Verification Examples
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1 Verification Examples 015
2 AxisVM 13 Verification Examples Linear static... 3 Supported bar with concentrated loads Thermally loaded bar structure Continously supported beam with constant distributed load External prestessed beam Periodically supported infinite membrane wall with constant distributed load Clamped beam examination with plane stress elements Clamped thin square plate Plate with fixed support and constant distributed load Annular plate All edges simply supported plate with partial distributed load Clamped plate with linear distributed load Hemisphere displacement Nonlinear static D beam structure Plate with fixed end and bending moment Dynamic Deep simply supported beam Clamped thin rhombic plate Cantilevered thin square plate Cantilevered tapered membrane Flat grillages Stability Simply supported beam Simply supported beam Design N-M interaction curve of cross-section EC, EN : RC beam deflection according to EC, EN : Required steel reinforcement of RC plate according to EC, EN : Interaction check of beam under biaxial bending EC3, EN : Interaction check of beam under normal force, bending and shear force EC3, EN : Buckling resistance of simply supported I beam EC3, EN : Buckling resistance of simply supported T beam EC3, EN : Buckling of a hollow cross-section beam EC3, EN : Lateral torsional buckling of a beam EC3, EN : Interaction check of beam in section class 4. EC3, EN :009, EN : Earth-quake design using response-spectrum method... 80
3 AxisVM 13 Verification Examples 3 Linear static
4 AxisVM 13 Verification Examples 4 Software Release Number: R1 Date: Tested by: InterCAD Page number: File name: beam1.axs Thema Analysis Type Geometry Supported bar with concentrated loads. Linear analysis. Side view Section Area = 100,0 cm (10 10) Loads Boundary Conditions Material Properties Element types Mesh Axial direction forces P1 = -00 kn, P = 100 kn, P3 = -40 kn Fix ends, at R1 and R5. E = 0000 kn / cm = 0,3 Beam element Target Results R1, R5 support forces Theory AxisVM % R 1 [kn] -,00 -,00 0,00 R 5 [kn] 118,00 118,00 0,00
5 AxisVM 13 Verification Examples 5 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: beam.axs Thema Analysis Type Geometry Thermally loaded bar structure. Linear analysis. z x Sections: Steel: AS = x 10-4 m (D=cm) Copper: AC = x 10-4 m (D=cm) Side view Loads Boundary Conditions Material Properties Element types Target Results P = -1 kn (Point load) Temperature rise of 10 C in the structure after assembly. The upper end of bars are fixed. Nodal DOF: Frame X-Z plane Steel: ES = 0700 kn / cm, = 0,3, S = 1, x 10-5 C -1 Copper: EC = kn / cm, = 0,3, C = 1,7 x 10-5 C -1 Beam element Smax in the three bars. Theory AxisVM % Steel S max [MPa] 3,84 3,848 0,10 Cooper S max [MPa] 7,185 7,199 0,19
6 AxisVM 13 Verification Examples 6 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: beam3.axs Thema Analysis Type Geometry Continously supported beam with point loads. Linear analysis. Side view (Section width = 1,00 m, height1 = 0,30 m, height = 0,60 m) Loads Boundary Conditions Material Properties Element types Target Results P1= -300 kn, P= -150 kn, P3= -800 kn, P4= -450 kn Elastic supported. From A to D is Kz = 5000 kn/m/m. From D to F is Kz = kn/m/m. Nodal DOF: Frame X-Z plane E = 3000 kn/cm = 0,3 Rib element: Three node beam element. Shear deformation is taken into account. ez, My, Vz, Rz Diagram ez Diagram My
7 AxisVM 13 Verification Examples 7 Results Diagram Vz Diagram Rz Reference AxisVM e [%] e A [m] 0,006 0,006 0,00 e B [m] 0,009 0,009 0,00 e C [m] 0,014 0,014 0,00 e D [m] 0,015 0,015 0,00 e E [m] 0,015 0,015 0,00 e F [m] 0,013 0,013 0,00 Reference AxisVM e [%] M A [KNm] 0,0 0, 0,00 M B [KNm] 88,5 87,1-1,58 M C [KNm] 636, 630,8-0,85 M D [KNm] 33,8 330,1-0,81 M E [KNm] 164, 163,0-0,73 M F [KNm] 0,0 0,4 0,00
8 AxisVM 13 Verification Examples 8 Results Reference AxisVM e [%] V A [KN] 0,0 0,1 0,00 V B [KN] 11,1 113,1 0,89 V C [KN] 646,8 647, 0,06 V D [KN] 335,0 334,9-0,03 V E [KN] 67,8 67,5-0,11 V F [KN] 0,0-0,1 0,00 Reference AxisVM e [%] R A [KN/m ] 145,7 154,0 5,70 R B [KN/m ] 19,5 19,4-0,05 R C [KN/m ] 343,8 346,0 0,64 R D [KN/m ] 386,9 386,4-0,13 R E [KN/m ] 4,5 4,7 0,09 R F [KN/m ] 01, 00,8-0,0
9 AxisVM 13 Verification Examples 9 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: beam4.axs Thema Analysis Type Geometry External prestessed beam. Linear analysis. Side view Loads Boundary Conditions Material Properties p = -50 kn /m distributed load Length change = -6,5E-3 at beam 5-6 ey = ez = = 0 at node 1 ex = ey = ez = 0 at node 4 E =,1E11 N / m Beam 1-5, 5-6, 6-4 A = 4,5E-3 m Iz= 0,E-5 m 4 Truss -5, 3-6 A = 3,48E-3 m Iz= 0,E-5 m 4 Beam 1-4 A = 1,516E- m Iz=,174E-4 m 4 Mesh Beam 1-4: division into N segment: N = 1 Element types Rib element: Three node beam element, 1-5, 5-6, 6-4, 1-4 (shear deformation is taken into account) Truss element -5, 3-6 Target NX at beam 1-4 My,max at beam -3 ez at node
10 AxisVM 13 Verification Examples 10 Results Diagram ez ROBOT V6 AxisVM % N x [kn] 584,56 584,81 0,04 M y [knm] 49,6 49,60 0,68 e z [mm] -0,541-0,5469 0,89
11 AxisVM 13 Verification Examples 11 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plane1.axs Thema Analysis Type Geometry Periodically supported infinite membrane wall with constant distributed load. Linear analysis. Loads p = 00 kn / m Side view (thickness = 0,0 cm) Boundary Conditions Material Properties Element types Mesh vertical support at every 4,0 m support length is 0,4 m (Rz = 1E+3) Symmetry edges Nodal DOF: (C C f C C C) E = 880 kn / cm = 0,16 Parabolic quadrilateral membrane (plane stress) Target Sxx at 1-10 nodes (1-5 at middle, 6-10 at support)
