Part 2: Beam analysis The timber beam in Figure 2 is simply supported at points A and E. The cross-section of the beam changes from segment AC to CE, as shown below. The Young's modulus of timber may be taken as 12 GPa. The load, geometry and cross-sections of the beam will be instructed to each student in class. :B A :B C D 0.5L 0.5L 0.75L 0.75L bị b2 0.25h h2 hi NA Section B-B Section D-D Figure 2 (a) Determine the deflection of the beam at point D by both Virtual Work Method and Castigliano's Theorem. Compare and comment on the differences in these approaches. (b) Calculate the bending and shear stresses at point F on the Section B-B. (c) Develop and sketch the Mohr's circle of stresses corresponding to point F. Show all necessary details, including principal stresses and maximum shear stress.
Part 2: Beam analysis The timber beam in Figure 2 is simply supported at points A and E. The cross-section of the beam changes from segment AC to CE, as shown below. The Young's modulus of timber may be taken as 12 GPa. The load, geometry and cross-sections of the beam will be instructed to each student in class. :B A :B C D 0.5L 0.5L 0.75L 0.75L bị b2 0.25h h2 hi NA Section B-B Section D-D Figure 2 (a) Determine the deflection of the beam at point D by both Virtual Work Method and Castigliano's Theorem. Compare and comment on the differences in these approaches. (b) Calculate the bending and shear stresses at point F on the Section B-B. (c) Develop and sketch the Mohr's circle of stresses corresponding to point F. Show all necessary details, including principal stresses and maximum shear stress.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Answer A only by Virtual Work Method with full details
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Transcribed Image Text:Part 2: Beam analysis
The timber beam in Figure 2 is simply supported at points A and E. The cross-section of the beam changes
from segment AC to CE, as shown below. The Young's modulus of timber may be taken as 12 GPa. The
load, geometry and cross-sections of the beam will be instructed to each student in class.
B
A
:B
C
D
E
0.5L
0.5L
0.75L
0.75L
bị
0.25hI
b2
h2
NA
hị
Section B-B
Section D-D
Figure 2
(a) Determine the deflection of the beam at point D by both Virtual Work Method and Castigliano's
Theorem. Compare and comment on the differences in these approaches.
(b) Calculate the bending and shear stresses at point F on the Section B-B.
(c) Develop and sketch the Mohr's circle of stresses corresponding to point F. Show all necessary details,
including principal stresses and maximum shear stress.
Transcribed Image Text:PART 2
Cross-section dimensions (mm)
Load Q (kN) Length L (m)
b1
h1
b2
h2
10.5
2.1
96
211
56
161
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