Report Rigid Slab
10
OBJECTIVE: To develop a computer program to analyze a 3D space frame with rigid slabs at each floor. The frame has ‘mxn’ number of bays (along x and y axis respectively) and ‘s’ number storeys. The frame is subjected to unsymmetrical lateral loads. THEORY: ASSUMPTIONS: 1. Members are assumed as line elements (Skeleton structures). 2. Hooke’s law of elasticity holds true. 3. Deflections are very small so that there is no change of geometry of structure. 4. Plane section remains plane after bending. 5. In bending, curvature = ∂ 2 y ∂x 2 (As slope is very small, dy dx =0 ). 6. Change in the length of an element due to the flexural deformation is negligible and due to the displacement taking place normal to the member is zero. 7. Principle of superposition holds good (for linear systems i.e., loads, displacements, Bending Moment Diagram, Shear Force Diagram, Boundary Conditions). 8. Members are assumed to be inextensible. 9. Slab is rigid and monolithic with beams and columns. 10. Slab is continuous and all joints lie on the floor slabs. IMPLICATIONS OF ASSUMPTIONS: 1. Points which are lying on the same slab undergo same rigid body translation and rotation. 2. Lateral bending of beams (in the plane of slab) do not occur.
-
Upload
akshaymnnit -
Category
Documents
-
view
14 -
download
1
description
vhgfh
Transcript of Report Rigid Slab
OBJECTIVE:To develop a computer program to analyze a 3D space frame with rigid slabs at each floor. The frame has mxn number of bays (along x and y axis respectively) and s number storeys. The frame is subjected to unsymmetrical lateral loads.THEORY: ASSUMPTIONS:1. Members are assumed as line elements (Skeleton structures).2. Hookes law of elasticity holds true.3. Deflections are very small so that there is no change of geometry of structure.4. Plane section remains plane after bending.5. In bending, curvature = (As slope is very small, ).6. Change in the length of an element due to the flexural deformation is negligible and due to the displacement taking place normal to the member is zero.7. Principle of superposition holds good (for linear systems i.e., loads, displacements, Bending Moment Diagram, Shear Force Diagram, Boundary Conditions).8. Members are assumed to be inextensible.9. Slab is rigid and monolithic with beams and columns.10. Slab is continuous and all joints lie on the floor slabs.IMPLICATIONS OF ASSUMPTIONS:1. Points which are lying on the same slab undergo same rigid body translation and rotation.2. Lateral bending of beams (in the plane of slab) do not occur.Due to the presence of slab, the displacements and forces along the floor degree of freedom for each beam on the same floor will be same.Modified stiffness matrix of beams in global coordinate (Considering rigid slab action) = = [C]T[T]T[Kl][T][C] Note: Two programs have been developed: Program (1): Considering only slab is rigid. Program (2): Considering slab and wall both are rigid i.e. rigid transformation has been applied in both slab and wall connecting columns.
