# CHAPTER 6 FINITE ELEMENT ANALYSIS

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1 105 CHAPTER 6 FINITE ELEMENT ANALYSIS 6.1 INTRODUCTION Several theoretical approaches are considered to analyze the yielding and buckling failure modes of castellated beams. Elastic Finite Element Analysis is used to predict the ultimate load capacity for comparison. Finite element model generation is done using ANSYS 14.0 (ANSYS 14- User s Manual) and it is described in this chapter. Figure 6.1 shows the Finite Element Model (FEM) of castellated beam. Figure 6.1 Finite Element model of castellated beam These finite element models are used to simulate the experimental work in order to verify the test results and to investigate the non-linear behaviour of failure modes such as web-post buckling, shear buckling and

2 106 vierendeel bending of castellated beam of two sections IC 225 and IC 300 respectively. ANSYS 14.0 workbench finite element modeling program is used to develop a three dimensional finite element model. Nonlinear finite element models of these sections(ic 225 and IC 300) are built to determine maximum values and locations of stress, strain and displacement concentrations under two point loading. The non-linear analyses results are compared with results obtained from experimental studies. 6.2 FINITE ELEMENT MODELING Today the Finite Element Method (FEM) is considered as one of the well - established and convenient technique for the computer solution of complex problems in different fields of engineering: civil engineering, mechanical engineering, nuclear engineering, biomedical engineering, hydrodynamics, heat conduction, geo-mechanics, etc. From other side, FEM can be examined as a powerful tool for the approximate solution of differential equations describing different physical processes. This powerful design tool has significantly improved both the standard of engineering designs and the methodology of the design process in many industrial applications the general applicability of the FEM makes it a powerful and universal tool for a wide range of problems. Hence a number of computer program packages have been developed for the solution of a variety of structural and solid mechanics problems. Among more widely used packages are ANSYS, NASTRAN, ADINA, LS-DYNA, MARC, SAP, COSMOS, ABAQUS, and NISA.

3 107 The following are the steps involved in finite element analysis. 1. Model discretization 2. Select element displacement function 3. Calculate element properties 4. Obtain the element load vector 5. Assemble element properties 6. Impose boundary conditions 7. Determine the displacement field 8. Assemblage of elements 1) Model discretization: This is the process of subdividing the body into a number of elements. In a two dimensional problem, the elements would be 2D elements like triangle, rectangle, quadrilateral, sector etc. Analysis of solid bodies such as (stresses in engine cyclinders, stress under foundations, contact stress under point loads etc.) call for the use of 3D solid elements these has the drawback that the visualization is complex. The size of the stiffness matrix is to be handled can become enormous and un widely. 2) Select element displacement function: Simple mathematical functions are assumed to approximate the displacement field within each element. Since strains are functions of displacements and stresses are function of strains, this step amounts to defining the stress field within each element (in terms of some unknown)

4 108 3) Calculate element properties: This step involves the use of element equilibrium equations to calculate element stiffness matrix k in (in terms of the unknowns in step 2) corresponding to a set of element co-ordinates chosen. We would end up with k such that { } = k {P}. 4) Obtain the element load vector: This is done, starting from the loading on the element. The loading can be concentrated, distributed or varying on the element area. This can be in the plane of the element or normal to the plane of the element. The load vector we want would be the equivalent set of loads at the element co-ordinates originally described in the step3. 5) Assemble element properties: Element load vectors are assembled to obtain structure load vector. This will accord with a set of chosen structure coordinates. Between the coordinates of all the elements making up the structure, and the co-ordinates of the structure itself, we can establish a unique number based relationship. This will depend upon the way the elements are connected or connectivity. Likewise, element stiffness matrices are assembled to generate the structure stiffness matrix. 6) Impose boundary conditions: The structure for which we generated a structure stiffness matrix in step 5 is just an assemblage of elements, not yet attached to the ground. When we put it on the ground, it becomes a bridge or a dome or a frame - a real structure. This involves imposing the condition that displacements at some of the structure co-ordinates (introduced in step5) touching the ground are either zero or restricted to a finite value. The structure stiffness matrix