12 AxisVM 13 Verification Examples 1 Results Node Analytical [kn/cm ] AxisVM [kn/cm ] % 1 0,1313 0,1310-0,3 0,0399 0,0395-1,00 3-0,0093-0,0095,15 4-0,041-0,0413 0,4 5-0,1073-0,1070-0,8 6-0,9317-0,9166-1,6 7 0,0401 0,046 6,3 8 0,0465 0,0469 0,86 9 0,0538 0,0537-0, ,149 0,145-0,3 Reference: Dr. Bölcskey Elemér Dr. Orosz Árpád: Vasbeton szerkezetek Faltartók, Lemezek, Tárolók
13 AxisVM 13 Verification Examples 13 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plane.axs Thema Analysis Type Geometry Clamped beam examination with plane stress elements. Linear analysis. Side view Loads Boundary Conditions Material Properties Element types Mesh p = -5 kn/m Both ends built-in. Line support component stiffness: 1E+10. Symmetry edge Nodal DOF: (C C f C C C) E = 880 kn / cm = 0 Parabolic quadrilateral membrane (plane stress) Side view
14 AxisVM 13 Verification Examples 14 Target Results xy, max at section C Diagram xy Diagram xy at section C
15 AxisVM 13 Verification Examples 15 V 65,65 kn ( from beam theory) S ' y 0, m 3 b 0,5 m I y 0, m 4 xy V S b I ' y y 65,650, ,5 0,50, kn/ m AxisVM result xy = 786,8 kn / m Difference = -0,09 % AxisVM result V nxy 65, 33 kn Difference = -0,45 %
16 AxisVM 13 Verification Examples 16 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plate1.axs Thema Analysis Type Geometry Clamped thin square plate. Linear analysis. Top view (thickness = 5,0 cm) Loads Boundary Conditions Material Properties Element types Mesh P = -10 kn (at the middle of the plate) ex = ez = ez = fix = fiy = fiz = 0 along all edges Nodal DOF: Plate in X-Y plane E = 0000 kn / cm = 0,3 Plate element (Parabolic quadrilateral, heterosis) Target Displacement of middle of the plate
17 AxisVM 13 Verification Examples 17 Results Displacements Mode Mesh Book 1 Timoshenko AxisVM Diff 1 [%] Diff [%] 1 x 0,40 0,40 4,48 10,53 4x4 0,416 0,369-11,30 -,89 3 8x8 0,394 0,38 0,381-3,30 0,6 4 1x1 0,387 0,383-1,03 0, x16 0,385 0,383-0,5 0,79 References: 1.) The Finite Element Method (Fourth Edition) Volume. /O.C. Zienkiewicz and R.L. Taylor/ McGraw-Hill Book Company 1991 London.) Result of analytical solution of Timoshenko Convergency 15,00 10,00 5,00 Displacements 0, Diff1 [%] Diff [%] -5,00-10,00-15,00 Mesh density
18 AxisVM 13 Verification Examples 18 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plate_1.axs Thema Analysis Type Geometry Plate with fixed support and constant distributed load. Linear analysis. Top view (thickness = 15,0 cm) Loads P = -5 kn / m Boundary ex = ey = ez = fix = fiy = fiz = 0 along all edges Conditions Nodal DOF: Plate in X-Y plane Material E = 990 kn/cm Properties = 0,16 Element Parabolic triangle plate element types Mesh Target Results Maximal ez (found at Node1) and maximal mx (found at Node) Component Nastran AxisVM % ez,max [mm] -1,613-1,593-1,4 mx,max [knm/m] 3,060 3,059-0,03
19 AxisVM 13 Verification Examples 19 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plate3.axs Thema Analysis Type Geometry Annular plate. Linear analysis. Top view (thickness =,0 cm) Loads Boundary Conditions Edge load: Q = 100 kn / m Distributed load: q = 100 kn / m Nodal DOF: Plate in X-Y plane Material Properties Element types E = 880 kn / cm = 0,3 Plate element (parabolic quadrilateral, heterosis)
20 AxisVM 13 Verification Examples 0 Mesh Target Smax, emax Results Theory AxisVM Model S max S max % [kn/cm] [kn/cm] a.),8,78-1,4 b.) 6,88 6,76-1,74 c.) 14, 14,10-0,84 d.) 1,33 1,33 0,00 e.),35,5-4,6 f.) 9,88 9,88 0,00 g.) 4,79 4,76-0,63 h.) 7,86 7,86 0,00 Theory AxisVM Model e max e max % [mm] [mm] a.) 77,68 76,10 -,03 b.) 6,76 0,84 -,61 c.) 355,17 35,89-0,64 d.) 3,8 3,4 0,60 e.) 44,6 44,50 0,54 f.) 13,19 13,17-0,0 g.) 11,14 111,94-0,18 h.) 16,83 16,81-0,0 Reference: S. Timoshenko and S. Woinowsky-Krieger: Theory of Plates And Shells
21 AxisVM 13 Verification Examples 1 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plate4.axs Thema Analysis Type Geometry All edges simply supported plate with partial distributed load. Linear analysis. Top view (thickness =,0 cm) Loads Boundary Conditions Material Properties Element types Mesh Distributed load: q = -10 kn / m (middle of the plate at,0 x,0 m area) a.) ex = ey = ez = 0 along all edges (soft support) b.) ex = ey = ez = 0 along all edges = 0 perpendicular the edges (hard support) Nodal DOF: Plate in X-Y plane E = 880 kn / cm = 0,3 Plate element (Heterosis)
22 AxisVM 13 Verification Examples Target Results mx, max, my, max a.) Moment Theory AxisVM % m x, max [knm/m] 7,4 7,34 1,38 m y, max [knm/m] 5,3 5,39 1,3 b.) Moment Theory AxisVM % m x, max [knm/m] 7,4 7,8 0,55 m y, max [knm/m] 5,3 5,35 0,56 Reference: S. Timoshenko and S. Woinowsky-Krieger: Theory of Plates And Shells
23 AxisVM 13 Verification Examples 3 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: plate5.axs Thema Analysis Type Geometry Clamped plate with linear distributed load. Linear analysis. Top view (thickness =,0 cm) Loads Distributed load: q = -10 kn / m Boundary Conditions Material Properties Element types Mesh ex = ey = ez = fix = fiy= fiz = 0 along all edges Nodal DOF: Plate in X-Y plane E = 880 kn / cm = 0,3 Plate element (Heterosis)
24 AxisVM 13 Verification Examples 4 Target mx, my Results Reference: Results Theory AxisVM % m x,1 [knm/m] 11,50 11,48-0,17 m y,1 [knm/m] 11,50 11,48-0,17 m x, [knm/m] 33,40 33,3-0,51 m x,3 [knm/m] 17,90 17,83-0,39 m y,4 [knm/m] 5,70 5,53-0,66 S. Timoshenko and S. Woinowsky-Krieger: Theory of Plates And Shells
