Analysis And Design Of Pyramidal Roof Slab

Analysis And Design Of Pyramidal Roof Slab

Patil S.S

Professor, Faculty of Engineering-Civil Walchand Institute of Technology, Solapur, India

Kondekar A.R

Walchand Institute of Technology, Solapur, India

Abstract: Many historical buildings/monuments have been built having shape of a pyramid. The mystery and attractiveness of pyramidal shape have made pyramidal building undergo a renaissance in todays architectural design. Pyramidal roof slab is not a common structure because of its typical formwork and expensiveness. In countries where there is heavy snowfall, pyramidal slab is adopted so that snow can slide easily due to its sloping pattern. But in India it is constructed rarely due to less snow fall, typical form work, requirement of skilled labor and its expensiveness. A roof/slab consisting of a plane surface triangular in shape and bounded on each side by a sloping ridge forming the intersection of adjacent planes and culminating in a common vertex is known as pyramidal roof. Triangular panels of pyramidal slabs make an angle with vertical axis. According to that angle effect of thrusts and moments is decided. There are two types of moments: i) Along the slope ii) Across the slope depending upon the boundary conditions. The primary aim of the work is to analyze and design the Pyramidal roof slab. Different boundary conditions are considered like Pyramidal panels

1. with and without ridge beam (b) with and without edge beam (c) supported on wall and (d) supported on columns with different conditions. Primary thrust, Secondary thrust, Moments in different direction as well as at the edges and ridges are determined. As per that Design is carried out using Limit State Method. Analysis is also checked using MATLAB. Behavior of slab, beam and column is critically studied by changing meshing till the required precision of output is achieved. Variation in forces and moments with change in height, thickness, base angle and base dimension are presented graphically. Detailing of various elements like slab, edge beam, ridge beam, and column is also shown.

   Keyword: Pyramidal roof slab

   1. INTRODUCTION

      Slabs are plate elements having the depth D much smaller than its span and width. They usually carry a uniformly distributed load from the floor or roof of the building. Like beams, slabs are also simply supported, cantilever or continuous. The slabs are classified as:

      Planar roof slab

      The planar roof slabs are further classified as follows:

      1. One way slab

      2. Two way slab

      3. Flat slab supported directly on columns without beams.

      4. Waffle slab / grid slab

      5. Circular slab

      Non-planer roof slab:

      1. Domes (concrete shell roofs)

      2. folded plates

      3. Pyramidal roof slab

      4. Arch ribs

      5. Long cylindrical shell

      A roof / slab consisting of a plane surfaces triangular in shape and bounded on each side by a sloping ridge forming the intersection of adjacent planes and culminating in a common vertex is known as pyramidal roof. Many historical buildings/monuments have been built in shape of a pyramid. The CHEOPS pyramid in Egypt is one of the Seven Wonders of the World. Today no one can give an exhaustive account of the reasons why a tomb was constructed as such a giant regularly shaped monument. How was it built? What techniques did the builders use?

      The mystery and attractiveness of pyramidal shape have made pyramidal building undergo a renaissance in todays architectural design. Buildings as a whole for various purposes such as residence, hotels, multifunctional halls, offices, museums as well as building components like roofs or entrance of halls are constructed in pyramidal shape.

      Pyramidal roof slab is not a common structure because of its typical formwork and expensiveness. Earlier it was not used much but now a day the trend is developed. In countries where there is heavy snowfall, pyramidal slab is adopted so that snow can slide easily due to its sloping pattern. But in India it is adopted rarely due to less snow fall, typical form work, requirement of skilled labor and its expensiveness. Behavior of pyramidal slab is not like one-way or two- way slab. In case of one way and two way slab bending moment along effective span is pre- dominant and according to that steel is provided in either direction. In normal cases the shear in slab is not critical.

      In case of pyramidal slabs, triangular panels make an angle with vertical axis. According to that angle effect of thrusts and moments decided.

      There are two types of moments: i) in panel, ii) at the edges according to the support given to them. Different types of triangular pyramid are shown below.

      A section which cuts each ridge at the same distance from vertex is a normal cross section; in general, a regular figure whose normal cross section has axis of Symmetry at right angles to one another is desirable in this form of construction. Therefore five or seven sided panel pyramids are avoided. They are often limited to four sides. The axis of pyramid may be defined as the line passing through the centre of all cross sections and the vertex. This axis should be vertical. For the investigation of the forces in the pyramid as detailed below can be considered:

      1. (a) Pyramidal panels without beams at ridges and edges and resting on wall.

2. Pyramidal panels with edge beam but without ridge beam and

1. (a) Pyramidal panels with ridge beam but without edge beam.

   3 (a) Pyramidal panels with ridge beam without edge beam with and resting on columns at corner.

   1. Pyramidal panels with ridge beam and edge beam with and resting on columns at corner.

      II. OBJECTIVE OF STUDY

      The project aims at Analysis and Design of Pyramidal slab as per standard provisions. Limit state method is used for analysis and design. . The project also consists of cross check of manual results with the.

      1. Detailed understanding of Pyramidal slab.

      2. Detailed analysis and design as per Indian standards.

      3. To compare manual results of analysis with software results.

      4. To carry out parametric study of forces and moments of pyramidal slab, edge beam and ridge beam with the variation in height, thickness, base dimension and base angle.

   1. ANALYSIS OF FORCES AND

      MOMENT

      Pyramidal roof consists of pyramidal panels without beams at the ridges and edges. In this type, equal triangular faces are supported by the sloping edges of the other faces as shown in fig.2 The pyramid so formed will remain in position because it is prevented from sliding outwards by giving them support at lower edges by wall.

      Meridional thrust (T)

      Secondary thrust (H)

      Moment

      19

      18

      17

      16

      15

      14

      13

      Meridional Thrust (kN/m)

   2. THICKNESS VARIATION

      Series1

      0.10 0.11 0.12 0.13 0.14 0.15

      Thickness (m)

      Horizontal thrust

      (kN/m)

      Meridional thrust (T) v/s Thickness

      18

      17

      16

      15

      14

      13

      12

      Series1

      0.100.110.120.130.140.15

      Thickness (m)

      Horizontal Thrust (H) v/s Thickness

   3. CONCLUSION

      The thickness of the slab is considered between 100mm to 150mm. Stresses in slab; moment and tension in edge beam are within permissible limit. Axial force, shear force and moment in ridge bem are also increase with the increase in thickness.

      • If the span/height ratio is within 1.75 to 2.3 than stresses and moment in slab; tension, moment, axial force in edge beam and ridge beam are also decrease as the height increases.

      • As the base angle increases

1. Stresses and moment in pyramidal slab will decrease

2. Shear force and bending moment in edge beam will decrease

3. Axial force, shear force and moment in ridge beam will increase.

1. REFERENCES

1. M. Ikhwan, B.Ruck, Flow and Pressure field characteristics around Pyramidal buildings, Journal of Wind Engineering and Industrial Aerodynamics 94 (2006) 745 765.

2. Richard Bradshaw, David Campbell, Mousa Gargari, Amir Mirmiran, and Patrick Tripeny (2002).

3. J.Terrington, Design of Non Planer roof, (1964).

4. P.C. Varghese Design of Reinforced concrete shells and Folded Plates.

5. G.S.Ramaswamy, Design and Construction of Concrete Shell Roof – First Edition, Delhi 1986.

6. N.K.Bairagi, Plate Analysis, First Edition- Delhi, 1986.

7. H.J.Shah Reinforced Concrete.