Answered: Determine with the finite element…

Engineering

Mechanical Engineering

Determine with the finite element method the magnitude of the slope at the free end of the beam

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

It is important that the problem is carried out by the method requested
Do not use CHATGPT

Determine with the finite element method
the magnitude of the slope at the free end
of the beam
$2 =___ rad
Beam
○ 3.2x10-5 rad
O 3x10-³ rad
○ 4x10-4 rad
O 8x10-5 rad
5x10-5 rad
M₂ = 5 kN-m
3
www
2
F₂ = 1 kN
k = 1 kN/m
L=10 m
E = 70 GPa
I= 1x104m+

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Step 1: Write the given data and what is to find

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Step 2: Assign the nodes and write the boundary conditions:

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Step 3: Write the element stiffness matrix:

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Step 4: Write the global stiffness matrix:

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Step 5: Determine the slope at the free and of the beam:

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