5 109 developed in step 5 shall therefore be modified to realize the condition that displacements at some of the coordinates need to be zero (or finite). When we modify the stiffness matrix thus, it will be nonsingular, positive definite. Its diagonal values would be positive and dominant. 7) Determine the displacement fields: From the structure displacement vector {u} obtained in step 6, we can infer the displacements of all co-ordinates in all elements using the connectivity information in step5. In each element, if the displacements at the co-ordinates are given by { }, we can go on to determine the displacement field, strains and stresses. 8) Assemblage of elements: Step 7 is almost the last step. But not quite. The assemblage of elements models (or approximates) the structural continuum. It is not the same as the continuum. Thus we may find some embarrassing results. 6.3 GENERAL PROCEDURE FOR FINITE ELEMENT Preprocessing ANALYSIS 1. Define the geometric domain of the problem. 2. Define the element types 3. Define the material properties of the elements. 4. Define the geometric properties of the elements (length, area) 5. Define the element connectivity (mesh the model). 6. Define the physical constraints (boundary conditions). 7. Define the loadings.

6 110 Solution 1. Computes the unknown values of the primary field variable(s) 2. Computed values are then used by back substitution to compute additional, derived variables, such as reaction forces, element stresses, and heat flow. Post Processing Postprocessor software contains sophisticated routines used for sorting, printing, and plotting selected results from a finite element solution. 6.4 ADVANTAGES OF FINITE ELEMENT ANALYSIS 1. Irregular Boundaries 2. General Loads 3. Different Materials 4. Boundary Conditions 5. Variable Element Size 6. Easy Modification 7. Dynamics 8. Nonlinear Problems (Geometric or Material) Before starting the process of analysis, Units should be selected and material properties should be assigned for the castellated beam section IC 225 and IC 300 respectively. Figure 6.2 shows the details of the units selected for the steel beam.

7 111 Figure 6.2 Unit selections for the section After applying inputs related with prepared models of beams, analysis process is initiated by using the software ANSYS. Material properties of castellated beams are extracted from material library; the library which covers standard concrete, steel and has the ability to create user defined custom materials for non-standard applications. Nonlinear elastic material model is used for the analysis with Young s modulus of 2 X10 5 and Poisson s ratio taken as 0.3 and the density of steel taken as 7850 kg/m 3. The material properties for the steel profile are shown in Figure 6.3.

8 112 Figure 6.3 Material properties of castellated beam 6.5 MESH GENERATION OF CASTELLATED BEAM WITH ANSYS 14.0 Mesh sizing is important for accurate stress and displacement values. For this purpose, selected meshing type, the tetrahedron mesh divides various sizing mesh starting with 400 mm. When the stress and displacement values are Table, this mesh sizing can be applicable for FEM analysis. Figure 6.4 shows the mesh generation of castellated beam.

9 113 Figure 6.4 Mesh generation of castellated beam 6.6 SECTION I IC Case- I Castellated beam without stiffeners (WOS 225) In this case castellated beam is analyzed without stiffeners. Figure 6.5 Geometric properties of IC 225

10 114 where L = 3.0m t f t w H w B f D hole = 7.5 mm = 5mm = 225 mm = 80mm = 150mm Figure 6.5 gives the geometric properties of IC 225 like length, thickness of flange, thickness of web, breadth of web, depth of the hole and over all depth of the section. Two point load is applied and the load is applied to the castellated beam as pressure as shown in the Figure 6.6. The main objective of this finite element analysis is to determine the stress concentration of the beam and to study the effect of stiffeners on the castellated beam. Figure 6.6 Load application of CB (WOS 225)