Welcome Screen FLOW CHART
Generate Figure for ReferenceGenerate CoordinatesForm Transformation MatrixForm Association MatrixStructural DimensionsA, Iyy, Izz, J of Beam and Column along with material properties (E and G)No. of bays, bay lengths in x, y direction, no of storeys and storey heightSectional PropertiesMagnitude of each LoadDirection of Load (x or y axis)Welcome ScreenActing NodeEnter Number of LoadsInput LoadsForm Half Banded MatrixGlobal Structural Stiffness MatrixForm Rigid Slab Transformation MatrixForm Local Stiffness MatrixInput Dialog Box
Generate Global Load Matrix
End of ProgramGenerate Output FileCalculate Fundamental Natural FrequencyCalculate Eigen ValuesCalculate Lumped Mass of the SystemCalculate Member End ForcesCalculate ReactionsCalculate Joint Displacements, Floor DisplacementsForm Kpp, Kpx, Kxx, Kxp
INPUT DATA:1. Number of bays in x and y axis (m,n) and storeys (s).2. Bay Lengths in x and y axis and storey height.3. Sectional properties of beams and columns and material properties used in structure.4. Horizontal loads magnitude, position of load action (joint number) and direction of load (x and y axis direction).OUTPUT DATA:1. All nodal displacements.2. All member end forces.3. All reactions.4. Fundamental natural frequency/time period.TRIAL RUN:Test Result:
Figure (1): Generated Skeletal 3D View of StructureGenerated Figure:Data Given by User: Number of spans (along x)=3. Number of bays (along y)=4. Number of storeys=2. Span Length(m)=5 Bay Length(m)=3 Storey Height(m)=3 Properties of beam: Youngs Modulus of Elasticity (E)=25000.000000 N/mm^2. Shear Modulus of Elasticity (G)=11000.000000 N/mm^2. Area of cross-section (A)=0.100000 m^2.Torsional Constant(J)=0.001250 m^4. Properties of columns: Youngs Modulus of Elasticity (E)=25400.000000 N/mm^2. Shear Modulus of Elasticity (G)=11400.000000 N/mm^2. Area of cross-section (A)=0.120000 m^2.Torsional Constant(J)=0.001280 m^4. The Given Loads are [Load Magnitude(kN),Node Number,Direction(1-x & 2-y)]:(1) 100, 2, 1, (1) -200, 11, 2, (1) -175, 19, 1, (1) 90, 5, 1, Floor Displacements(m and radians) U(x) U(y) theta(z):(1) 0.001216, -0.004972, 0.000451, (2) -0.001578, -0.007114, 0.000739, Nodal Displacements(m and radians) U(z) theta(x) theta(y):(1) -0.000030, 0.001039, -0.000164, (2) -0.000010, 0.000521, -0.000172, (3) 0.000009, 0.000002, -0.000164, (4) -0.000005, 0.000669, -0.000513, (5) 0.000002, 0.000328, -0.000424, (6) 0.000009, -0.000013, -0.000513, (7) -0.000017, 0.000669, -0.000882, (8) -0.000002, 0.000328, -0.000688, (9) 0.000014, -0.000013, -0.000882, (10) 0.000007, 0.001039, -0.001231, (11) 0.000010, 0.000521, -0.000940, (12) 0.000014, 0.000002, -0.001231, (13) -0.000039, 0.000233, -0.000770, (14) -0.000011, 0.000037, -0.000406, (15) 0.000016, -0.000159, -0.000770, (16) -0.000011, 0.000182, -0.000898, (17) 0.000002, 0.000051, -0.000501, (18) 0.000014, -0.000079, -0.000898, (19) -0.000024, 0.000182, -0.001034, (20) -0.000002, 0.000051, -0.000602, (21) 0.000021, -0.000079, -0.001034, (22) 0.000004, 0.000233, -0.001161, (23) 0.000011, 0.000037, -0.000697, (24) 0.000018, -0.000159, -0.001161, Reactions(kN) R(x) R(y) R(z) M(x) M(y) M(z):25. -11.388082 27.355637 30.187983 -47.282087 -16.123249 -2.195133 26. -11.474874 15.504959 10.582456 -26.388318 -16.210041 75.329660 27. -11.388082 3.654281 -9.023071 -5.494549 -16.123249 34.347674 28. -4.917723 31.815352 5.387428 -51.741803 -4.379877 12.558037 29. -3.879868 17.828375 -1.814070 -28.711734 -3.342021 98.586343 30. -4.917723 3.841397 -9.015568 -5.681665 -4.379877 50.972007 31. 