Influence Lines notes_06b
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Qualitative Influence Lines In 1886, Heinrich Müller-Breslau develop a method for rapidly constructing the shape of an influence line. Heinrich Franz Bernhard Müller was born in Wroclaw (Breslau) on 13 May 1851. In 1875 he opened a civil engineer's office in Berlin. Around this time he decided to add the name of his hometown to his surname, becoming known as Müller-Breslau. Qualitative Influence Lines In 1886, Heinrich Müller-Breslau develop a method for rapidly constructing the shape of an influence line. In 1883 Müller-Breslau became a lecturer and in 1885 a professor in civil engineering at the Technische Hochschule in Hanover. Qualitative Influence Lines The Muller-Breslau principle states: The influence line influence line for a function (reaction, shear, moment) is to the same scale as the deflected shape of the beam when the beam is acted on by the function. To draw the deflected shape properly, the ability of the beam to resist the applied function must be removed. Qualitative Influence Lines For example, consider the following simply supported beam. A B Let’s try to find the shape of the influence line for the vertical reaction at A. Qualitative Influence Lines Remove the ability to resist movement in the vertical direction at A by using a guided roller A B A y A y x 1 Qualitative Influence Lines Consider the following simply supported beam. Let’s try to find the shape of the influence line for the shear at the mid-point (point C). A B C CIVL 3121 Influence Lines - Muller-Breslau Principle 1/5
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Transcript of Influence Lines notes_06b
Qualitative Influence Lines
In 1886, Heinrich Müller-Breslau develop a method for rapidly constructing the shape of an influence line.
Heinrich Franz Bernhard Müller was He nr ch Franz Bernhard Müller was born in Wroclaw (Breslau) on 13 May 1851.
In 1875 he opened a civil engineer's office in Berlin. Around this time he decided to add the name of his hometown to his surname, becoming known as Müller-Breslau.
Qualitative Influence Lines
In 1886, Heinrich Müller-Breslau develop a method for rapidly constructing the shape of an influence line.
In 1883 Müller-Breslau became a n 883 Müller Breslau ecame a lecturer and in 1885 a professor in civil engineering at the TechnischeHochschule in Hanover.
Qualitative Influence Lines
The Muller-Breslau principle states:
The influence lineinfluence line for a function (reaction, shear, moment) is to the same scale as the deflected )shape of the beam when the beam is acted on by the function.
To draw the deflected shape properly, the ability of the beam to resist the applied function must be removed.
Qualitative Influence Lines
For example, consider the following simply supported beam.
A B
Let’s try to find the shape of the influence line for the vertical reaction at A.
Qualitative Influence Lines
Remove the ability to resist movement in the vertical direction at A by using a guided roller
A BAy
Ay
x
1
Qualitative Influence Lines
Consider the following simply supported beam.
Let’s try to find the shape of the influence line for the shear at the mid-point (point C).
A BC
CIVL 3121 Influence Lines - Muller-Breslau Principle 1/5
Qualitative Influence Lines
Remove the ability to resist shear at point C
V
A BVVC
x
The change in shear is equal to 1
Qualitative Influence Lines
Consider the following simply supported beam.
Let’s try to find the shape of the influence line for the moment at the mid-point (point C).
A BC
Qualitative Influence Lines
Remove the ability to resist moment at C by using a hinge
A BMC
x
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point B
A B
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point B
A BBy
x
1
By
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point A
A B
CIVL 3121 Influence Lines - Muller-Breslau Principle 2/5
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point A
A BAyAy
x
1
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point B
A B
Qualitative Influence Lines
Sketch the shape of the influence line for the reaction at point B
A BBy
x
1
By
Qualitative Influence Lines
Sketch the shape of the influence line for the shear at point C
C
A B D
Qualitative Influence Lines
Sketch the shape of the influence line for the shear at point C
C
V
VC
x
A B DV
The change in shear is equal to 1
Qualitative Influence Lines
Sketch the shape of the influence line for the moment at point C
C
A B D
CIVL 3121 Influence Lines - Muller-Breslau Principle 3/5
Qualitative Influence Lines
Sketch the shape of the influence line for the moment at point C
C
MC
x
A B D
Qualitative Influence Lines
Sketch the shape of the influence line for the moment at point B
B
A C D
Qualitative Influence Lines
Sketch the shape of the influence line for the moment at point B
B
MB
x
A C D
Qualitative Influence Lines
Sketch the shape of the influence line for the shear at point B
BB
A C D
Qualitative Influence Lines
Sketch the shape of the influence line for the shear at point B
B
V
VB
x
B
A C DV
The change in shear is equal to 1
Qualitative Influence Lines
Draw the influence lines for the vertical reaction at D and the shear at E.
CE
A B
C
D
E
10 ft 10 ft 15 ft 15 ft
CIVL 3121 Influence Lines - Muller-Breslau Principle 4/5
Qualitative Influence Lines
Draw the influence lines for the vertical reaction at D and the shear at E.
CE
A B
C
D
E
10 ft 10 ft 15 ft 15 ft
Dy
x
1
15 ft35 ft
Dy
Qualitative Influence Lines
Draw the influence lines for the vertical reaction at D and the shear at E.
CE
A B
C
D
E
10 ft 10 ft 15 ft 15 ft
Qualitative Influence Lines
Draw the influence lines for the vertical reaction at D and the shear at E.
CEV
A B
C
D
E
10 ft 10 ft 15 ft 15 ft
VE
x
The change in shear is equal to 1
V
Qualitative Influence Lines
Draw the influence lines for the vertical reaction at D and the shear at E.
The change in shear at point E is equal to 1 The influence lines can be determined by
VE
x
The influence lines can be determined by similar triangles the values of
-0.75
10ft
0.510 15
xft ft
0.750.5(15 )
10ftx
ft
-0.5
0.510 ft 15 ft 15 ft
Qualitative Influence Lines
Determine the maximum positive moment that can be developed at point D in the beam shown below due to a concentrated live load of 4 k, a uniform live load of 300 lb/ft, and a dead load of 200 lb/ft.
A B C D E
5 ft 5 ft 5 ft 10 ft
End of Influence Lines – Part 2
Any questions?
CIVL 3121 Influence Lines - Muller-Breslau Principle 5/5
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