 100mmside from Table 10 for height to width ratio of 90 x 100mm Height/ Width = 90/100 = 0.9 For Ht/W = 0.75 1 For Ht/W = 11.1 For Ht/W = 0.9 1.06 Ksh = 1.06 ?per modified= Kst.KA.Ksh. ?per =0.55 x 0.85 x 1.06 x 0.96 = 0.48 N/mm2 > act? Provided masonry wall of thickness 100mm with M1mortar and compressive strength of each unit 10 N/mm2 issafe. 3. Design an interior crosswall for a two storeyed building to carry 100mm thick RC slab. Check the safetyof the wall if the wall is continuous and cross wall is available on only oneside and the storey height is 3.5m. The wall supports 2.65m wide slabs on bothsides. Loading on the slab is given as below: i) Liveload on floor slab = 2 kN/m2 ii) Liveload on roof slab = 1.5 kN/m2 iii) Floorfinish = 0.2 kN/m2 Roof finish = 1.96 kN/m2 Assume the compressive strength of brick as 10N/mm2and mortar type as M1. Loading on slab: Live load: on floor slab = 2 kN/m2 on roof slab = 1.5 kN/m2 Dead load: Floor finish = 0.2 kN/m2 Roof finish = 1.96kN/m2 Self weight of slabs = 2 x 0.1 x 25 = 5 kN/m2Load from slab = 10.66 kN/m2 For 2.65m length of slab, Load from slab Self weight of masonry Total ?act /m = 42.36x103 /100x1000 =0.4236 N/mm2 Permissible stress of masonry for M1 mortar and masonryunit of compressive strength 10N/mm2 is taken from Table 8, IS 1905-1987. Permissible stress = 0.96 N/mm2 Stress reduction factor, Area reduction factor, Shapemodification factor are applied as per Cl.5.4. Stress reduction factor (Kst) Slenderness ratio (Least of le/t & he/t) From Table 4, Effective height, he= 0.75 H = 0.75 x 3.5 = 2.625m [Bothends fixed] Effective length, le= 1.5 L = 1.5 x 3.65 = 5.475m [One endfixed, other end free] he/t= 2.625 / 0.1 = 26.25 < 27 Therefore, thestress reduction factorfrom condition is, For 26 à0.45 (e = 0) For 27 à0.43 For 26.25 à0.3375 + 0.1075 = 0.445 Kst =0.445 Area reduction factor (KA) [Cl.5.4.1.2,IS1905-1987] A = 0.1 x 1 = 0.1m2 < 0.2 m2 KA = = 0.7 + (1.5 x 0.1) = 0.85 Shape modification factor (Ksh) [Cl. 5.4.1.3, IS1905-1987] Ksh for block of size 200 x 100 x 90 mm laidalong 100mm side, from Table 10 for Height to Width ratio of 90 x 100, Height/ Width = 90/100 = 0.9 For 0.75xo à 1 For 1xo à 1.1 For 0.9xo à1.06 Ksh =1.06 ?permodified = Kst.KA.Ksh. ?per = 0.445 x 0.85 x 1.06 x 0.96 = 0.385 N/mm2< act?/m [0.4236 N/mm2] Hence the adopted thickness of 100mm with M1 mortar andmasonry unit with compressive strength 10N/mm2 is not safe incarrying the load from slab. The thickness of wall is increased to 200mm. Load from slab = 10.66 kN/m2 For 2.65m length of slab, Load from slab =10.66 x 2.658 = 28.36 kN/m2 Self weight of masonry= 2 x 0.2 x 20 x 3.5 = 28 kN/m Total = 56.36 kN/m Loading on masonry wall = 56.36 kN/m Actual actstress= 56.36x1000/ 200x1000 ?=0.2818 N/mm2 Permissible stress of masonry for M1 mortar and masonryunit of compressive strength 10N/mm2 is taken from Table 8, IS 1905 -1987. Permissible ? per=0.96stressN/mm2 Stress reduction factor, Area reduction factor, Shape modificationfactor are applied as per Cl.5.4. Stress reduction factor (Kst) Slenderness ratio (Least of le/t & he/t) From Table 4, Effective height, he= 0.75 H = 0.75 x 3.5 = 2.625m [Bothends fixed] Effective length, le= 1.5 L = 1.5 x 3.65 = 5.475m [One endfixed, other end free] he/t= 2.625 / 0.2 = 13.125 < 27 Therefore, thestress reduction 22.5and no eccentricity condition is, For12 - > 0.84 (e = 0) For14 - > 0.78 For 13.125 à0.3675 + 0.439 = 0.806 Kst =0.806 Area reduction factor (KA) [Cl.5.4.1.2, IS1905-1987] A = 0.2 x 1 = 0.2m2 KA = 1 Shape modification factor (Ksh) [Cl. 5.4.1.3, IS1905-1987] Ksh for block of size 200 x 100 x 90 mm laidalong 100mm side, from Table 10 for Height to Width ratio of 90 x 100, Height/ Width = 90/100 = 0.9 For 0.75xo à 1 For 1xo à 1.1 For 0.9xo à1.06 Ksh =1.06 ?permodified = Kst.KA.Ksh. ?per = 0.806 x 1 x 1.06 x 0.96 = 0.82 N/mm2 > act?