1.314595 31.815352 17.457960 -51.741803 7.125455 -10.082703 32. 3.586125 17.828375 1.814070 -28.711734 9.396985 65.429993 33. 1.314595 3.841397 -13.829820 -5.681665 7.125455 28.331267 34. 7.784954 27.355637 -7.342595 -47.282087 18.868828 -72.259716 35. 11.181131 15.504959 -10.582456 -26.388318 22.265005 -25.300520 36. 7.784954 3.654281 -13.822317 -5.494549 18.868828 -35.716908 Member Forces(kN and kNm):(1) End 1-> 0.000000, 1.357832, 0.000000, 1.426276, 0.000000, 3.368952, End 2-> 0.000000, -1.357832, 0.000000, -1.426276, -0.000000, 3.420207, (2) End 1-> 0.000000, 1.357832, -0.000000, 1.426276, 0.000000, 3.420207, End 2-> 0.000000, -1.357832, 0.000000, -1.426276, 0.000000, 3.368952, (3) End 1-> 0.000000, 3.867821, 0.000000, 0.937630, 0.000000, 9.976006, End 2-> 0.000000, -3.867821, 0.000000, -0.937630, -0.000000, 9.363100, (4) End 1-> 0.000000, 3.867821, -0.000000, 0.937630, 0.000000, 9.363100, End 2-> 0.000000, -3.867821, 0.000000, -0.937630, 0.000000, 9.976006, (5) End 1-> 0.000000, 6.473891, 0.000000, 0.937630, 0.000000, 16.855455, End 2-> 0.000000, -6.473891, 0.000000, -0.937630, -0.000000, 15.514001, (6) End 1-> 0.000000, 6.473891, -0.000000, 0.937630, 0.000000, 15.514001, End 2-> 0.000000, -6.473891, 0.000000, -0.937630, 0.000000, 16.855455, (7) End 1-> 0.000000, 8.983881, 0.000000, 1.426276, 0.000000, 23.462510, End 2-> 0.000000, -8.983881, 0.000000, -1.426276, -0.000000, 21.456893, (8) End 1-> 0.000000, 8.983881, -0.000000, 1.426276, 0.000000, 21.456893, End 2-> 0.000000, -8.983881, 0.000000, -1.426276, 0.000000, 23.462510, (9) End 1-> 0.000000, 4.822604, -0.000000, 0.537876, -0.000000, 13.314326, End 2-> 0.000000, -4.822604, 0.000000, -0.537876, -0.000000, 10.798696, (10) End 1-> 0.000000, 4.822604, -0.000000, 0.537876, 0.000000, 10.798696, End 2-> 0.000000, -4.822604, 0.000000, -0.537876, 0.000000, 13.314326, (11) End 1-> 0.000000, 5.769813, -0.000000, 0.359171, -0.000000, 15.795065, End 2-> 0.000000, -5.769813, 0.000000, -0.359171, -0.000000, 13.054000, (12) End 1-> 0.000000, 5.769813, -0.000000, 0.359171, 0.000000, 13.054000, End 2-> 0.000000, -5.769813, 0.000000, -0.359171, 0.000000, 15.795065, (13) End 1-> 0.000000, 6.733862, -0.000000, 0.359171, -0.000000, 18.323926, End 2-> 0.000000, -6.733862, 0.000000, -0.359171, -0.000000, 15.345386, (14) End 1-> 0.000000, 6.733862, -0.000000, 0.359171, 0.000000, 15.345386, End 2-> 0.000000, -6.733862, 0.000000, -0.359171, 0.000000, 18.323926, (15) End 1-> 0.000000, 7.681071, -0.000000, 0.537876, -0.000000, 20.804665, End 2-> 0.000000, -7.681071, 0.000000, -0.537876, -0.000000, 17.600690, (16) End 1-> 0.000000, 7.681071, -0.000000, 0.537876, 0.000000, 17.600690, End 2-> 0.000000, -7.681071, 0.000000, -0.537876, 0.000000, 