25 AxisVM 13 Verification Examples 5 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: hemisphere.axs Thema Analysis Type Geometry Hemisphere displacement. Linear analysis. Hemisphere (Axonometric view) t = 0,04 m Loads Point load P =,0 kn
26 AxisVM 13 Verification Examples 6 Boundary Conditions Material Properties Element types Target ex = ey = ez = fix = fiy = fiz= 0 at C Symmetry in X-Z plane on A-C edge Symmetry in Y-Z plane on B-C edge E = 685 kn / cm = 0,3 Shell element 1.) guadrilateral parabolic.) triangle parabolic ex at point A Results e x [m] e [%] Theory 0,185 AxisVM quadrilateral 0,185 0,00 AxisVM triangle 0,18-1,6
27 AxisVM 13 Verification Examples 7 Nonlinear static
28 AxisVM 13 Verification Examples 8 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: nonlin1.axs Thema Analysis Type Geometry 3D beam structure. Geometrical nonlinear analysis. 1,73 m F y =-300,00 kn F z =-600,00 kn Node1 F y =-300,00 kn F z =-600,00 kn 3,000 m 1,73 m Beam1 D Y X 1,73 m 3,000 m 1,73 m A F z =-600,00 kn C B 4,000 m Z Z Y X X Loads Boundary Conditions Material Properties Cross- Section Properties Element types Target Py = -300 kn Pz = -600 kn ex = ey = ez = 0 at A, B, C and D S 75 E = 1000 kn / cm = 0,3 HEA 300 Ax = cm ; Ix = 85.3 cm 4 ; Iy = cm 4 ; Iz = cm 4 Beam ex, ey, ez, at Node1 Nx, Vy, Vz, Tx, My, Mz of Beam1 at Node1
29 AxisVM 13 Verification Examples 9 Results Comparison with the results obtained using Nastran V4 Component Nastran AxisVM % ex [mm] 17,898 17,881-0,09 ey [mm] -75,70-75,663-0,05 ez [mm] -4,63-4,597-0,06 Nx [kn] -83,15-83,5 0,04 Vy [kn] -8,09-8,10 0,04 Vx [kn] -106,57-106,48-0,08 Tx [knm] -4,57-4,57 0,00 My [knm] -519,00-518,74-0,05 Mz [knm] 148,94 148,91-0,0
30 AxisVM 13 Verification Examples 30 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: nonlin.axs Thema Analysis Type Geometry Plate with fixed end and bending moment. Geometrical nonlinear analysis. Loads Boundary Conditions Material Properties Cross Section Properties Element types Mz = 600 knm (x1300 Nm) acting on Edge ex = ey = ez = fix = fiy = fiz = 0 along Edge1 (Use Constrained nodes instead of line support; Nodal DOF on Edge 1: Fixed node) E = 0000 N / mm = 0 Plate thickness: 150 mm Rib on Edge: circular D = 500 mm (for distributing load to the mid-side-node) Parabolic quadrilateral shell (heterosis) Rib on Edge for distributing load to the mid-side-node
31 AxisVM 13 Verification Examples 31 Target Results Z at Edge I I E z plate plate plate plate M.610 Theoretical results based on the differential equation of the flexible beam: M E plate plate 3 ab N m 1 m M z I platee Nm.610 z plate plate rad Comparison the AxisVM result with the theoretical one: Component Theory AxisVM % fiz [rad] 5,5467 5,550 0,06
32 AxisVM 13 Verification Examples 3 BLANK
33 AxisVM 13 Verification Examples 33 Dynamic
34 AxisVM 13 Verification Examples 34 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: dynam1.axs Thema Analysis Type Geometry Deep simply supported beam. Vibration analysis. Beam (Axonometric view) Cross section (square,0 m x,0 m) Loads Boundary Conditions Material Properties Element types Target Self-weight (Other option: Apply Masses only option on Vibration analysis window) ex = ey = ez = fix = 0 at A ey = ez = 0 at B E = 0000 kn / cm = 0,3 = 8000 kg / m 3 Rib elemen: Three node beam element (shear deformation is taken into account) First 7 mode shapes
35 AxisVM 13 Verification Examples 35 Results Mode 1: f = 43,16 Hz Mode : f = 43,16 Hz Mode 3: f = 14,01 Hz Mode 4: f = 15,50 Hz Mode 5: f = 15,50 Hz Mode 6: f = 93,55 Hz Mode 7: f = 93,55 Hz
36 AxisVM 13 Verification Examples 36 Results Comparison with NAFEMS example Mode NAFEMS (Hz) AxisVM (Hz) % 1 4,65 43,16-1,0 4,65 43,16-1,0 3 15,00 14,01 0, ,31 15,50 -, ,31 15,50 -, ,55 93,55-3, ,55 93,55-3,16
37 AxisVM 13 Verification Examples 37 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: dynam.axs Thema Analysis Type Geometry Clamped thin rhombic plate. Vibration analysis. Top view of plane (thickness = 5,0 cm) Loads Boundary Conditions Material Properties Element types Mesh Self-weight ex = ey = fiz = 0 at all nodes (i.e.: ex, ey, fiz constrained at all nodes; Nodal DOF: Plate in X-Y plane) ez = fix = fiy = 0 along the 4 edges (Line support) E = 0000 kn / cm = 0,3 = 8000 kg / m 3 Parabolic quadrilateral shell element (heterosis)
38 er 0,506 0,470 0,433 0,397 0,361 0,35 0,89 0,53 0,17 0,181 0,144 0,108 0,07 0,036 0 er 0,486 0,451 0,416 0,38 0,347 0,31 0,78 0,43 0,08 0,174 0,139 0,104 0,069 0,035 0 er 0,498 0,46 0,47 0,391 0,356 0,30 0,84 0,49 0,13 0,178 0,14 0,107 0,071 0,036 0 er 0,463 0,49 0,396 0,363 0,330 0,97 0,64 0,31 0,198 0,165 0,13 0,099 0,066 0,033 0 er er 0,449 0,417 0,385 0,353 0,31 0,89 0,57 0,5 0,19 0,160 0,18 0,096 0,064 0,03 0 0,50 0,483 0,446 0,409 0,37 0,335 0,97 0,60 0,3 0,186 0,149 0,11 0,074 0,037 0 AxisVM 13 Verification Examples 38 Target First 6 mode shapes Results Mode 1: f = 8,0 Hz Mode : f = 13,0 Hz Mode 3: f = 18,41 Hz Mode 4: f = 19,33 Hz Mode 5: f = 4,6 Hz Mode 6: f = 8,4 Hz Results Comparison with NAFEMS example Mode NAFEMS (Hz) AxisVM (Hz) % 1 7,94 8,0 1,01 1,84 13,0 1, ,94 18,41,6 4 19,13 19,33 1,05 5 4,01 4,6,54 6 7,9 8,4 1,15
39 AxisVM 13 Verification Examples 39 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: dynam3.axs Thema Analysis Type Geometry Cantilevered thin square plate. Vibration analysis. Top view (thickness = 5,0 cm) Loads Boundary Conditions Material Properties Element types Mesh Self-weight ex = ey = ez = fix = fiy = fiz = 0 along y-axis E = 0000 kn / cm = 0,3 = 8000 kg / m 3 Parabolic quadrilateral shell element (heterosis).
