CHAPTER 7 BEHAVIOUR OF THE COMBINED EFFECT OF ROOFING ELEMENTS

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1 CHAPTER 7 BEHAVIOUR OF THE COMBINED EFFECT OF ROOFING ELEMENTS 7.1 GENERAL An analytical study on behaviour of combined effect of optimised channel sections using ANSYS was carried out and discussed in this chapter. The ANSYS is a powerful multi purpose program that can be used in a wide variety of industries and in all disciplines of engineering. ANSYS is a sophisticated and comprehensive finite element program that has capabilities in many different physics fields such as static structural, nonlinear, thermal, implicit and explicit dynamics, fluid flow, electromagnetic, and electric field analysis. 7.2 PROBLEM DEFINITION The simulation is done for roof using optimised ferrocement channel sections for a room size of 2.3m x 2.8m as shown in Fig.7.1. Ferrocement channel sections are connected together using 12mm diameter high strength bolts along the web in different spacing. The connection details are shown in Fig 7.2. One of the parameters of this study is the spacing between the bolts along the length of the web. As the clear depth of web is 82mm, only one bolt is possible and is positioned at 40mm height from the bottom. For reducing the computing time advantage of symmetry is taken and one fourth of the problem only taken into consideration and modelled with symmetric boundary conditions. The axis of symmetry is shown in Fig. 7. I. 209

y x ::>300 M X 2800 ~M 200 X 320011Ull I" 2700null T' ill JO~ y All c1imensi ons in mm Fig. 7.

2 y x ::>300 M X 2800 ~M 200 X Ull I" 2700null T' ill JO~ y All c1imensi ons in mm Fig. 7.1 Plan of a room roof with ferrocement Channel elements 40mm rih- 500mm (All dimensions in mm ) Fig. 7.2 Connection details 210

3 7.3 DETAILS OF ANALYSIS The analysis of structure performed in AN SYS 10 was done in following 3 stages, 1. Pre processing 11. Solution 111. Post Processing PRE PROCESSING The key points defining the section were first created in the space and area was patched on it. These areas are meshed and are extruded along the required direction to get the volume. Two types of elements have been used for modelling the section. Shell 93 for creating area mesh and node brick element (solid95) to create volume meshing Element Input Brick elements, SOLID 95 were used in the three dimensional modelling of channel and bolts. The element is defined by 20 nodes each having three degrees of freedom per node, translations in the nodal x, y, and z directions. The element may have any spatial orientation. It can tolerate irregular shapes without as much loss of accuracy. SOLID95 elements have compatible displacement shapes and are well suited to model curved boundaries. The geometry, node locations, and the coordinate system for this element are shown in Fig The contact surfaces including the areas anticipated to be contact were defined and paired using CONTA174 and TARGEl70. It has the same geometric characteristics as the solid element face with which it is connected. CONT A 174 is used to represent contact and sliding between 3-D "target" surfaces and a deformable surface, defined by this element. This eleml.!nt is located on the surfaces of 3-D solid elements with mid side nodes. It has the same geometric characteristics as the solid element face with which it is connected 211

~M'N'O'P'U'V'W'X Y A.S Z - - KlS I ~~T R" Q J TetrahedralOplial I M,N,a,p.U,vW,X A Y Z T - - K.-r L R Q J Pyramid Oplial M~Xa.p.w y U N AS Z I - T K,L,S Q R J Prism Oplioo Fig. 7.

4 ~M'N'O'P'U'V'W'X Y A.S Z - - KlS I ~~T R" Q J TetrahedralOplial I M,N,a,p.U,vW,X A Y Z T - - K.-r L R Q J Pyramid Oplial M~Xa.p.w y U N AS Z I - T K,L,S Q R J Prism Oplioo Fig D 20 Node Brick Element SOLID 95 Contact occurs when the element surface penetrates one of the target segment elements on a specified target surface. The element is defmed by eight nodes (the underlying solid element has mid side nodes). The CONTAl74 element is shown in Fig.7.4. TARGE170 is used to represent various 3-D "target" surfaces for the associated contact elements. Associa ed Target Surfaces Fig. 7.4 Contact Element-CONTA 174 The contact elements themselves overlay the solid elements describing the boundary ofa deformable body and are potentially in contact with the target surface, defined by TARGEl70. The geometry oftarge170 is shown in Fig

Target segment Element n SUrfaee-to-SlJrface Oontact Element CONTA174 n z X,Lv Fig. 7.S.Contact element- TARGE 170 7.3.1.2 Material Properties Anumber of material-related factors can cause structural stiffness to change during the course of an analysis.

