A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonded to its bottom surface. The cross section of the composite beam is shown in figure below. The elastic modulus of the wood is E= 12 GPa and the elastic modulus of the CFRP is 112 GPa. The simply supported beam spans L = 6 m and carries a concentrated load P= 3.8 kN at midspan, see figure below. b₁ A L/2 P B L/2 C CFRP 250 mm 3 mm If b₁ = 88 mm and b₂ = 41 mm determine: b) centroid location of the transformed section in the vertical direction. Enter your answer in mm to 1 decimal place. Hint: transform CFRP into an equivalent amount of wood. Calculate the position of the centroid relative to the bottom edge of the transformed section, i.e. centroid position is measured upward from bottom edge of section.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter5: Stresses In Beams (basic Topics)
Section: Chapter Questions
Problem 5.6.25P: A beam of square cross section (a = length of each side) is bent in the plane of a diagonal (see...
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A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonded to its bottom surface. The cross
section of the composite beam is shown in figure below. The elastic modulus of the wood is E= 12 GPa and the elastic modulus of the
CFRP is 112 GPa. The simply supported beam spans L= 6 m and carries a concentrated load P= 3.8 kN at midspan, see figure below.
b₁
If b₁ =
L/2
= 88 mm and b₂ = 41 mm determine:
B
L/2
C
CFRP
b₂
250 mm
3 mm
b) centroid location of the transformed section in the vertical direction. Enter your answer in mm to 1 decimal place.
Hint: transform CFRP into an equivalent amount of wood. Calculate the position of the centroid relative to the bottom edge of the
transformed section, i.e. centroid position is measured upward from bottom edge of section.
Transcribed Image Text:A glue-laminated timber beam is reinforced by carbon fiber reinforced plastic (CFRP) material bonded to its bottom surface. The cross section of the composite beam is shown in figure below. The elastic modulus of the wood is E= 12 GPa and the elastic modulus of the CFRP is 112 GPa. The simply supported beam spans L= 6 m and carries a concentrated load P= 3.8 kN at midspan, see figure below. b₁ If b₁ = L/2 = 88 mm and b₂ = 41 mm determine: B L/2 C CFRP b₂ 250 mm 3 mm b) centroid location of the transformed section in the vertical direction. Enter your answer in mm to 1 decimal place. Hint: transform CFRP into an equivalent amount of wood. Calculate the position of the centroid relative to the bottom edge of the transformed section, i.e. centroid position is measured upward from bottom edge of section.
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