40 AxisVM 13 Verification Examples 40 Target First 5 mode shapes Results Mode 1: f = 0,4 Hz Mode 3: f =,53 Hz Mode 5: f = 3,68 Hz
41 AxisVM 13 Verification Examples 41 Mode : f = 1,0 Hz Mode 4: f = 3, Hz Comparison with NAFEMS example Mode NAFEMS (Hz) AxisVM (Hz) % 1 0,41 0,40-0,4 1,09 1,00-0,87 3,580,530-1,94 4 3,310 3,0 -,7 5 3,750 3,680-1,87
42 AxisVM 13 Verification Examples 4 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: dynam4.axs Thema Analysis Type Geometry Cantilevered tapered membrane. Vibration analysis. Side view (thickness = 10,0 cm) Loads Boundary Conditions Material Properties Element types Mesh Self-weight Edge 1: Nodal DOF: Fixed node Other nodes: DOF: (f f C C C C) (f: free; C: constrained) E = 0000 kn / cm = 0,3 = 8000 kg / m 3 Parabolic quadrilateral membrane (plane stress)
43 AxisVM 13 Verification Examples 43 Target First 4 mode shapes Results 5,000 1,000 10,000 Y X Mode 1: f = 44,50 Hz Mode : f = 18,60 Hz
44 AxisVM 13 Verification Examples 44 Mode 3: f = 16,48 Hz Mode 4: f = 41,46 Hz Results Comparison with NAFEMS example Mode NAFEMS (Hz) AxisVM (Hz) % 1 44,6 44,33-0,65 130,03 18,36-1,8 3 16,70 16,48-0, ,05 41,46-1,87
45 AxisVM 13 Verification Examples 45 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: dynam5.axs Thema Analysis Type Geometry Flat grillages. Vibration analysis. Top view Loads Boundary Conditions Material Properties Cross Section Element types Mesh Self-weight ex = ey = ez = 0 at the ends (simple supported beams) Nodal DOF: Grillage in X-Y plane E = 0000 kn / cm G = 7690 kn / cm = 0,3 = 7860 kg / m 3 A = 0,004 m Ix =,5E-5 m 4 Iy = Iz = 1,5E-5 m 4 Rib element: Three node beam element (shear deformation is taken into account)
46 AxisVM 13 Verification Examples 46 Target First 3 mode shapes Results Mode 1: f = 16,90 Hz Mode : f = 0,64 Hz Mode 3: f = 51,76 Hz
47 AxisVM 13 Verification Examples 47 Reference: Mode Reference AxisVM (Hz) % 1 16,85 16,90 0,30 0,1 0,64, ,30 51,76 -,89 C.T.F. ROSS: Finite Element Methods In Engineering Science
48 AxisVM 13 Verification Examples 48 BLANK
49 AxisVM 13 Verification Examples 49 Stability
50 AxisVM 13 Verification Examples 50 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: buckling1.axs Thema Analysis Type Geometry Simply supported beam. Buckling analysis. Front view Cross section(iz =168,3 cm 4, It =1,18 cm 4, Iw =16667 cm 6 ) Loads Boundary Conditions Material Properties Element types Mesh Bending moment at both ends of beam MA = 1,0 knm, MB = -1,0 knm (Moments are applied as surface edge loads) ex = ey = ez = 0 at A ex = ey = ez = 0 at B kz = kw = 1 E = 0600 kn / cm = 0,3 Parabolic quadrilateral shell element (heterosis)
51 AxisVM 13 Verification Examples 51 Target Mcr =? (for lateral torsional buckling) Results Analytical solution M cr E I Z W L IZ I L G It E I Z , ,18 M cr 1451 kncm 14, , ,3 knm AxisVM result Mcr = 15,3 knm Difference +0,6%
52 AxisVM 13 Verification Examples 5 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: buckling.axs Thema Analysis Type Geometry Simply supported beam. Buckling analysis. Front view (L = 1,0 m) S G 1 10,0 S G 1 10, z 1,0 30,0 y z y Loads P = -1,0 kn at point B. Section A1 Cross-sections Section A Boundary Conditions Material Properties Element types Target Results ex = ey = ez = 0 at A ey = ez = 0 at B E = 0000 kn / cm = 0,3 Beam element Pcr =? (for inplane buckling) Theory AxisVM e [%] P cr [kn] 3,340 3,337-0,09
53 AxisVM 13 Verification Examples 53 Design
54 AxisVM 13 Verification Examples 54 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: RC column1.axs Thema N-M interaction curve of cross-section (EN :004). Analysis Type Geometry Linear static analysis+design Section: 300x400 mm Covering: 40 mm Loads Boundary Conditions Material Properties Target Results Arbitrary. Arbitrary. Concrete: fcd=14, N/mm ec1=0,00 ecu=0,0035 (parabola-constans - diagram) Steel: fsd=348 N/mm esu=0,015 Compare the program results with with hand calculation at keypoints of M-N interaction curve. N N [kn] M [knm] N AxisVM M(N) AxisVM e % ,5 +61,4 +0, ,7-0, ,5 +0, ,5-61,4 +0, , +0, ,7-0,6 Reference: Dr. Kollár L. P., Vasbetonszerkezetek I. Műegyetemi kiadó
55 AxisVM 13 Verification Examples 55 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: beam1.axs Thema RC beam deflection according to EC, EN :010. Analysis Type Geometry Material nonlinear analysis. q = 17 kn/m L = 5,60 m Side view 0 35 cm covering = 3 cm = 0, cm Section Loads Boundary Conditions Material Properties Element types Target q = 17 kn /m distributed load Simply supported beam. Concrete: C5/30, =,1 Steel: B500B Parabolic quadrilateral plate element (Heterosis) ez, max
56 AxisVM 13 Verification Examples 56 Results Diagram ez Aproximate calculation: e e where, II ( 1 ) e 0,06 _ I mm ei is the deflection which was calculated with the uncracked inertia moment eii is the deflection which was calculated with the cracked inertia moment sr 1 s Calculation with integral of : e = 19,8 mm Calculation with AxisVM: e = 19,65 mm (different -,0%)