5 Target segment Element n SUrfaee-to-SlJrface Oontact Element CONTA174 n z X,Lv Fig. 7.S.Contact element- TARGE Material Properties Anumber of material-related factors can cause structural stiffness to change during the course of an analysis. Material nonlinearities occur because of the nonlinear relationship between stress and strain. Most common engineering materials exhibit a linear stressstrain relationship up to a stress level known as the proportional limit. Beyond this limit, the stress-strain relationship will become nonlinear, but will not necessarily become inelastic. Plastic behaviour, characterised by non-recoverable strain, begins when stresses exceed the material's yield point. The ANSYS program assumes that these two points are coincident in plasticity analyses. The Bilinear Kinematic Hardening (BKIN) option assumes the total stress range is equal to twice the yield stress. The stress-strain curve for bilinear kinematic hardening option given in Fig. 7.6 was adopted for the analysis. 213

T ---f'-------,f-----tr- Sh"llin fi Fig. 7.6. Bilinear kinematic stress-strain curve For ferrocement the yield stress was taken as 2.

6 T ---f' ,f-----tr- Sh"llin fi Fig Bilinear kinematic stress-strain curve For ferrocement the yield stress was taken as 2.7 N/mm 2 and tangent modulus as 116 N/mm 2 For the high strength bolts yield stress of 640 N/mm 2, ultimate stress of 800 N/mm 2, and 12% elongation were adopted as per IS 1367 (Part 3), (2002). The modulus of elasticity of steel was taken as 2x 10 5 N/mm 2 (IS 456, 2000) and for ferrocement is N/mm Boundary conditions Boundary condition was defined by arresting displacement in X, Y & Z directions. On the axis symmetry sides symmetric boundary conditions were applied (Faella et a ) Load Application Load was defined as area pressure of intensity 2.5kN/mm 2 Load is applied in 7 load steps. A load step is a set of loads applied over a given time span. Sub steps are time points within a load step at which intermediate solutions are calculated. The difference in time between two successive sub steps can be called a time step or time increment. In a nonlinear static or steady-state analysis, sub steps are used to apply the loads gradually so that an accurate solution can be obtained SOLUTION Here we define the analysis type, load step, time etc. the stored data was subjected to static analysis which forms the processing stage. Each load step is processed and 214

7 convergence was checked. The sparse direct solver is the default solver for all analyses. The sparse direct solver is based on a direct elimination of equations POST PROCESSING Post processor is the section where the results of analysis through graphic displays and tabular listing were reviewed. Two postprocessors are available for reviewing the results, POST1, the general post processor, and POST26, the time-history postprocessor. Post processing results includes deformed shape, contour plots for displacements and stresses etc. 7.4 STEPS INVOLVED The various steps for finite element modelling and analysis are as follows. The detailed input data is shown in Appendix B. };,, Invoking ANSYSlO };,, Pre processor Element data Material data Geometry creation Contact manager Loads };,, Solution };,, General post process 7.5 MODELLING OF SECTIONS The following phases of work have been carried out to study the behaviour of single element and the combined effect of number of individual elements (Faella et al. 1998). 1. Modelling of single optimised channel section 2. Simply placing all the channel elements in position without bolt connection for a room size of 2.3m X 2.8m. 3. Four models were created by varying the number of bolts from 4 to 10 with an increment of

$Figure 7.7 shows the brick meshed model ofone forth ofthe roof slab. ELEMENTS J\NSYS DEC 20 2007 1l,45,13 Fig 7.7 Ferrocement Channel meshed model Figure 7.$

