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2. A steel plate (dimension in mm) is loaded and supported as shown in Figure 2. Assume that a downward settlement of 0.01 mm occurs at support 2. Using the finite element method with two 3-noded triangular elements, determine the horizontal and vertical displacements of the plate at the right top corner. Young's modulus E = 200GPA Poisson's ratio v = 0.3 Plate thickness t= 5mm 5kN %3D

2. A steel plate (dimension in mm) is loaded and supported as shown in Figure 2. Assume that a downward settlement of 0.01 mm occurs at support 2. Using the finite element method with two 3-noded triangular elements, determine the horizontal and vertical displacements of the plate at the right top corner. Young's modulus E = 200GPA Poisson's ratio v = 0.3 Plate thickness t= 5mm 5kN %3D

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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2. A steel plate (dimension in mm) is loaded and supported as shown in Figure 2. Assume that a downward settlement of 0.01 mm occurs at support 2. Using the finite element method with two 3-noded triangular elements, determine the horizontal and vertical displacements of the plate at the right top corner. Young's modulus E = 200GPA Poisson's ratio v = 0.3 5kN Plate thickness t= 5mm 0.03m 0.01 m 0.05 m Figure 2 Note: if the connectivity of element 1 is 1-2-3 and element 2 is 1-3-4, the stiffness matrices of elements 1 and 2 can be calculated as (using the units m and N): 0.110 0.000 -0.110 0.165 0.000 -0.165 0.000 0.038 0.192 -0.038 -0.192 0.000 [K]] = 10°x -0.110 0.192 1.071 -0.357 -0.962 0.165 0.165 -0.038 -0.357 2.786 0.192 -2.747 0.000 -0.192 -0.962 0.192 0.962 0.000 -0.165 0.000 0.165 -2.747 0.000 2.747 0.467 0.238 -0.220 -0.192 -0.247 -0.046 0.238 0.967 -0.165 -0.077 -0.073 -0.890 [K2] = 10° x -0.220 -0.165 0.330 0.000 -0.110 0.165 -0.192 -0.077 0.000 0.115 0.192 -0.038 -0.247 -0.073 -0.110 0.192 0.357 -0.119 -0.046 -0.890 0.165 -0.038 -0.119 0.929)
Transcribed Image Text:2. A steel plate (dimension in mm) is loaded and supported as shown in Figure 2. Assume that a downward settlement of 0.01 mm occurs at support 2. Using the finite element method with two 3-noded triangular elements, determine the horizontal and vertical displacements of the plate at the right top corner. Young's modulus E = 200GPA Poisson's ratio v = 0.3 5kN Plate thickness t= 5mm 0.03m 0.01 m 0.05 m Figure 2 Note: if the connectivity of element 1 is 1-2-3 and element 2 is 1-3-4, the stiffness matrices of elements 1 and 2 can be calculated as (using the units m and N): 0.110 0.000 -0.110 0.165 0.000 -0.165 0.000 0.038 0.192 -0.038 -0.192 0.000 [K]] = 10°x -0.110 0.192 1.071 -0.357 -0.962 0.165 0.165 -0.038 -0.357 2.786 0.192 -2.747 0.000 -0.192 -0.962 0.192 0.962 0.000 -0.165 0.000 0.165 -2.747 0.000 2.747 0.467 0.238 -0.220 -0.192 -0.247 -0.046 0.238 0.967 -0.165 -0.077 -0.073 -0.890 [K2] = 10° x -0.220 -0.165 0.330 0.000 -0.110 0.165 -0.192 -0.077 0.000 0.115 0.192 -0.038 -0.247 -0.073 -0.110 0.192 0.357 -0.119 -0.046 -0.890 0.165 -0.038 -0.119 0.929)
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