/m[0.2818 N/mm2] Hence the adopted thickness of 200mm with M1 mortar andmasonry unit with compressive strength 10N/mm2 is safe in carryingthe load from slab. 4. Design the interior wallof a single storey building shown in figure. The height of the ceiling is 3.5mand the load from slab including self weight is 30kN/m2. Load from slab = 30 x 3.65 = 109.5 kN/m Self weight of wall = 0.15 x 3.5 x 1 x 20 = 10.5 kN/m Total =120 kN/m Actual stress = 120x1000 / 150x1000=0.8 N/mm2 Permissible stress of masonry for M1 mortar and masonryunit of compressive strength 10N/mm2 is taken from Table 8, IS 1905-1987. 2 Permissibleper= 0.96stressN/mm ? Stress reduction factor, Area reduction factor, Shapemodification factor are applied as per Cl.5.4. Stress reduction factor (Kst) Slenderness ratio (Least of le/t & he/t) From Table 4, Effective height, he = 0.75 H =0.75 x 3.5 = 2.625m [Bothends fixed] Effective length, le = 1 L = 1.0 x 8.15 =8.15m he/t= 2.625 / 0.2 = 13.125 < 27 For the cross walls provided, stiffening coefficients arefound from Table 6, IS1905 -1987. Se = 1 Thickness of wall = 1 x 0.2 = 0.2m [Consideringstiffness] ?=2.625 / 0.2= 17.5 <27 Therefore, the stressreduction factor from Table 10 for ? = 17.5 condition is, For 16 à0.73 (e = 0) For 18 à0.67 For 13.125 à0.1825 + 0.5025 = 0.685 Kst =0.685 Area reduction factor (KA) [Cl.5.4.1.2,IS1905-1987] A = 0.15 x 1 = 0.15m2 KA =0.7 + (1.5 x 0.15) = 0.925 Shape modification factor (Ksh) [Cl. 5.4.1.3, IS1905-1987] Ksh for block of size 200 x 100 x90 mm laid along 100mm side, from Table 10 for Height to Width ratio of 90 x100, Height/ Width = 90/100 = 0.9 For 0.75xo à 1 For 1xo à 1.1 For 0.9xo à1.06 Ksh =1.06 ?per modified= Kst.KA.Ksh. ?per = 0.685 x 0.925 x 1.06 x 0.96 = 0.647 N/mm2< act?/m [0.8 N/mm2] Hence the adopted M1 mortar and masonry unit withcompressive strength 10N/mm2 is not sufficient in carryingthe load. Increase the strength of brick unit and mortar as, H1 mortar and masonry unitcompressive strength 15N/mm2 ?per = 1.31 N/mm2 ?per modified = 0.88 N/mm2 Therefore, the interior wallof 150mm thickness is safe with H1 mortar and brick units of compressivestrength 15 N/mm2. 5. Design a masonry wall ofheight 4m subjected to a load of 20kN/m. Use M1 mortar. The wall isunstiffened[no need to find effective length] at the ends. Assume a thickness of wall of 300mm Actual stress = 20x1000 / 300x1000 =0.066N/mm2 ?per = 0.96 N/mm2 He = 0.75 H = 0.75 x 4 = 3m ?= 3/0.3 = 10 Kst = 0.89 For A = 0.3 x 1 = 0.3 m2, KA = 1 Ksh = 1.06 ?per modified = 0.27 N/mm2 > act?[0.066N/mm2] Hence, safe. 6. Design the wall in the GF level for the loadingcondition as shown in figure. Loading on brick wall: Load from slab = 12 + 10 + 10 Weight of wall =32 kN/m (self wt.) = 3 x 2 x 0.1 x 3 x 20 = 36 kN/m Total = 68 kN/m Actual stress = 68x1000 / 2x100x1000= = 0.34 N/mm2 Use M1 mortar and brick of compressive strength 10 N/mm2.?per = 0.96 N/mm2 [From Table 8, IS1905 -1987] (? ? 6) heff = 0.75 x h = 0.75 x 3 = 2.25m te = 2/3(tw + tw)= 2/3(0.1 + 0.1) = 0.133m Area of wall (each leaf) = 0.1 x 1 = 0.1m2< 0.2 m2 KA = 0.85 Ksh = 1.06 ?per (modified)= Kst x KA x Ksh x per? =0.704 x 0.85 x 1.06 x 1.96 = 0.61 N/mm2 > act? Therefore, the cavity wallis safe with M1 mortar and masonry unit of compressive strength 10N/mm2. 2.Design a cavity wall of overall thickness250mm and thickness of each leaf 100mm for a three storeyed building. The wallis stiffened by intersecting walls 200mm thick at 3600mm c/c. The ceilingheight is 3m and the loading from roof is 16 kN/m. The loading from each flooris 12.5kN/m. Load from roof = 16kN/m Load from floor = 12.5 + 12.5 kN/m Wall load [3x0.2x20] = 36 kN/m Total= 77 kN/m Actualstress = ?ac= 77x103/ 200x1000 = ==0.39N/mm2 ?per : Assume M1 mortar and brick of compressive strength 10N/mm2. From Table 7, IS1905 -1987, ?per = 0.96 N/mm2 (? ? 