11 115 When load is applied over the beam from 10kN and as we increase the load stress concentration across the holes along the shear zone increases, which is clear in the Figure 6.7. Results of castellated beam without stiffeners are shown in Figure 6.8. Figure 6.7 Stress concentration of CB (WOS 225) Figure 6.8 Results of WOS 225

12 116 As we increase the load deflection also increases as shown in Figure 6.9. For the load increment of 110 kn, which is the average value obtained from experiments, deflection is mm. The results obtained are plotted in Figure Figure 6.9 Deflection of CB (WOS 225) Figure 6.10 Load - Deflection of CB (WOS 225)

13 117 For the first case as we increase the load stress concentration is higher across the hole corners along the shear zone and at the load application point leading to higher deflection. Hence to reduce the stress concentration and to reduce the deflection stiffeners are introduced on the opening of the web and on the other case it is provided on the solid portion of the web Case- II Castellated Beam with WDS 225 To reduce the stress concentration and deflection in this case stiffeners are introduced diagonally on the opening of the web on either side of the beam along the shear zone as shown in the Figure Figure 6.11 Diagonal stiffeners (IC 225) When stiffeners are introduced diagonally on the opening of the web stresses across the hole corners are reduced when compare to the first case without stiffeners and deflection of the beam is also reduced to mm for the load of 110 kn. Table 6.1 gives the test results of castellated beam with diagonal stiffeners and the results obtained are graphically plotted in the Figure 6.12.

14 118 Table 6.1 Deflection of CB (WDS 225) S.No Load (kn) Deflection (mm) Figure 6.12 Load-Deflection curve of CB (WDS 225)

15 Case- III Castellated Beam with WVS 225 From Figure 6.7 it is clear that stresses are distributed along the hole corners of the web and also between the opening along the shear zone. Hence in the third case, stiffeners are introduced on the solid portion of the web on either side of the beam along the shear zone as shown in the Figure Figure 6.13 Stress concentration of CB (WVS 225) In the third case with vertical stiffeners (WVS), when the stiffeners are provided on the solid portion of the web on either side along the shear zone, stress concentration along the holes increases and web panel starts to buckle leading to higher deflection. Table 6.2 gives the test results of castellated beam with vertical stiffeners. For the load of 110 kn deflection is increased to 15.4 mm.

16 120 Table 6.2 Deflection of CB (WVS 225) S.No Load (kn) Deflection (mm) The main purpose of these stiffeners is to provide stiffeners to the web rather to resist the applied loads. The shear capacity of the web has two components, Strength before the onset of the buckling and strength after buckling. As the shear load is increased on a stiffened web panel, the web panel buckles which leads to higher deflection as shown in the Figure Figure 6.14 Deflection of CB (WVS 225)

17 121 Figure 6.15 Comparisons of WOS, WDS and WVS (IC 225) Figure 6.15 shows the comparison between without stiffeners, with diagonal stiffeners and with vertical stiffeners. From the Figure 6.15 it is clear that diagonal stiffeners are more effective than vertical stiffeners and stresses can be minimized by providing diagonal stiffeners along the shear zone. 6.7 SECTION II IC Case- I Castellated Beam WOS 300 Figure 6.16 gives the geometric properties of the section IC 300. In this case castellated beam without stiffeners is analyzed.

18 122 Figure 6.16 Geometric properties of IC 300 where L = 3.0m t f t w H w B f D hole = 10 mm = 6 mm = 300 mm = 100 mm = 200 mm Figure 6.17 demonstrates the load application of IC 300 castellated beam without stiffeners in ANSYS Workbench. Two point loads is applied from 10kN and for each incremental load deflection of the beam is studied. As load increases stresses are developed at the hole corners and at load application point along the shear zone. When 130 kn load which is obtained from experimental tests was reached deflection is 7.46 mm. Figure 6.18

19 123 shows the stress distribution of castellated beam without stiffeners for IC 300 section. Figure 6.17 Load application of CB (WOS 300) Figure 6.18 Stress distribution of CB (WOS 300)

