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

x

y

::>300 M X 2800 ~M

200

320011UllX

y

I" 2700null

JO~ T' ill

All c1imensions in mm

Fig. 7.1 Plan of a room roof with ferrocement Channel elements

500mm

40mm riH-(All dimensions in mm )

Fig. 7.2 Connection details

210

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

7.3.1 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 30 20 node brick element (solid95) to create volume meshing.

7.3.1.1 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. 7.3.

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

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~M'N'O'P'U'V'W'X

Y A.SZ

- - KlSI ~~T R"

Q J

TetrahedralOplial

M,N,a,p.U,vW,XI A

Y • ZT • - - K.-r L

RQ J

Pyramid Oplial

M~Xa.p.wy U N AS

• ZI - T K,L,S

Q RJ

Prism Oplioo

Fig. 7.3 3D 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 of a

deformable body and are potentially in contact with the target surface, defined by

TARGEl70. The geometry ofTARGE170 is shown in Fig. 7.5.

212

Target segment Element

n n

z

,LvX

SUrfaee-to-SlJrfaceOontact ElementCONTA174

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. Material nonlinearities occur because of the nonlinear relationship

between stress and strain. Most common engineering materials exhibit a linear stress­

strain 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 2.7 N/mm2 and tangent modulus as 116

N/mm2• For the high strength bolts yield stress of 640 N/mm2

, ultimate stress of 800

N/mm2, and 12% elongation were adopted as per IS 1367 (Part 3), (2002). The modulus

of elasticity of steel was taken as 2x 105 N/mm2 (IS 456, 2000) and for ferrocement is

32420 N/mm2•

7.3.1.3 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 a1. 1998).

7.3.1.4 Load Application

Load was defined as area pressure of intensity 2.5kN/mm2• 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.

7.3.2 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

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.

7.3.3 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 2.

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Figure 7.7 shows the brick meshed model of one forth of the roof slab.

J\NSYSELEMENTS

DEC 20 20071l,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/m2. The maximum central deflection noted as 9.583mrn.

NODAL SOLUTION

STEP-1SUB -7TIME=.0025USUM (AVG)RSYS-ODMX -9.587SMX -9.58

ANJAN 2 2008

12,12,57

o 2.13 4.261 6.391 8.5211.065 3.196 5.326 7.456 9.587

(Mid span deflection = 9.583mm)

Fig 7.8 Detlection contour for single Channel element

216

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/m2

intensity, are shown in Fig. 7.9 to Fig. 7.13.

NODAL SOLUTION

STEP=lSUB =7TIME:.0025USUM IAVGIRSYS=QDMX =9.579SMX =9.579

J\NSYSDEC 18 2007

15:28:18

1.0642.129

3.1934.257

5.3226.386

7.458.515

9.579

(Mid span deflection = 9.579mm)

Fig. 7.9 Deflection contour of slab without bolt

NODAL SOLUTION

STEP-lSUB =7TIME-.0025USUM (AVGIRSYS-ODMX -8.214SMX -8.214

J\Nr V

DEC 31 200715: 10: 30

o 1.825 3.651 5.476 7.301.912682 2.738 4.563 6.389 8.214

(Mid span deflection = 8.214mm)

Fig. 7.10 Deflection contour of slab with 4 bolt

217

NODAL SOLUTION

STEP~1

SUB =7TIME~.0025

USUMTOPRSYS=ODMX -6.839SMX ~6. 839

o 1. 52.759908 2.28

3.043.8

ANSYSDEC 18 2007

12:06:00

4.559 6.0795.319 6.839

(Mid span deflection = 6.839mm)

Fig. 7.11 Deflection contour of slab with 6 bolt

NODAL SOLUTION

STEP~1

SUB ~7

TIME=.0025USUM (AVG)RSYS=ODMX -5.307SMX ~5.307

J\NSYSDEC 31 2007

15:24:52

o 1.179 2.359 3.538 4.717.589685 1.769 2.948 4.128 5.307

(Mid span deflection = 5.307mm)

Fig. 7.12 Deflection contour of slab with 8 bolt

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NODAL SOLUTION

STEP=lSUB -7TIME-.0025USUM (AVG)RSYS-ODMX -4.692SMX -4.692

J\NSYSJAN 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. 7.13 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 of 2.5 kN/m2 are given in Table 7.1.

Table 7.1 Maximum deflection for slab

Spacing of Mid span % decrease inSection description bolts deflection deflection

(mm) (mm)

Combined Elementwithout bolt - 9.579 0

Element connected by4 Bolt 675 8.214 14.25

Element connected by6 bolt 450 6.839 28.60

Element connected by8 bolt 337.50 5.307 44.59

Element connected by10 bolt 270 4.692 51.018

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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