57 AxisVM 13 Verification Examples 57 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: beam.axs Thema Required steel reinforcement of RC plate according to EC, EN :004. Analysis Type Geometry Linear analysis. Side view Cross-section Loads Boundary Conditions Material Properties Element types Mesh Pz = -50 kn point load Clamped cantilever plate. Fix line support on clamped edge. Nodal DOF: Plate in X-Y plane Concrete: C5/30 Steel: B500A Parabolic quadrilateral plate element (heterosis) Top view
58 AxisVM 13 Verification Examples 58 Target AXT steel reinforcement along x direction at the top of the support Results Diagram AXT Calculation according to EC: 5 1, ,15 f cd 16,6 N / mm f yd 435 N / mm c E 0,850, , cu S c0 cu ES f yd d = = 47 mm 0,54 xc M sd M Rd b xc fcdd 00 knm x c 439 h 55 xc 55 c 0, c0 0,54 Steel reinforcement is yielding d 47 A S b xc f f yd cd ,6 099 mm 435 Calculation with AxisVM: AXT = 093 mm / m Different = -0,3 %
59 AxisVM 13 Verification Examples 59 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: 3_10 Plastic biaxial bending interaction.axs Thema Interaction check of simply supported beam under biaxial bending (EN ). Analysis Type Geometry Steel Design h = 70 mm b = 135 mm tf = 10 mm tw = 7 mm l = 6000 mm A = 45,95 cm Wy,pl = 484,1 cm 3 Wz,pl = 97 cm 3 IPE70 cross section Loads Boundary Conditions Material Properties qy = 1,5 kn/m qz = 0,4 kn/m ex = ey = ez = 0 at A ey = ez = 0 at B S 35 E = 1000 kn/cm = 0,3
60 AxisVM 13 Verification Examples 60 Element types Target Results Beam element Interaction check taking into account plastic resistances Analytical solution in the following book: Dunai, L., Horváth, L., Kovács, N., Verőci, B., Vigh, L. G.: Acélszerkezetek méretezése az Eurocode 3 alapján, Gyakorlati útmutató (Design of steel structures according to Eurocode 3, ) Magyar Mérnök Kamara Tartószerkezeti tagozata, Budapest, 009. Exercise 3.10., page 8. Analitical solution AxisVM e[%] My,Ed [knm] 91,8 91,8 - Mz,Ed [knm] 6,75 6,75 - Mpl,y,Rd [knm] 113,74 113,76 +0,0 Mpl,z,Rd [knm],78,79 +0,04 α - β capacity ratio [-] 0,948 0,947-0,11
61 AxisVM 13 Verification Examples 61 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: 3_1 _MNV_Interaction.axs Thema Analysis Type Geometry Interaction check of simply supported beam under normal force, bending and shear force. (EN , EN ) Steel Design h = 00 mm b = 00 mm tf = 15 mm tw = 9 mm l = 1400 mm A = 78,1 cm Av = 4,83 cm Iy = 5696 cm 3 Wy,pl = 643 cm 3 IPE70 cross section Loads Boundary Conditions Material Properties Element types Target Fz = 300 kn at thirds of beam N = 500 kn at B ex = ey = ez = fix = 0 at A ey = ez = fix =0 at B S 35 E = 1000 kn/cm = 0,3 Beam element Interaction check of axial force, shear force and bending moment.
62 AxisVM 13 Verification Examples 6 Results Analytical solution in the following book: Dunai, L., Horváth, L., Kovács, N., Verőci, B., Vigh, L. G.: Acélszerkezetek méretezése az Eurocode 3 alapján, Gyakorlati útmutató (Design of steel structures according to Eurocode 3, ) Magyar Mérnök Kamara Tartószerkezeti tagozata, Budapest, 009. Exercise 3.1., page Analytical solution AxisVM results e[%] NEd [kn] Vz,Ed [kn] My,Ed [knm] Pure compression Npl,Rd [kn] capacity ratio [-] 0,33 0,33 - Pure shear Vpl,z,Rd [kn] 394, 394,5 +0,08 capacity ratio [-] 0,761 0,761 - Pure bending Mpl,y,Rd [knm] 176,8 176,7-0,06 capacity ratio [-] 0,79 0,79 - Interaction check 0,73 0,71-0,73 MV,Rd [knm] 163,96 163,93-0,0 n 0,33 0,33 - a 0,3 0,3 - MNV,Rd [knm] 14, 14, - capacity ratio [-] 0,985 0,984-0,10
63 AxisVM 13 Verification Examples 63 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: 3_15 Központosan nyomott rúd - I szelvény.axs Thema Buckling resistance of simply supported beam (EN ). Analysis Type Geometry Steel Design h = 300 mm b = 50 mm tf = 14 mm tw = 8 mm l = 4500 mm A = 94 cm Iy = 19065,8cm 4 Iz = 3647,1 cm 4 iy = 14,1 cm iz = 6, cm I cross section, symmetric about y and z axis Loads Normal force at point A NA= -1,0 kn Boundary ey = 0 at A Conditions ex = ey = ez = fix = fiz= 0 at B kz = kw = 1 Material S 35 Properties E = 1000 kn / cm = 0,3 Element Beam element types Target Buckling resistance Nb,Rd =?
64 AxisVM 13 Verification Examples 64 Results Analytical solution in the following book: Dunai, L., Horváth, L., Kovács, N., Verőci, B., Vigh, L. G.: Acélszerkezetek méretezése az Eurocode 3 alapján, Gyakorlati útmutató (Design of steel structures according to Eurocode 3, ) Magyar Mérnök Kamara Tartószerkezeti tagozata, Budapest, 009. Exercise 3.15., P Analytical solution AxisVM e[%] y [-] * 0,673 0,673 - z [-] 0,771 0,769-0,6 Χy [-] * 0,8004 0,7989-0,19 Χz [-] 0,6810 0, ,07 Nb,Rd [kn] 1504,3 1505,3 +0,07
65 AxisVM 13 Verification Examples 65 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: 3_1 Központosan nyomott rúd - T szelvény.axs Thema Buckling resistance of simply supported beam (EN ). Analysis Type Geometry Steel Design h = 180 mm b = 50 mm tf = 16 mm tw = 16 mm l = 3000 mm A = 68,8 cm Iy = 394,5cm 4 Iz = 089,48 cm 4 Ics= 58,71 cm 4 Iw = 1108,0 cm 6 iy = 5,90 cm iz = 5,51 cm Welded T section, symmetric to z but not y Loads Normal force at point A NA= -1,0 kn Boundary ey = 0 at A Conditions ex = ey = ez = fix = 0 at B kz = kw = 1 Material S 35 Properties E = 1000 kn/cm = 0,3 Element Beam element types Target Buckling resistance Nb,Rd =?