20 124 Figure 6.19 Deflection of CB (WOS 300) As the depth of the beam is increased deflection is reduced. For IC 225 maximum deflection was mm for a load of 110 kn. As the depth of the beam is increased deflection is reduced to 7.46mm for IC 300 for a maximum load of 130kN. But stress concentration is similar for both the section. Figure 6.19 shows the deflection of castellated beam without stiffeners. The results obtained are plotted in the Figure Figure 6.20 Load - Deflection curve of CB (WOS 300)

21 Case- II Castellated Beam WDS 300 For the first case without stiffeners stresses are distributed across the hole corners and load application point, our main objective is to reduce the stress concentration, increase the shear strength by reducing deflection. Hence to reduce the stress concentration stiffeners are introduced on the web along the shear zone. In this case diagonal stiffeners are introduced on either side of the web opening along the shear zone. Figure 6.21 shows the castellated beam with diagonal stiffeners. Figure 6.21 CB with diagonal stiffeners (WDS 300) Figure 6.22 Deflection of CB (WDS 300)

22 126 When stiffeners are provided diagonally, deflection of castellated beam is reduced to 4.94 mm when compared to beam without stiffeners. Figure 6.22 shows the deflection of castellated beam with diagonal stiffeners. Figure 6.23 shows the load - deflection of castellated beam with diagonal stiffeners. Figure 6.23 Load - Deflection of CB (WDS 300) Case- III Castellated Beam WVS 300 In the third case stiffeners are introduced vertically on the solid portion of the web on either side of the beam along the shear zone. Figure 6.24 shows the castellated beam with vertical stiffeners of IC 300 section.

23 127 Figure 6.24 CB with vertical stiffeners (WVS 300) When the stiffeners are provided on the solid portion of the web on either side along the shear zone, stress concentration along the holes increases and web panel starts to buckle leading to higher deflection. Figure 6.25 shows the deflection of castellated beam with vertical stiffeners and Figure 6.26 gives the test results of castellated beam with vertical stiffeners. For the load of 130 kn deflection is increased to 8.92mm. Figure 6.25 Deflection of CB (WVS 300)

24 128 Figure 6.26 Load - Deflection of CB (WVS 300) Figure 6.27 Comparison between WOS, WDS and WVS (IC 300) Figure 6.27 gives the comparison between without stiffeners, with diagonal stiffeners and with vertical stiffeners of (IC300). Table 6.3 gives the ratio between experimental and analytical studies and the difference between experimental and analytical is 4.34 % which shows the discrepancy is within 5%. Load-deflection diagrams obtained by the finite element analysis and experimental test for WOS 225 are compared in Figure 6.28.

25 129 Table 6.3 Ratio between experimental and analytical work WOS 225 WOS 225 Load Experimental Analytical Analytical (kn) Deflection Deflection Diffence in % (mm) (mm) Experimental Difference between experimental and analytical = ( )/14.03*100 = 4.34% Figure 6.28 Comparison of analytical and experimental WOS 225

26 130 Table 6.4 gives the comparison between theoretical, experimental and analytical work on castellated beam without stiffeners, it correlates with each other and the discrepancy is within 5% and there is a good correlation between theoretical, experimental and analytical results. Table 6.4 Comparison between theoretical, experimental and analytical work WOS 225 Specimen Type Deflection (mm) Theoretical Experimental Analytical WOS Figure 6.29 Comparisons between theoretical, experimental and analytical Table 6.4 gives the ratio between Experimental and analytical work of castellated beam with diagonal stiffener 225. When the experimental results of castellated beam with diagonal stiffeners are compared with analytical work, it is noticed that the deflection values obtained experimentally for WDS 225 is 1.57% more than the values obtained by analytical work and the discrepancy is within 2%. Figure 6.29 gives the comparison between experimental and analytical work of WDS 225.