8 Figure 7.7 shows the brick meshed model ofone forth ofthe roof slab. ELEMENTS J\NSYS DEC l,45,13 Fig 7.7 Ferrocement Channel meshed model Figure 7.8 shows the deflection contour for a single channel element under a load of 2.5kN/m 2. The maximum central deflection noted as 9.583mrn. NODAL SOLUTION STEP-1 SUB -7 TIME=.0025 USUM (AVG) RSYS-O DMX SMX AN JAN ,12,57 o (Mid span deflection = 9.583mm) Fig 7.8 Detlection contour for single Channel element 216

$NODAL SOLUTION STEP=l SUB =7 TIME:.0025 USUM IAVGI RSYS=Q DMX =9.579 SMX =9.579 J\NSYS DEC 18 2007 15:28:18 1.064 2.129 3.193 4.257 5.322 6.386 7.$

9 7.6 DEFLECTION CONTOURS OF THE COMBINED EFFECT OF OPTIMISED SECTION Deflection contours for channel shaped sections subjected to a loading of 2.5 kn/m 2 intensity, are shown in Fig. 7.9 to Fig NODAL SOLUTION STEP=l SUB =7 TIME:.0025 USUM IAVGI RSYS=Q DMX =9.579 SMX =9.579 J\NSYS DEC :28: (Mid span deflection = 9.579mm) Fig. 7.9 Deflection contour of slab without bolt NODAL SOLUTION STEP-l SUB =7 TIME USUM (AVGI RSYS-O DMX SMX J\Nr DEC : 10: 30 V o (Mid span deflection = 8.214mm) Fig Deflection contour of slab with 4 bolt 217

$11 Deflection contour of slab with 6 bolt NODAL SOLUTION STEP~1 SUB ~7 TIME=.0025 USUM (AVG) RSYS=O DMX -5.307 SMX ~5.307 J\NSYS DEC 31 2007 15:24:52 o 1.179 2.359 3.538 4.717.589685 1.769 2.948 4.$

10 NODAL SOLUTION STEP~1 SUB =7 TIME~.0025 USUM TOP RSYS=O DMX SMX ~ ANSYS DEC :06:00 o (Mid span deflection = 6.839mm) Fig Deflection contour of slab with 6 bolt NODAL SOLUTION STEP~1 SUB ~7 TIME=.0025 USUM (AVG) RSYS=O DMX SMX ~5.307 J\NSYS DEC :24:52 o (Mid span deflection = 5.307mm) Fig Deflection contour of slab with 8 bolt 218

$NODAL SOLUTION STEP=l SUB -7 TIME-.0025 USUM (AVG) RSYS-O DMX -4.692 SMX -4.692 J\NSYS JAN 2 2008 16:20:35 o 1.043 2.085 3.128 4.171.52137 1.564 2.607 3.65 4.692 (Mid span deflection = 4.692mm) Fig.$

11 NODAL SOLUTION STEP=l SUB -7 TIME USUM (AVG) RSYS-O DMX SMX J\NSYS JAN :20:35 o (Mid span deflection = 4.692mm) Fig Deflection contour of slab with 10 bolt 7.7 COMPARISON OF RESULTS Output contours obtained for deflection distribution of roof slab subjected to an imposed loading intensity of2.5 kn/m 2 are given in Table 7.1. Table 7.1 Maximum deflection for slab Spacing of Mid span % decrease in Section description bolts deflection deflection (mm) (mm) Combined Element without bolt Element connected by 4 Bolt Element connected by 6 bolt Element connected by 8 bolt Element connected by 10 bolt

12 From Table 7.1 it may be noted that mid span deflection decreases with increase in rigidity of the structure due the bolts. This may be due to the combined effect of individual channels as a single unit. 7.8 SUMMARY AND CONCLUSIONS The combined effect of ferrocement channel roofing elements with and without bolted connections along the web of the element was analysed using AN SYS 10. The roofing elements without bolted connection behaved as single elements and suffered maximum deflection, on the other hand elements with bolted connection behaved like a single unit and the maximum deflection for this case was found to be less than the system without bolt. However the analysis indicate that the optimum number of bolts required for connecting the channels side by side was found to be 4 bolts with respect to the maximum allowable deflection criteria as per IS 456, 2000 is (L/250). 220

CHAPTER 4. Numerical Models. descriptions of the boundary conditions, element types, validation, and the force

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