66 AxisVM 13 Verification Examples 66 Results Analytical solution in the following book: Dunai, L., Horváth, L., Kovács, N., Verőci, B., Vigh, L. G.: Acélszerkezetek méretezése az Eurocode 3 alapján, Gyakorlati útmutató (Design of steel structures according to Eurocode 3, ) Magyar Mérnök Kamara Tartószerkezeti tagozata, Budapest, 009. Exercise 3.1., P Analitical solution AxisVM e[%] zs [cm] 49,0 49,0 - zw [cm] 4,10 4,04-1,46 iw [cm] * 9,05 9,03-0, y [-] 0,54 0,54 - Χy [-] 0,804 0,8195-0,11 Nb,Rd,1 [kn] 136,4 135,0-0,11 z [-] * 0,667 0,667 - Χz [-] * 0,743 0, ,19 Nb,Rd, [kn] * 101,6 103,9 +0,19 * hidden partial results, Axis does not show them among the steel design results
67 AxisVM 13 Verification Examples 67 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: Külpontosan nyomott rúd - RHS szelvény.axs Topic Buckling of a hollow cross-section beam (EN ). Analysis Type Geometry Steel Design h = 150 mm b = 100 mm tf = 10 mm tw = 10 mm L = 4,000 m A = 43,41 cm Iy = 109,8 cm 4 Iz = 635,7 cm 4 iy = 5,8 mm iz = 38,3 mm Wel,y = 161,3 cm 3 Wel,z = 17,1 cm 3 Wpl,y = 05,6 cm 3 Wpl,z = 154,6 cm 3 RHS 150x100x10,0 cross section (hot rolled) Loads Boundary Conditions Material Properties Element types Steel Design Parameters Target Bending moment at both ends of beam and axial force NEd,C = 00 kn MEd,A = MEd,B = 0 knm ex = ey = ez = 0, warping free at A ey = ez = 0, warping free at B S 75 E = 1000 kn / cm = 0,3 Beam element Buckling length: Ly = L Lz = L Lw = L Check for interaction of compression and bending.
68 AxisVM 13 Verification Examples 68 Results Analytical solution: Section class: 1. Compression flexural buckling E I y ,8 N cr,y 1567,kN K y L 400 E I z ,7 N cr,z 83,5kN K z L 400 N pl,rd A f y 43,41 7,51193,8kN y N pl N cry 1193,8 0, ,16 z N pl N crz 1193,8 1,040 83,48 imperfection factor based on buckling curve a (hot rolled RHS section): y z 0,1 1 ( - 0.) 1 : - y 0,7516 z 0,575 N b,rd y A f y 1 0,575 43,41cm 7,5kN/cm 1,0 69,7kN N Ed,x 00 kn Bending lateral torsional buckling M pl,rd, y W f y 3 pl,y 05,6 cm 7,5kN/cm 1 1,0 C 1 1,000 k k w 1 z 56,54kNm M Ed 10kNm M cr C 1 E I z (kl) kn ,7cm cm M cr 1,0 (400cm) M cr 977,41kNm k z k w I w (kl) G I t I z E I z 6 766cm 4 635,7cm kn 4 (400cm) , cm cm kn ,7 cm cm
69 AxisVM 13 Verification Examples 69 LT LT 0, W y f y M cr 3 05,6cm 7,5kN/cm 977,41kNm torsional buckling may occur 0,405 LT 0,76 1 ( - 0.) LT LT LT LT : 1 0, LT 0,5443 M M knm knm b Rd LT 0, ,54 54, 76, pl, Rd, y Interaction of bending and buckling N Rk A f y 43,41cm 7,5kN/cm M y,rk M pl,rd, y 56,54kNm 1193,8kN Equivalent uniform moment factors according to EN Annex B, Table B.3.: 1,0 C my 0,6 0,4 1,0 0,4 For members susceptible to torsional deformations the interaction factors may be calculated according to EN Annex B, Table B..: k yy C my 1 ( LT k yy 1,0 1-0,) (0,87-0,) y k yy min (1,149;1,178) 1,149 N Ed N Rk C my 1 0,8 / M1 y 00 1,0 1 0,8 0, ,78/1,0 N Ed N Rk / M1 00 0, ,78/1,0 0,1 k zy 1 z C 0,5 mlt z k zy N Ed,x N Rk 0,11, , ,0 0,5 0, ,78/1,0 1,0 0,5 k zy max (0,9490; 0,9577) 0,9577 0,1 1 / C 0,5 M1 mlt z N Ed,x N Rk / M1 00 0, ,78/1,0
70 AxisVM 13 Verification Examples 70 N M Ed y,ed k yy y N Rk / M1 y M y,rk / M ,149 0,646 0, ,78 0, ,54 N Ed k zy z N Rk / M1 M y,ed M y,rk / M ,9577 0,6674 0, ,78 0, ,54 Analytical solution AxisVM e [%] NRk = Npl,Rd [kn] 1193,8 1193,9 - y [-] 0,873 0,870-0,3 z [-] 1,04 1,01-0, Χy [-] 0,7516 0, Χz [-] 0,575 0,574 - Nb,Rd [kn] 69,7 69,7 - Mc,Rd = Mpl,Rd [knm] 56,54 56,54 - C1 1,000 1,000 - Mcr [knm] 977,41 977,40 - LT [-] 0,405 0,405 - ΧLT [-] 0,9684 0, Mb,Rd [knm] 54,76 54,75 - Cmy [-] 1,0 1,0 - kyy [-] 1,149 1,150 - kzy [-] 0,9577 0, Interaction capacity ratio 1 [-] 0,643 0,643 - Interaction capacity ratio [-] 0,667 0,667 -
71 AxisVM 13 Verification Examples 71 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: 3_6 Külpontosan nyomott rúd - I szelvény.axs Thema Lateral torsional buckling of a beam (EN ). Analysis Type Geometry Steel Design h = 171 mm b = 180 mm tf = 6 mm tw = 9,5 mm L = 4,000 m A = 45,6 cm Iy = 510,7 cm 4 Iz = 94,6 cm 4 iy = 74 mm iz = 45 mm Wel,y = 93,7 cm 3 Wel,z = 10,7 cm 3 Wpl,y = 34,9 cm 3 Wpl,z = 156,5 cm 3 HEA180 Iw = 5893 cm 6 It = 15 cm 4 Loads Boundary Conditions Material Properties Element types Axial force at B: Nx = -80 kn Point load in y direction at the thirds of the beam: Fy = 5 kn Distributed load in z direction: qz = 4,5 knm ex = ey = ez = 0, warping free at A ey = ez = 0, warping free at B S 35 E = 1000 kn / cm = 0,3 Beam element