27 131 Table 6.5 Ratio between experimental and analytical work WDS 225 WDS 225 Load Experimental Analytical Analytical Difference in (kn) Deflection Deflection % Experimental (mm) (mm) Difference between experimental and analytical = ( )/10.76*100 = 1.57% Figure 6.30 Comparison of analytical and experimental WDS 225

28 132 Table 6.6 gives the ratio between experimental and analytical work of castellated beam with vertical stiffeners. It is noticed that the ratio between experimental and analytical is 1. Figures 6.31 give the comparison between experimental and analytical work of castellated beam with vertical stiffeners. Table 6.6 Ratio between experimental and analytical work WVS 225 WVS 225 Load (kn) Experimental Deflection (mm) Analytical Deflection (mm) Analytical Experimental Difference in % Difference between experimental and analytical = ( )/15.73*100 = 2.0%

29 133 Figure 6.31 Comparison of analytical and experimental WVS 225 When depth of the beam is increased from 225mm to 300 mm deflection is reduced to 50%. Table 6.7 gives the ratio between experimental and analytical studies of castellated beam without stiffeners. When the experimental results are compared with those of finite element analysis for the section IC 300, it is noticed that the discrepancy is within 2%. Loaddeflection diagram obtained by finite element analysis is compared with experimental results and are illustrated in Figures 6.32.

30 134 Table 6.7 Ratio between experimental and analytical work WOS 300 WOS 300 Load Analytical Analytical Experimental Difference in % (KN) Deflection Deflection (mm) Experimental (mm) Difference between experimental and analytical = ( )/7.46*100 = 2.1% Figure 6.32 Comparison of analytical and experimental WOS 300

31 135 Table 6.8 gives the ratio between experimental and analytical results of castellated beam with diagonal stiffeners for the section IC 300. When the experimental results are compared with analytical work, it is noticed that the deflection values obtained analytically for WDS 300 is 3.8% more than the values obtained by experimental work Since the discrepancy is within 5% it is acceptable. Figure 6.33 illustrates the comparison between experimental and analytical test results of CB with diagonal stiffeners. Table 6.8 Ratio between experimental and analytical work WDS 300 WDS 300 Load Analytical Experimental Analytical Difference in % (kn) Deflection Deflection (mm) (mm) Experimental Difference between experimental and analytical = ( )/4.94*100 = 3.8 %

32 136 Figure 6.33 Comparison of analytical and experimental WDS 300 When the experimental results of castellated beam with vertical stiffeners are compared with analytical work, it is noticed that the deflection values obtained analytically for WVS 300 is 1.34% more than the values obtained by experimental work. Table 6.9 gives the ratio between experimental and analytical test results of beam with vertical stiffeners. Figures 6.34 illustrate the comparison between experimental and analytical work.

33 137 Table 6.9 Ratio between experimental and analytical work WVS 300 WVS 300 Load Experimental Analytical Analytical (kn) Deflection Deflection Difference in % Experimental (mm) (mm) Difference between experimental and analytical = ( )/8.92*100 = 1.34% Figure 6.34 Comparison of analytical and experimental WVS 300

34 138 Finite element analysis is an extremely useful tool in the design and analysis of castellated beams. FEA enables a more complete view of the stress distribution across the hole corners. The stress distribution and deflection thus obtained is compared with the experimental results. There is a good correlation between experimental and analytical results. 6.8 NON LINEAR ANALYSIS Non Linear analysis is done using ANSYS by modified riks method. Different Yield stress and plastic strain are found out by true stress and true strain and the values are given in the property module of plastic analysis. In a nonlinear analysis ANSYS automatically chooses appropriate load increments and convergence tolerances and continually adjusts them during the analysis to ensure that an accurate solution is obtained efficiently. Figure 6.35 shows the material properties for non linear analysis. Case-I Increased depth of castellated beam(ic 225) - With Out Stiffeners (WOS) Figure 6.35 Material properties of castellated beam IC 225

