QUESTION 1(a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes andnodal degrees of freedom (dof). Identify the physical quantity of each dof.(b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a materialwith E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).کسیس2 kN/m16 m10 KN(a)24 m8 kN40 kN-mFigure Q1200 mm(b)400 mm By using two (2) beam elements to model the beam, the nodal degrees of freedom are:NODE 2NODE 3-0.014-0.031-0.004-0.005Deflection (m)Rotation (radian)NODE 100At a section 3 m from the fixed end of the beam, calculate by using finite element method:(i) the deflection;(ii) the shear force;(iii) the bending moment;(iv) the maximum bending stress.

Answered: Image /qna-images/answer/f5e06e96-7c8b-47ba-bd2f-e1bfc3e2738d.jpg

QUESTION 1 (a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes and nodal degrees of freedom (dof). Identify the physical quantity of each dof. (b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a material with E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).

QUESTION 1 (a) Sketch a bar element, a plane truss element, and a beam element. Label the axes, nodes and nodal degrees of freedom (dof). Identify the physical quantity of each dof. (b) Figure Q1(a) below shows a loaded cantilevered beam. The beam is made of a material with E = 200 GPa while the cross section of the beam is shown in Figure Q1(b).

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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Concept explainers

Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

By using two (2) beam elements to model the beam, the nodal degrees of freedom are:
NODE 2
NODE 3
-0.014
-0.031
-0.004
-0.005
Deflection (m)
Rotation (radian)
NODE 1
0
0
At a section 3 m from the fixed end of the beam, calculate by using finite element method:
(i) the deflection;
(ii) the shear force;
(iii) the bending moment;
(iv) the maximum bending stress.

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Step 1: Introduce the problem statement

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Step 2: State the characteristics of bar, truss and beam element

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Solution

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Step 3: Determine flexural rigidity of the beam

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Step 4: Formulate element stiffness matrices

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Step 5: Formulate global stiffness matrix

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Step 6: Formulate load vector matrix

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Step 7: Formulate displacement vector

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Step 8: Determine joint displacement

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Step 9: Determine support reactions

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Step 10: Compute maximum bending stress

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