**Text:**Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. *Do not rename the nodes or elements.*Assume that bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed. Elements 1, 2 and 3 have Young’s Modulus of E₁=250 Pa, E₂=100 Pa, E₃=150 Pa. All elements have length of 1 m and cross-sectional area of 1.5 m². There is an applied external force acting at Node 2 of 20 N.**Diagram Explanation:**The diagram illustrates a system of three linearly connected bar elements, labeled as Element 1, Element 2, and Element 3. These elements are aligned horizontally and connected at three nodes labeled Node 1, Node 2, Node 3, and Node 4.- **Node 1** is fixed and located at the leftmost end of the system, represented by a thick slanted line indicating restriction in movement.- **Node 2** is where an external force of 20 N is applied in the positive x-direction, indicated by an arrow.- **Node 3** connects Element 2 and Element 3.- **Node 4** is also fixed, represented similarly to Node 1, and is located at the rightmost end.Each element has a different Young's Modulus (E₁, E₂, E₃) and shares the same cross-sectional area and length.

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Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements. Assume that bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed. Elements 1, 2 and 3 have Young's Modulus of Ei=250 Pa, E2=100 Pa, E3=150 Pa. All elements have length of 1 m and cross-sectional area of 1.5 m². There is an applied external force acting at Node 2 of 20 N. 20 N Element 1 Element 2 Element 3 Node 2 Node 3 Node 1 Node 4

Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. Do not rename the nodes or elements. Assume that bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed. Elements 1, 2 and 3 have Young's Modulus of Ei=250 Pa, E2=100 Pa, E3=150 Pa. All elements have length of 1 m and cross-sectional area of 1.5 m². There is an applied external force acting at Node 2 of 20 N. 20 N Element 1 Element 2 Element 3 Node 2 Node 3 Node 1 Node 4

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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Measuring site work, Excavation and Piling

Bid drawings typically include very little material about the precise requirements of site work operations, measuring site work and excavation work differs from measuring most other works on a construction project. The actual site work conditions are not provided and also the dimensions of the excavations are not known during the pre-construction phase. The precise measurement of the excavation and backfill of the earth material and topsoil is important for a contractor to decide upon the total cost required for the process. All the works should be carried out under OSHA (Occupational Safety and Health Administration) standards to ensure the safety of the workers.

Question

**Text:**

Determine the nodal displacements and reaction forces using the finite element direct method for the 1-D bar elements connected as shown below. *Do not rename the nodes or elements.*

Assume that bars can only undergo translation in x (1 DOF at each node). Nodes 1 and 4 are fixed. Elements 1, 2 and 3 have Young’s Modulus of E₁=250 Pa, E₂=100 Pa, E₃=150 Pa. All elements have length of 1 m and cross-sectional area of 1.5 m². There is an applied external force acting at Node 2 of 20 N.

**Diagram Explanation:**

The diagram illustrates a system of three linearly connected bar elements, labeled as Element 1, Element 2, and Element 3. These elements are aligned horizontally and connected at three nodes labeled Node 1, Node 2, Node 3, and Node 4.

- **Node 1** is fixed and located at the leftmost end of the system, represented by a thick slanted line indicating restriction in movement.
- **Node 2** is where an external force of 20 N is applied in the positive x-direction, indicated by an arrow.
- **Node 3** connects Element 2 and Element 3.
- **Node 4** is also fixed, represented similarly to Node 1, and is located at the rightmost end.

Each element has a different Young's Modulus (E₁, E₂, E₃) and shares the same cross-sectional area and length.

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