35 139 Figure 6.36 shows the stress strain curve for increased depth of castellated beam IC 225 for the case without stiffeners. It is found that the material reaches the yield stress at 25MPa and ultimate stress at 450Mpa. Figure 6.36 Stress-Strain curve for IC 225 and ISMB 200. Table 6.10 gives the material properties of the section ISMB 150

36 140 Table 6.10 Material properties of castellated beam S.No. Section Modulus of Elasticity (E s ) Yield Stress (f y ) Ultimate Stress (f u ) 1. ISMB X MPa 460MPa 2. ISMB X MPa 460MPa Type I Castellated Beam With Out Stiffners The ultimate load carrying capacity of Castellated Beam without stiffeners is 110kN and the Yield load is found to be 84.0 kn. The Figure 6.37 shows non linear pattern of load Vs deflection graph. 120 IC 225 (WOS) Load (kn) Deflection (mm) Figure 6.37 Load Vs deflection (WOS 225) Table 6.11 shows load Vs deflection values. The Figure 6.38 shows the Von-Mises stress of the section and the Figure 6.39 shows the web buckling mode of castellated beam.

37 141 Table 6.11 Deflection of Castellated Beam (WOS 225) S.No Load (kn) Deflection (mm) Figure 6.38 Von-Mises stress of the section (WOS 225)

38 142 Figure 6.39 Web buckling (WOS 225) Type II Castellated Beam With Diagonal Stiffners Figure 6.40 shows the stress strain curve for the Castellated Beam With Diagonal Stiffners (WDS) for the increased depth of castellated section IC 225. Figure 6.40 Stress-Strain curve for IC225 (WDS)

39 143 Figure 6.41 shows the non linear pattern of load Vs deflection graph. The material starts to yield at 100kN and reaches the ultimate at 120kN. Figure 6.41 Load Vs deflection (WDS 225) Figure 6.42 Von-Mises stress of the section (WDS 225) Figure 6.42 shows the Von mises stress distribution of castellated beam for diagonal stiffeners. Figure 6.43 shows the web buckling mode of castellated beam for diagonal stiffeners.

40 144 Figure 6.43 Web buckling mode (WDS 225) Type III: Castellated Beam With Vertical Stiffeners (WVS) vertical stiffeners. Figure 6.44 shows the stress strain curve for the third section with Figure 6.44 Stress-Strain curve for IC 225 (WVS)

41 145 The material starts to yield at 70kN and reaches the ultimate by 100kN. The Figure 6.46 shows the Von-Mises stress of the section and Figure 6.47 shows the top compression flange failure mode of the section. Figure 6.45 Load Vs deflection (WVS 225) graph. The Figure 6.45 shows non linear pattern of load Vs deflection Figure 6.46 Von-Mises stress of the section (WVS 225)

42 146 Figure 6.47 Top compression flange failure (WVS) Case-II Increased depth of castellated beam (IC 300) - With Out Stiffeners (WOS) Figure 6.48 shows the material properties for the second case Increased depth of Castellated beam (IC 300). Figure 6.48 Material properties of IC 300

43 147 Figure 6.49 shows the detail of stress strain curve for the case without stiffeners. Material reaches the yield stress at 250Mpa and reaches the ultimate at 450Mpa. Figure 6.49 Stress-strain curve for IC 300 (WOS) The Figure 6.50 shows non linear pattern of load Vs deflection graph. The material starts to yield at 110kNand reaches the ultimate at 130kN. Figure 6.50 Load Vs deflection (WOS 300)

44 148 Type II: Castellated Beam With Diagonal Stiffeners(WDS 300) Figure 6.51 Load Vs deflection (WDS 300) The Figure 6.51 shows the load Vs deflection curve for the section with diagonal stiffeners. Figure 6.52 Von-Mises stress of the section (WDS 300)

45 149 Figure 6.52 shows the Von-Mises stress of the beam.when the material starts to yield web starts to buckle and shear strength of the beam is reduced while the stiffeners play the role and the shear flows through the stiffeners and stresses are reduced. When the load reaches the ultimate along with the web, stiffeners starts to buckle. Figure 6.53 shows the web buckling of the section. Figure 6.53 Web buckling of the section (WDS 300) TYPE III: Castellated Beam With Vertical Stiffeners (WVS) The Figure 6.54 shows non linear pattern of load Vs deflection graph for the third case with vertical stiffeners of IC 300. The material starts to yield at 100kNand reaches the ultimate at 120kN. The Figure 6.55 shows the Von-Mises stress distribution of section.

