Exercise 5 Consider a simply supported beam ABC of the total length L and a constant flexural rigidity El in Figure Q2. The beam supports a concentrated load P, located at half length of the beam. Use the Moment-Area method to determine: (a) The diagram of the beam, through drawing. ΕΙ M (b) The areas A₁ and A₂ when the diagram is divided into two areas. ΕΙ (c) The equation of the angle of rotation 8c at point 'C'. (d) The equation of maximum deflection &c at point 'C'. Exercise 6 B A (a) The diagram of the beam, by drawing. (b) The equation of angle of rotation , at point A. (c) The equation of maximum deflection & at point A. P₁ P Figure Q2 Consider a cantilever beam AB in Figure Q1, with the length L and the point load P, applied at the free-end. A dummy moment M, is applied at the free-end, which results in the slope 8. Assume that the flexural rigidity of the beam El is constant in the beam. Use the Castigliano's theorem to determine the displacement UA and slope 8 at the free-end. Exercise 7 Consider a cantilever beam ABC of the total length L and a constant flexural rigidity El in Figure Q3. The beam supports two concentrated loads P, and P₂ located at full length and at half length of the beam, respectively. Determine: P₂ Figure Q1 1 (3) (7) (10) ·L C A (3) (4) (5) (7)
Exercise 5 Consider a simply supported beam ABC of the total length L and a constant flexural rigidity El in Figure Q2. The beam supports a concentrated load P, located at half length of the beam. Use the Moment-Area method to determine: (a) The diagram of the beam, through drawing. ΕΙ M (b) The areas A₁ and A₂ when the diagram is divided into two areas. ΕΙ (c) The equation of the angle of rotation 8c at point 'C'. (d) The equation of maximum deflection &c at point 'C'. Exercise 6 B A (a) The diagram of the beam, by drawing. (b) The equation of angle of rotation , at point A. (c) The equation of maximum deflection & at point A. P₁ P Figure Q2 Consider a cantilever beam AB in Figure Q1, with the length L and the point load P, applied at the free-end. A dummy moment M, is applied at the free-end, which results in the slope 8. Assume that the flexural rigidity of the beam El is constant in the beam. Use the Castigliano's theorem to determine the displacement UA and slope 8 at the free-end. Exercise 7 Consider a cantilever beam ABC of the total length L and a constant flexural rigidity El in Figure Q3. The beam supports two concentrated loads P, and P₂ located at full length and at half length of the beam, respectively. Determine: P₂ Figure Q1 1 (3) (7) (10) ·L C A (3) (4) (5) (7)
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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Exercise 5
Consider a simply supported beam ABC of the total length L and a constant flexural rigidity El
in Figure Q2. The beam supports a concentrated load P, located at half length of the beam.
Use the Moment-Area method to determine:
Exercise 6
M
ΕΙ
(a) The diagram of the beam, through drawing.
M
ΕΙ
(b) The areas A₁ and A₂ when the diagram is divided into two areas.
(c) The equation of the angle of rotation cat point 'C'.
(d) The equation of maximum deflection &c at point 'C'.
B
24
A
Exercise 8
(a) The diagram of the beam, by drawing.
(b) The equation of angle of rotation
(C)
P₁
1|2
S
at point A.
The equation of maximum deflection & at point A.
Exercise 7
Consider a cantilever beam ABC of the total length L and a constant flexural rigidity El in
Figure Q3. The beam supports two concentrated loads P₁ and P2 located at full length and at
half length of the beam, respectively.
Determine:
P₂
P
B
Figure Q2
Consider a cantilever beam AB in Figure Q1, with the length L and the point load P, applied
at the free-end. A dummy moment Mo is applied at the free-end, which results in the slope 8.
Assume that the flexural rigidity of the beam El is constant in the beam. Use the Castigliano's
theorem to determine the displacement UA and slope 0 at the free-end.
Figure Q1
L
NIT
(3)
(7)
(10)
2
L
P
с
A
(3)
(4)
(5)
(7)
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