Design of spherical dome to carry Load YASH PAL, May 26, 2021July 12, 2025 In this tutorial, we will use the 5-step approach to design a spherical dome to carry a load.Design step of the spherical domeWith the help of the data given finalized the geometry of the dome.Calculate the various loads coming on the structure.Calculate the maximum tensile and maximum compressive stress on the dome with the help of the values of meridional and hoop stress.Tabulate the design table starting with the value of meridional & hoop stress with respect to the critical angle.Find the reinforcement required against the value of maximum tensile stress.Analysis of spherical domea) Stress under UDL of ‘W’ per unit surface areaT =H = –At crown = 0H = 0.5At the base of the hemispherical dome= 90H = –For zero hoop stress, H = 00 = –W r ( = 0= 0= 0.618= 51.83b) Stress under concentrated load ‘W’ at the crownT = cosec 2C’; B’;0.9 m 0.9 mD’;C 4.5 m 4.5 m DBGH = – cosec 2c) Stress under combined UDL & concentrated loadT = + cosec 2H = – – cosec 2Q. The inside diameter of the circular room is 9m. Design a spherical dome to carry a uniform distribution live load of 1.5 KN/m 2. It has to support a lantern of 18 KN as a point load. It has a circular opening of 1.8 m at crown use M-20 & Fe 415.GivenDiameter of room = 9mLive load = 1.5 KN/m 2Cone load = 18 KNOpening at crown = 1.8 mM-20, Fe 415Design and Analysis of Spherical Dome1) Geometry of dome (Rise, R, h, )i) Rise = = to= and =AB = 1.8 mii) For RBy chord propertyCB x BD = AB x BO4.5 x 4.5 = 1.8 x (2R – AB )R = 6.525 miii) For hBy chord propertyC’B’ x B’D’ = AB’ x B’O0.9 x 0.9 = h x (2R – h )0.81 = h x (13.05 – h )0 = h 2 – 13.05h + 0.81h = 12.98 m , 0.062 mh = 0.062 m = 62 mmiv) ForSin = 43.6v) ForSin = 7.922) Load calculationLet the thickness of the dome bet = 100 mm = 0.1 mTotal load per unit area = DL + LLW = 25 x .1 + 1.5W = 4 KN/m 2Area of the opening C, A, D= 2rh = 2 x 3.14 x 0.9 x 0.062 = 0.35 m 2Load of the opening = 4 x 0.35 x 1.4 KNEffective load at crown = 18 – 1.4 = 16.6 KN3) Stress calculationMeridional stress for comdined loadT = + cosec 2T = + cosec 2T = + 4. 05 cosec 2 KN/mm 2A BHoop stressH = cos – – cosec 2H = cos – – cosec 2H = 0.261 cos – – 0.004 cosec 2 N/mm 2C DIn the absence of a live loadLoad per unit areaW I = DL = 25 x 0.1 = 2.5 KN/m 2Load of opening = 2.5 x area of opening= 2.5 x 0.35 = 0.87 KNEffective load of crownW = 18 – 0.87 = 17.13 KNH = cos – – cosecH = cos – – cosec 2H = 163 cos – – 4.18 cosec 2H = 0.163 cos – – 0.00418 cosec 2 N/mm 2E FMaximum compressive stress = 0.3317 N/mm 2Maximum temsile stress = 0.1311 N/mm 2Analysis and Design of Spherical Dome4) ReinforcementForce = stress x areaMax. tensile force = 0.1311 x 100 x 1000 = 13110 NArea of steel = = = 57 mm 2Ast minimum = x 100 x 1000 = 120 mmTotal Ast = 120 + 57 = 177 mm 2Using 8 mm dia of barsNo. of bar = = 3.52 4 barSpacing = x 1000 = 280 mmAlso, readDesign step for cantilever retaining wallDesign a rectangular beam civil engineering engineering subjects civil engineeringengineering subjects