72 AxisVM 13 Verification Examples 7 Steel Design Parameters The elastic critical load factor is: αcr = 4,8 As αcr = 4,8 < 15 II. order analysis is required. For this, the beam element needs to be meshed. Divison of the beam element into 4. Buckling length: Ly = L Lz = L LT buckling length: Lw = L Target Results Buckling check for interaction of axial force and bi-axial bending. Internal forces from the second order analysis NEd,x = 80 kn MEd,y = 9,84 knm MEd,z = 8,81 knm VEd,y = 6,50 kn VEd,z = 9,61 kn
73 AxisVM 13 Verification Examples 73 Analytical solution: Section class: 1. Normal force E I y N cr,y K y L E I N z cr,z K z L N pl,rd ,7 35,3kN ,6 1197,7kN 400 A f y 45,6 3,51063,6kN y N pl N cry 1063,6 0, ,3 z N pl N crz 1063,6 0, ,7 based on buckling curve b in y direction and c in z direction: y 0,8508 z 0,5741 N b,rd,1 N b,rd, y A f y 0, ,6cm 3,5kN/cm 904,9kN N Ed,x 80kN 1 1,0 A f z y 0, ,6cm 3,5kN/cm 610,6kN N Ed,x 80 kn 1 1,0 Bending M pl,rd, y M pl,rd, z W 3 pl,y f y 34,9cm 3,5kN/cm 1 1,0 W f y 3 pl,z 156,5cm 3,5kN/cm 1 1,0 76,35kNm M Ed,y 9,84 knm 36,78kNm M Ed,z 8,81kNm Calculation of the critical moment: C 1 1,13 (due to the My moment diagram) E I k z I w (kl) G I M z t cr C 1 k I (kl) w z E I z kN/cm 94,6cm M cr 1,13 (400cm) M cr 174,1 knm cm (400cm) 8077 kn/cm 15cm ,6cm 1000kN/cm 94,6cm
74 AxisVM 13 Verification Examples 74 For rolled section, the following procedure may be used to determine the reduction factor (EN ,Paragraph ): LT 1 ( LT LT LT : W y f y M cr 3 34,9cm 3,5kN/cm 0,66 174,10kNm - 0.4) 0.75 LT 1 0, LT 0,7090 M M knm knm b Rd LT 0, ,35 67, 81, pl, Rd, y Interaction of axial force and bi-axial bending N Rk M y,rk M z,rk N pl,rd M pl,rd, y M pl,rd, z 1063,6kN 76,35kNm 36,78kNm Equivalent uniform moment factors according to EN Annex B, Table B.3.: 0, 0 C my Cmz in both directions C 0,95 0,05 0,95 (distributed load) mlt 0,90 0,10 0,90 (concentrated load) k yy C my k yy 0,95 1 ( y - 0,) y N Ed,x N Rk 80 1 (0,5719-0,) 0, ,6/1,0 k yy min (1,0593;1,1851) 1,0593 / M1 C my 1 0,8 y 0,95 N Ed,x N Rk / M1 1 0,8 80 0, ,6/1,0 k zy k zy 0,1 1 z C 0,5 mlt z N Ed,x N Rk 0,1 0, ,95 0,5 0, ,6/1,0 k zy max (0,9383; 0,9345) 0,9383 / M1 0,1 1 C 0,5 mlt z 0,1 1 0,95 0,5 N Ed,x N Rk / M1 80 0, ,6/1,0
75 AxisVM 13 Verification Examples 75 k zz C 1 ( mz z k zz 0,901 ( 0,944-0,6) 0,901 1,4 0, ,6/1,0 0, ,6/1,0 k zz min (1,4303;1,478) 1,4303 k yz 0,6 k 0,858 zz - 0,6) z N Ed,x N Rk / M1 C mz 1 1,4 z N Ed,x N Rk / M1 N Ed,x k yy y N Rk / M1 M y,ed k yz M y,rk / LT M1 80 9,84 8,81 1,0593 0,858 0,3094 0,1537 0,056 0,6687 0, ,6 0, ,35 36,78 N M Ed,x y,ed k zy k zz z N Rk / M1 M y,rk / LT M1 M z,rk M z,ed M z,rk M z,ed / M1 / M1 80 9,84 8,81 0,9383 1,4303 0,4586 0,136 0,346 0,9374 0, ,6 0, ,35 36,78
76 AxisVM 13 Verification Examples 76 Analytical solution AxisVM e [%] Npl,Rd [kn] 1063,6 1063,6 - Ncr,y [kn] 35,3 35,4 - Ncr,z [kn] 1197,7 1197,7 - λy, rel [-] 0,5719 0, λz, rel [-] 0,944 0,944 - Χy [-] 0,8508 0, Χz [-] 0,5741 0, Mpl,Rd,y [knm] 76,35 76,36 - Mpl,Rd,z [knm] 36,78 36,78 - C1 [-] 1,13 1,15-0,6* Mcr [knm] 174,1 173,0-0,63 λlt, rel [-] 0,66 0, ,3 ΧLT [-] 0,8881 0, ,1 Mb,Rd [knm] 67,81 67,73-0,1 Cmy = CmLt [-] 0,95 0,95 - Cmz [-] 0,90 0,95 +5,5** kyy 1,0593 1, kzz 1,4303 1, ,5*** kyz 0,858 0, ,5*** kzy 0,9383 0, Interaction capacity ratio 1 0,6687 0, ,7*** Interaction capacity ratio 0,9374 0,9564 +,0*** * AxisVM calculates this factor using a closed form expression, while in the hand calculation C1 was derived from a table. The effect of this on the final result (efficiency) is 10-4, thus on the safe side. ** See EC3 Annex B, Table B.3: the difference is due to the fact, that AxisVM calculates the equivalent uniform moment factor (Cmy, Cmz, CmLT) for both uniform load and concentrated load, and then takes the higher value. The effect on the final result (efficiency) is +1~%. *** the difference is due to the different Cmz value
77 AxisVM 13 Verification Examples 77 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: Double-symmetric I - Class 4.axs Thema Interaction check of beam in section class 4 (EN , EN ) Analysis Type Geometry Steel Design h = 114 mm tw = 8 mm b = 30 mm tf = 1 mm L = 8,000 m A = 164,8 cm Iy = 36159,4 cm 4 Wel,y = 5803,6 cm 3 Double-symmetric welded I shape Loads Boundary Conditions Material Properties Element types Target Axial force at B: N Ed,C = 700 kn Distributed load in z direction: qz = 16,5 knm The internal forces in the mid-section: MEd,y = 1300 knm, NEd,x = kn ex = ey = ez = fix = 0 at A ey = ez = fix = 0 at B S 355 E = 1000 kn / cm ε=0,81 = 0,3 Beam element Check the strength capacity ratios for axial force, bending and interaction.