20.804665, (17) End 1-> 0.000000, 19.454951, 0.000000, 1.598780, -0.000000, 31.315344, End 2-> 0.000000, -19.454951, -0.000000, -1.598780, -0.000000, 27.049508, (18) End 1-> 0.000000, 9.663127, 0.000000, 1.157610, -0.000000, 15.605896, End 2-> 0.000000, -9.663127, -0.000000, -1.157610, -0.000000, 13.383487, (19) End 1-> 0.000000, -0.128696, 0.000000, 1.598780, -0.000000, -0.103553, End 2-> 0.000000, 0.128696, -0.000000, -1.598780, -0.000000, -0.282535, (20) End 1-> 0.000000, 15.467341, 0.000000, 1.692157, -0.000000, 23.201011, End 2-> 0.000000, -15.467341, -0.000000, -1.692157, -0.000000, 23.201011, (21) End 1-> 0.000000, 7.561639, 0.000000, 1.208219, -0.000000, 11.342459, End 2-> 0.000000, -7.561639, -0.000000, -1.208219, -0.000000, 11.342459, (22) End 1-> 0.000000, -0.344062, 0.000000, 1.692157, -0.000000, -0.516093, End 2-> 0.000000, 0.344062, -0.000000, -1.692157, -0.000000, -0.516093, (23) End 1-> 0.000000, 19.454951, 0.000000, 1.598780, -0.000000, 27.049508, End 2-> 0.000000, -19.454951, -0.000000, -1.598780, -0.000000, 31.315344, (24) End 1-> 0.000000, 9.663127, 0.000000, 1.157610, -0.000000, 13.383487, End 2-> 0.000000, -9.663127, -0.000000, -1.157610, -0.000000, 15.605896, (25) End 1-> 0.000000, -0.128696, 0.000000, 1.598780, -0.000000, -0.282535, End 2-> 0.000000, 0.128696, -0.000000, -1.598780, -0.000000, -0.103553, (26) End 1-> 0.000000, 4.552596, 0.000000, 0.585082, 0.000000, 7.119518, End 2-> 0.000000, -4.552596, -0.000000, -0.585082, 0.000000, 6.538270, (27) End 1-> 0.000000, 0.919329, 0.000000, 0.435337, 0.000000, 1.295960, End 2-> 0.000000, -0.919329, -0.000000, -0.435337, 0.000000, 1.462026, (28) End 1-> 0.000000, -2.713939, 0.000000, 0.585082, 0.000000, -4.527598, End 2-> 0.000000, 2.713939, -0.000000, -0.585082, 0.000000, -3.614217, (29) End 1-> 0.000000, 4.290000, 0.000000, 0.621993, -0.000000, 6.435000, End 2-> 0.000000, -4.290000, -0.000000, -0.621993, -0.000000, 6.435000, (30) End 1-> 0.000000, 1.206747, 0.000000, 0.464251, -0.000000, 1.810121, End 2-> 0.000000, -1.206747, -0.000000, -0.464251, -0.000000, 1.810121, (31) End 1-> 0.000000, -1.876506, 0.000000, 0.621993, -0.000000, -2.814759, End 2-> 0.000000, 1.876506, -0.000000, -0.621993, -0.000000, -2.814759, (32) End 1-> 0.000000, 4.552596, -0.000000, 0.585082, 0.000000, 6.538270, End 2-> 0.000000, -4.552596, 0.000000, -0.585082, 0.000000, 7.119518, (33) End 1-> 0.000000, 0.919329, -0.000000, 0.435337, 0.000000, 1.462026, End 2-> 0.000000, -0.919329, 0.000000, -0.435337, 0.000000, 1.295960, (34) End 1-> 0.000000, -2.713939, -0.000000, 0.585082, 0.000000, -3.614217, End 2-> 0.000000, 2.713939, 0.000000, -0.585082, 0.000000, -4.527598, (35) End 1-> 9.375200, 1.871397, -10.846804, -1.399809, 19.811169, -2.043203, End 2-> -9.375200, -1.871397, 10.846804, 1.399809, 12.729244, 7.657394, (36) End 1-> 0.919329, -1.074901, -15.019814, -1.399809, 23.897386, -4.520662, End 2-> -0.919329, 1.074901, 15.019814, 1.399809, 21.162055, 1.295960, (37) End 1-> -7.536543, -4.021199, -10.846804, -1.399809, 19.811169, -6.998122, End 2-> 7.536543, 4.021199, 10.846804, 1.399809, 12.729244, -5.065475, (38) End 1-> 5.507217, 