Marc.Truss - Application of the Finite Element Method Using...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Application of the Finite Element Method Using MARC and Mentat 5-1 Chapter 5: Analysis of a Truss 5.1 Problem Statement and Objectives A truss will be analyzed in order to predict whether any members will fail due to either material yield or buckling. The geometrical, material, and loading specifications for the truss are given in Figure 5.1. Each member of the truss has a solid circular cross section. Geometry: Material: Steel Area of members 1 and 2: 30 cm 2 Yield Strength: 250 MPa Area of members 3 and 4: 20 cm 2 Modulus of Elasticity: 200 GPa Area of member 5: 25 cm 2 Poisson’s Ratio: 0.3 Loading: Vertical Load: P=18kN Figure 5.1 Geometry, material, and loading specifications for the truss. 1 m 1 m 3 m 3 m P 30 o 1 5 2 3 4
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Application of the Finite Element Method Using MARC and Mentat 5-2 5.2 Analysis Assumptions 1. No friction is present in any of the truss pin joints. Thus, each truss member is an ideal two-force member. Also, there is no friction between the ground and the rollers. 2. Deflections are small enough that geometrically linear analysis is valid. 3. Because the geometry, material properties, and loading conditions are all symmetric about the vertical plane of symmetry that passes through member 5, the response of the structure (i.e., displacements, strains, and stresses) will also be symmetric about this plane. Therefore, a symmetric model may be used. 5.3 Mathematical Idealization Other than the assumptions above, no additional simplifications need be made for a truss. Each truss member can be represented by a two-noded linear truss finite element. This model should yield the correct analytical values for displacements and stresses. 5.4 Finite Element Model The finite element model of this structure will be developed using 3D linear two-noded truss finite elements. The present analysis can be greatly simplified by taking advantage of the vertical plane of symmetry in the truss. Hence, it is necessary to model only one-half of the truss, as shown in Figure 5.2. The boundary conditions on the symmetry plane are those that occur naturally on this plane, as can be verified by obtaining a solution using the entire truss. Taking advantage of symmetry reduces the modeling effort, the amount of computer memory, and the amount of CPU time required to obtain a solution. Admittedly, the savings are small in this simple problem. When a reduced model is developed due to symmetry, note that loads and truss members that lie within the plane of symmetry should be treated in a special way. If a load is within a plane of symmetry, then only one-half that load should be applied to the symmetric model. Similarly, if a truss member lies in a plane of symmetry, then only one-half of the cross-sectional area of that member should be assigned to the element representing the member. In other words, member 5 will be modeled as having one-half of its actual cross-sectional area.
Background image of page 2
Application of the Finite Element Method Using MARC and Mentat 5-3 5.4 Model Validation
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

Marc.Truss - Application of the Finite Element Method Using...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online