6) Effectiveheight = heff = 0.75 x 3 = 2.25m Effective length = leff = 0.8 l = 0.8 x 3600 =2880mm = 2.88m Stiffening Coefficient: Since cross wall is available along one leaf,Sc for 3. Design a masonry column to carry a load of 150kN. Theheight of the column is 2000mm. The column is restrained against translation(hinged) only. Assume a column of size 400 x 400mm. Use M1 mortar and brick of compressive strength 10 N/mm2. heff = h [Table 4, IS1905-1987] ?=2000/400 = 5< 6 There is no need for Stress reduction factor (Kst= 1) 2 From Tableper=0.967,N/mm? Ast = 0.4 x 0.4 = 0.16m2 < 0.2m2KA = 0.7 + (1.5 x 0.4 x 0.4) = 0.94 Ksh = 1.06 ?per (modified) = 0.94 x 0.96 x 1 x 1.06 =0.98 N/mm2. ?act < per? Therefore, the masonrycolumn of size 400 x 400mm with M1 mortar and brick unit of compressive strength10N/mm2 is safe to carry a load of 150kN. Note: Boundary condition is assumed if not given. 4.Design an interior wall of a singlestoreyed workshop building of height 5.4m supporting a RC roof. Assume roofload as 45kN/m. The wall is stiffened by piers at equal intervals shown infigure. Height = 5.4m, w = 45 kN/m Since there is an increasein width at the pier, the actual stress is found for the wall length of 3.6m(One bay). C/s area of one bay = (3.6 x 0.2) + 4(0.1 x0.1) = 0.76 m2 ?per: heff = 0.75h = 4.05m [Table 4, IS1905-1987]demise leff = 0.8l = 0.8 x 3.6 = 2.88m ?=2.88 < 6 There is no need for Stress reduction factor (Kst= 1) 2 From Tableper=0.967,N/mm? Ast = 0.4 x 0.4 = 0.16m2 < 0.2m2KA = 0.7 + (1.5 x 0.4 x 0.4) = 0.94 Ksh = 1.06 ?per (modified) = 0.94 x 0.96 x 1 x 1.06 =0.98 N/mm2. ?act < per? Therefore, the masonrycolumn of size 400 x 400mm with M1 mortar and brick unit of compressivestrength 10N/mm2 is safe to carry a load of 150kN. Stiffening coefficient, ?per (modified) = 0.785 x 0.96 x 1 x 1.06 =0.79 N/mm2 > act? Inference : Hence the brickwall is safe with M1 mortar and brick of compressive strength 10N/mm2. 5.Design a brick masonry column of height 3m,tied effectively, fixed at top and bottom. The load from slab is 100kN,including self weight of the brick pillar. Load from slab = 100Kn Self weight of brick pillar = 0.4 x 0.4 x 20x 3 = 9.6kN Total =109.6 kN Assume a column size of 400mm x 400mm. Actual stress = 109.6x103 / 400x400 =0.685 N/mm2 Assume grade of mortar as M1 and compressivestrength of 0.96N/mm2 heff = 0.75.H = 2.25m There is no need of stress reduction factor. Kst= 1 A = 0.4 x 0.4 = 0.16 m2 < 0.2m2KA = 0.7 + (1.5 x 0.4 x 0.4) = 0.94 Ksh = 1.06[Brick unit 200 x 100 x 90] ?per (modified) = 0.9565 N/mm2 >act? Hence the brick wall is safe with M1 mortarand compressive strength of 10N/mm2. 6.Design an interior wall of a 3 storeyedbuilding with ceiling height of each storey as 3m. The wall is unstiffened and3.6m in length. Load from roof is 12kN/m and from each floor is 10kN/m. Selecta cavity wall with overall thickness 250mm and length between each leaf as50mm. h = 3m, l = 3.6m Load from roof = 12kN/m Load from each floor = 10+ 10 kN/m Self weight of wall= 3 x 2 x 0.1 x 3 x 20 = 36 kN/m Total = 68 kN/m Use M1 mortar and brick of compressive strength 10N/mm2,?per = 0.96 N/mm2 heff = 0.75 x 3 = 2.25m te = 2/3(tw+ tw) = 0.133m From Table 8, IS1905 -1987, Kst = 0.704 Area of wall = 0.1 x 1 = 0.1 m2 < 0.2 m2KA = 0.85 Ksh = 1.06 ?per (modified) = 0.704 x 0.85 x 1.06x 0.96 = 0.61 N/mm2 > act? Hence the brickwork is safe with M1 mortar and brick ofcompressive strength 10N/mm2.
?à 16.875,(0.421875 + 0.293125 = 0.715)
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Civil : Design Of Reinforced Concrete And Brick Masonry Structures- Design Of Brick Masonry : Design Of Brick Masonry: Solved Design Problems |