78 AxisVM 13 Verification Examples 78 Results Analytical solution in the following book: Dunai, L., Horváth, L., Kovács, N., Verőci, B., Vigh, L. G.: Acélszerkezetek méretezése az Eurocode 3 alapján, Gyakorlati útmutató (Design of steel structures according to Eurocode 3, ) Magyar Mérnök Kamara Tartószerkezeti tagozata, Budapest, 009. Exercise 3.4., P Exercise 3.6., P Exercise 3.13., P. 34. Analytical solution AxisVM e [%] Uniform compression Uniform bending 0,43 0,43-0,831 0,858 +3,1 0,931 0,910 -,3 140,0 14,0 +1, ,957,975 +0,6 0,313 0,311-0,6 340,8 34,4 +0,5 99,98 97,46 -, ,6 0, 0, - 0,43 0,43-0,831 0,858 +3,1 0,931 0,910 -,3 139,95 14,0 +1,4-0,969-0,959 +1,0 3,09,84-1,1 1,31 1,45 +1,1 0,739 0,731-1,1 408,6 410,4 +0, ,1 181,5 1766,5-3,1 0,71 0,74 +4,1 0,91 0,94 +3,3 Small differences occur because AxisVM does not take into account welding when calculating the effective section sizes.
79 AxisVM 13 Verification Examples 79
80 AxisVM 13 Verification Examples 80 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: Earthquake-01-EC.axs Thema Analysis Type Geometry Earth-quake design using response-spectrum method. Linear frequency analysis with 5 modes. Linear static analysis. Top view Front view
81 AxisVM 13 Verification Examples 81 Perspective view Section beams: 60x40 cm Ax=400 cm Ay=000 cm Az=000 cm Ix=75100 cm4 Iy=70000 cm Iz= cm4 Section columns: 60x40 cm Ax=400 cm Ay=000 cm Az=000 cm Ix=75100 cm4 Iy=70000 cm Iz=30000 cm4 Loads Nodal masses on eight nodes. Mx=My=Mz= kg Model self-weight is excluded. qd = 1 Spectrum for X and Y direction of seismic action: T[s] S d,156 S d [m/s ] 1 0 1,150 0,000, ,6000, ,3000 0, ,0000 0, ,0000 0, ,150 0,709 0,300,0000 T[s] Boundary Conditions Material Properties Nodes at the columns bottom ends are constrained in all directions. ex=ey=ez=fix=fiy=fiz=0 C5/30 E=3050 kn/cm =0, = 0
82 AxisVM 13 Verification Examples 8 Element types Target Results Rib element: Three node straight prismatic beam element. Shear deformation is taken into account. Compare the model results with SAP000 v6.13 results. The results are combined for all modes and all direction of spectral acceleration. CQC combination are used for modes in each direction of acceleration. SRSS combination are used for combination of directions. Period times of first 5 modes Mode T[s] SAP000 T[s] AxisVM Difference [%] 1 0,7450 0, ,7099 0, ,3601 0, ,314 0, ,054 0,054 0 Modal participating mass ratios in X and Y directions Mode X SAP000 X AxisVM Difference % Y SAP000 Y AxisVM Difference % 1 0,5719 0, ,3153 0, ,03 0,3650 0, ,4761 0,4760-0, ,161 0, ,0460 0, ,0131 0, ,0170 0, ,056 0,056 0 Summ 1,0000 1, ,9868 0, Internal forces at the bottom end of Column A and Column B Column A SAP000 Column A AxisVM Difference % Column B SAP000 Column B AxisVM Difference % Nx [kn] 315,11 315,15 +0,01 557,6 557,9 +0,005 Vy [kn] 80,34 80,34 0 3,88 3,88 0 Vz [kn] 53,49 53, ,04 41,04 0 Tx [knm] 34,4 34,41-0,03 34,47 34,46-0,03 My [knm] 65,13 65,1-0, , ,70-0,004 Mz [knm] 61,31 61, ,41 553,41 0 Support forces of Support C Support C SAP000 Support C AxisVM Difference % Rx [kn] 80,34 80,34 0 Ry [kn] 53,49 53,49 0 Rz [kn] 315,11 315,15 +0,01 Rxx [knm] 65,13 65,1-0,00 Ryy [knm] 61,31 61,31 0 Rzz [knm] 34,4 34,41-0,03 Displacements of Node D Node D SAP000 Node D AxisVM Difference % ex [mm] 33,51 33,51 0 ey [mm] 19,944 19,945 +0,005 ez [mm] 0,9 0,9 0 X [rad] 0, , Y [rad] 0, , Z [rad] 0,0057 0,0057 0
83 AxisVM 13 Verification Examples 83 Normal forces:
84 AxisVM 13 Verification Examples 84 Bending moments:
85 AxisVM 13 Verification Examples 85
86 AxisVM 13 Verification Examples 86 Displacements:
87 AxisVM 13 Verification Examples 87 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: Plastic_1.axs Thema Analysis Type Geometry Plastic material Nonlinear static analysis Cross-section: D = 30mm Loads Boundary Conditions Material Properties Element types Target Axial force at A: N Solution control: Displacement at A ex = ey = ez = 0 at B, C and D S 35 E = 1000 kn / cm = 0,3 Linear elastic perfectly plastic material model Truss element Check the load vertical displacement (A) curve Results Analytical results: [u;f(u)] AxisVM: [Axisi,1; Axisi,0]
88 AxisVM 13 Verification Examples 88 Software Release Number: R3 Date: Tested by: InterCAD Page number: File name: Plastic_1.axs Thema Analysis Type Geometry Clamped beam with plastic material under cyclic loading Nonlinear static analysis Fz A L = 100 cm B Nx Cross-section: Z = 30mm Loads Boundary Conditions Material Properties Element types Target Results Nx = 63,333 kn; Fz =,666 kn Solution control: Displacement at B ez = -70 mm Increment function: 1, ,5 0-0, ,5 ex = ey = ez = fix = fiy = fiz = 0 at A Steel E = kn/cm ; ET = 1000 kn/cm ; y = 10 kn/cm = 0,3 Linear elastic plastic material model Hardening rule: Isotropic hardening Beam element Check the load displacements and beam strains curves AxisVM: Beam element
89 AxisVM 13 Verification Examples 89 Rib element (shear deformation is taken into account) ANSYS 14.0 Beam element (unrestrained warping) Fx [kn] Axis beam ANSYS beam Axis Rib -400 ex [mm] Fz [kn] Axis beam ANSYS beam Axis Rib -0 ez [mm]
90 AxisVM 13 Verification Examples Fz [kn] 5 Fz [kn] Axis beam ANSYS beam Axis Rib -0 ey [mm] Fz [kn] 0-0,004-0,003-0,00-0, ,001 0,00 0,003 0,004 0,005-5 Axis beam ANSYS beam Axis Rib exx [] , -0,1 0 0,1 0, 0,3-5 Axis beam ANSYS beam Axis Rib kyy [1/m]
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