y1/4F₁X1(У1Y₂Y₁1/4F2X21Matrix and DeterminantsDisplacement y = y(x)911:) = *- ( ²17 1/437111/4Y₂ УзF3X317K 11 16 11 F₂FDue to three forces F₁, F2 and F3 appliedperpendicular a beam is displaced, as indicated in1/4the figure. The relationship between the appliedforces and the displacements can be expressed asXwith K ==[³768 E IFor the three forces applied, F₁ = 2000 N, F₂ =4000 N and F3 = 3000 N, determine thedisplacements y₁, Y2 and y3. Assume a beamlength | = 1 m, and the product E-I = 5.10¹0N/mm².Use for your calculations two decimal places andstate your result as a vector including units.

Given: To find: Displacements y1, y2, y3

Due to three forces F₁, F2 and F3 applied perpendicular a beam is displaced, as indicated in the figure. The relationship between the applied forces and the displacements can be expressed as У1 Y₂ = K Y3 11 7 9 11 16 11 7 11 9 F₁ F₂ F3/ with K = 1³ 768 E I . For the three forces applied, F₁ = 2000 N, F₂: 4000 N and F3 = 3000 N, determine the displacements y₁, Y2 and y3. Assume a beam length I = 1 m, and the product E•l = 5.10¹0 N/mm². ||

Due to three forces F₁, F2 and F3 applied perpendicular a beam is displaced, as indicated in the figure. The relationship between the applied forces and the displacements can be expressed as У1 Y₂ = K Y3 11 7 9 11 16 11 7 11 9 F₁ F₂ F3/ with K = 1³ 768 E I . For the three forces applied, F₁ = 2000 N, F₂: 4000 N and F3 = 3000 N, determine the displacements y₁, Y2 and y3. Assume a beam length I = 1 m, and the product E•l = 5.10¹0 N/mm². ||

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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Question

y
1/4
F₁
X1
(У1
Y₂
Y₁
1/4
F2
X2
1
Matrix and Determinants
Displacement y = y(x)
9
11
:) = *- ( ²17 1/4
3
7
11
1/4
Y₂ Уз
F3
X3
1
7
K 11 16 11 F₂
F
Due to three forces F₁, F2 and F3 applied
perpendicular a beam is displaced, as indicated in
1/4
the figure. The relationship between the applied
forces and the displacements can be expressed as
X
with K =
=
[³
768 E I
For the three forces applied, F₁ = 2000 N, F₂ =
4000 N and F3 = 3000 N, determine the
displacements y₁, Y2 and y3. Assume a beam
length | = 1 m, and the product E-I = 5.10¹0
N/mm².
Use for your calculations two decimal places and
state your result as a vector including units.

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Draw the Shear force and Bending moment diagrams
]: A horizontal beam with a length of 4.5 m is subjected to the shown loading. The forces are vertical and the couple moment is applied at point D. The figure is not to scale. 3 kN/ m 1 kN/ m 3 kNm A В C D E 1 т 1.5 m 0.5m 1.5m 0.6 KN 1.35KN (a) Motivate with substantiating explanations and clear and applicable calculations why the beam is in equilibrium. (b) Draw the shear force and bending moment diagrams for the beam. Calculate all local maxima and minima, zeros and points where the diagrams change shape, and show these values and points on the diagrams.
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When a beam section is subjected to a shear load, a shear stress distribution is developed on the section. The distribution of the shear stress is not linear. Elasticity theory can be used to calculate the shear stress at any point. However, a simpler method can be used to calculate the average shear stress across the width of the section, a distance y above or below the neutral axis. The average VQ shear stress is given by T = Here V is the shear It force on the section, I is the moment of inertia of the entire section about the neutral axis, and t is the width of the section at the distance y where the shear stress is being calculated. Q is the product of the area of the section above (or below) y and the distance from the neutral axis to the centroid of that area (Figure 1). In short, Q is the moment of the area about the neutral axis. I Figure 1 of 1 An I-beam has a flange width b = 250 mm, height h = 250 mm, web thickness tw = 9 mm, and flange thickness tf = 14 mm. Use the…
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