46 150 Figure 6.54 Load Vs deflection (WVS 300) Figure 6.55 Von-Mises stress of the section (WVS)

47 151 Figure 6.56 shows the Von-Mises stress of the castellated beam with vertical stiffeners. When stiffeners are provided vertically web buckling is arrested but the failure is seen at the top compression flange leading to higher deflection. Figure 6.56 Top compression flange failure (WVS 300) For the first case with out stiffeners (WOS), when load is applied over the beam, stresses are distributed across the holes of the corners and deflection of the beam increases. In the second case, the castellated beam with diagonal stiffeners (WDS), stiffeners yield lesser deflection because of the truss action is takes through diagonal stiffener. In the shear span that is between load and support point the shear is dominating and hence forces flows through diagonal stiffener. The shear force causes diagonal tension and compression in the web and hence the diagonal stiffeners are provided in the direction of diagonal tension and diagonal compression for the smooth flow of shear forces. In the third case with vertical stiffeners (WVS),when the stiffeners are provided on the solid portion of the web on either side along the shear zone, stress concentration along the holes increases and web panel starts to

48 152 buckle leading to higher deflection. Which inferes that when solid portion of the web is stiffened, shear strength across the holes decreases which leads to higher deflection, because stresses across the opening are higher than the solid portion. When the web holes are stiffened deflection is reduced and when the solid portion of the web is stiffened, strength across the holes are reduced and deflection of the beam increases. MISES STRESSES These are failure criteria which predict failure based on different mechanisms. Von Mises criteria use Distortion energy theory whereas Maximum principal stress criteria use Maximum Principal Stress theory. The maximum, minimum principal stresses and Von Misses stresses are calculated analytically and compared with experimental results as shown below. Table 6.12 Comparison of experimental and analytical stress value (WOS) IC 225 S.No. Max.stress EXPERIMENTAL Minor stress Von-Mises stress Max.stress ANALYTICAL Minor stress 6.9 COMPARISON OF PRINCIPAL STRESSES AND VON- Von- Mises stress

49 153 Table 6.13 Comparison of experimental and analytical stress value (WDS) IC 225 S.NO. EXPERIMENTAL ANALYTICAL Max.stress Minor stress Von-Mises stress Max.stress Minor stress Von- Mises stress Table 6.14 Comparison of experimental and analytical stress value (WVS) IC 225 S.NO. Max.stress EXPERIMENTAL Minor stress Von-Mises stress Max.stress ANALYTICAL Minor stress Von- Mises stress

50 154 Table 6.15 Comparison of experimental and analytical stress value (WOS) IC 300 S.NO. Max.stress EXPERIMENTAL Minor stress Von-Mises stress Max.stress ANALYTICAL Minor stress Von-Mises stress Table 6.16 Comparison of experimental and analytical stress value (WDS) IC 300 S.NO. Max.stress EXPERIMENTAL Minor stress Von-Mises stress Max.stress ANALYTICAL Minor stress Von-Mises stre3ss

51 155 Table 6.17 Comparison of experimental and analytical stress value (WVS) IC 300 S.NO. Max.stress EXPERIMENTAL Minor stress Von-Mises stress Max.stress ANALYTICAL Minor stress Von-Mises stress Hence from the above results it is clearly understood that the experimental value is nearly coincide with the analytical value. Meanwhile the flow of shear forces along the edges of opening is carried effectively by the diagonal stiffeners than others. Therefore diagonal stiffeners are more effective in carrying the stresses.