Question 1: Beam Analysis Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these moments is PL. Moment Release A B с ° MB = PL Mc= = PL -L/2- -L/2- → P D Figure 1: Two beam arrangement for question 1. To analyse this structure, you will: a) Construct the free body diagrams for the structure shown above. When constructing your FBD's you must make section cuts at point B and C. You can represent the structure as three separate beams. Following this, construct the bending moment and shear force diagrams for each segment of the beam. Do not substitute in values for P, L etc. Keep your answer in algebraic form. Clearly label all the key features of the shear force and bending moment diagrams (include features such as maximum values shear force and bending moment, and the locations where the values change from positive to negative). Hint: Start by solving beam either AB or CD. Take care with your sign convention! (3%) b) Both beams (ABC and CD) have a solid square cross-section with side lengths 'ABC' and 'aco'. Design the beams to withstand the applied loading. Clearly state your calculated value of a in mm for each possible failure mode for both beams to one decimal place. Use the parameters shown in Table 1 to calculate the beam dimensions. Table 1: The material properties used in part (b) of question 1 (2%) Symbol E Value Units 200.0 GPa Gallow 250.0 MPa Tallow 150.0 MPa P 2.0 KN L 2.0 m
Question 1: Beam Analysis Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these moments is PL. Moment Release A B с ° MB = PL Mc= = PL -L/2- -L/2- → P D Figure 1: Two beam arrangement for question 1. To analyse this structure, you will: a) Construct the free body diagrams for the structure shown above. When constructing your FBD's you must make section cuts at point B and C. You can represent the structure as three separate beams. Following this, construct the bending moment and shear force diagrams for each segment of the beam. Do not substitute in values for P, L etc. Keep your answer in algebraic form. Clearly label all the key features of the shear force and bending moment diagrams (include features such as maximum values shear force and bending moment, and the locations where the values change from positive to negative). Hint: Start by solving beam either AB or CD. Take care with your sign convention! (3%) b) Both beams (ABC and CD) have a solid square cross-section with side lengths 'ABC' and 'aco'. Design the beams to withstand the applied loading. Clearly state your calculated value of a in mm for each possible failure mode for both beams to one decimal place. Use the parameters shown in Table 1 to calculate the beam dimensions. Table 1: The material properties used in part (b) of question 1 (2%) Symbol E Value Units 200.0 GPa Gallow 250.0 MPa Tallow 150.0 MPa P 2.0 KN L 2.0 m
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter6: Beams And Cables
Section: Chapter Questions
Problem 6.42P: For the beam AB shown in Cases 1 and 2, derive and plot expressions for the shear force and bending...
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Transcribed Image Text:Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the bending moment and shear force diagrams
for each segment of the beam. Do not substitute in values for P, L etc. Keep your answer in
algebraic form. Clearly label all the key features of the shear force and bending moment
diagrams (include features such as maximum values shear force and bending moment, and
the locations where the values change from positive to negative).
Hint: Start by solving beam either AB or CD. Take care with your sign convention!
(3%)
b) Both beams (ABC and CD) have a solid square cross-section with side lengths 'ABC' and 'aco'.
Design the beams to withstand the applied loading. Clearly state your calculated value of a
in mm for each possible failure mode for both beams to one decimal place. Use the
parameters shown in Table 1 to calculate the beam dimensions.
Table 1: The material properties used in part (b) of question 1
(2%)
Symbol
E
Value
Units
200.0
GPa
Gallow
250.0
MPa
Tallow
150.0
MPa
P
2.0
KN
L
2.0
m
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