6.938778, -12.004693, -1.399809, 20.255923, 7.483894, End 2-> -5.507217, -6.938778, 12.004693, 1.399809, 15.758155, 13.332440, (39) End 1-> 0.287418, 1.074901, -17.684086, -1.399809, 26.973172, -0.047444, End 2-> -0.287418, -1.074901, 17.684086, 1.399809, 26.079086, 3.272147, (40) End 1-> -4.932380, -4.788976, -12.004693, -1.399809, 20.255923, -7.578783, End 2-> 4.932380, 4.788976, 12.004693, 1.399809, 15.758155, -6.788146, (41) End 1-> 6.996458, 6.938778, -12.830446, -1.399809, 20.130503, 7.483894, End 2-> -6.996458, -6.938778, 12.830446, 1.399809, 18.360836, 13.332440, (42) End 1-> -0.287418, 1.074901, -20.145636, -1.399809, 29.717222, -0.047444, End 2-> 0.287418, -1.074901, 20.145636, 1.399809, 30.719686, 3.272147, (43) End 1-> -7.571295, -4.788976, -12.830446, -1.399809, 20.130503, -7.578783, End 2-> 7.571295, 4.788976, 12.830446, 1.399809, 18.360836, -6.788146, (44) End 1-> 3.128475, 1.871397, -13.988335, -1.399809, 20.575257, -2.043203, End 2-> -3.128475, -1.871397, 13.988335, 1.399809, 21.389747, 7.657394, (45) End 1-> -0.919329, -1.074901, -22.809909, -1.399809, 32.793008, -4.520662, End 2-> 0.919329, 1.074901, 22.809909, 1.399809, 35.636717, 1.295960, (46) End 1-> -4.967132, -4.021199, -13.988335, -1.399809, 20.575257, -6.998122, End 2-> 4.967132, 4.021199, 13.988335, 1.399809, 21.389747, -5.065475, (47) End 1-> 30.187983, 27.355637, 11.388082, -2.195133, -16.123249, 47.282087, End 2-> -30.187983, -27.355637, -11.388082, 2.195133, -18.040997, 34.784823, (48) End 1-> 10.582456, 15.504959, 11.474874, -2.195133, -16.210041, 26.388318, End 2-> -10.582456, -15.504959, -11.474874, 2.195133, -18.214581, 20.126558, (49) End 1-> -9.023071, 3.654281, 11.388082, -2.195133, -16.123249, 5.494549, End 2-> 9.023071, -3.654281, -11.388082, 2.195133, -18.040997, 5.468293, (50) End 1-> 5.387428, 31.815352, 4.917723, -2.195133, -4.379877, 51.741803, End 2-> -5.387428, -31.815352, -4.917723, 2.195133, -10.373294, 43.704254, (51) End 1-> -1.814070, 17.828375, 3.879868, -2.195133, -3.342021, 28.711734, End 2-> 1.814070, -17.828375, -3.879868, 2.195133, -8.297582, 24.773390, (52) End 1-> -9.015568, 3.841397, 4.917723, -2.195133, -4.379877, 5.681665, End 2-> 9.015568, -3.841397, -4.917723, 2.195133, -10.373294, 5.842526, (53) End 1-> 17.457960, 31.815352, -1.314595, -2.195133, 7.125455, 51.741803, End 2-> -17.457960, -31.815352, 1.314595, 2.195133, -3.181670, 43.704254, (54) End 1-> 1.814070, 17.828375, -3.586125, -2.195133, 9.396985, 28.711734, End 2-> -1.814070, -17.828375, 3.586125, 2.195133, 1.361389, 24.773390, (55) End 1-> -13.829820, 3.841397, -1.314595, -2.195133, 7.125455, 5.681665, End 2-> 13.829820, -3.841397, 1.314595, 2.195133, -3.181670, 5.842526, (56) End 1-> -7.342595, 27.355637, -7.784954, -2.195133, 18.868828, 47.282087, End 2-> 7.342595, -27.355637, 7.784954, 2.195133, 4.486033, 34.784823, (57) End 1-> -10.582456, 15.504959, -11.181131, -2.195133, 22.265005, 26.388318, End 2-> 10.582456, -15.504959, 11.181131, 2.195133, 11.278388, 20.126558, (58) End 1-> -13.822317, 3.654281, -7.784954, -2.195133, 18.868828, 5.494549, End 2-> 13.822317, -3.654281, 7.784954, 2.195133, 4.486033, 5.468293,
