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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=2.8 kN at midspan, see figure below. L/2 If b₁ = 86 mm and b₂ = 36 mm determine: a) the modular ratio n. Enter your answer to 4 decimal places. B L/2 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. c) moment of inertia about the horizontal centroidal axis for timber. Enter your answer in mm² to 1 decimal place. d) moment of inertia about the horizontal centroidal axis for transformed CFRP. Enter your answer in mm² to 2 decimal places. e) moment of inertia about the horizontal centroidal axis for the whole section. Enter your answer in mm² to 2 decimal places.

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=2.8 kN at midspan, see figure below. L/2 If b₁ = 86 mm and b₂ = 36 mm determine: a) the modular ratio n. Enter your answer to 4 decimal places. B L/2 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. c) moment of inertia about the horizontal centroidal axis for timber. Enter your answer in mm² to 1 decimal place. d) moment of inertia about the horizontal centroidal axis for transformed CFRP. Enter your answer in mm² to 2 decimal places. e) moment of inertia about the horizontal centroidal axis for the whole section. Enter your answer in mm² to 2 decimal places.

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter6: Stresses In Beams (advanced Topics)
Section: Chapter Questions
Problem 6.3.14P: A reinforced concrete beam (see figure) is acted on by a positive bending moment of M = 160 kN · m....
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Answer for A is 9.3333 and B is 122.33. Answer c,d and e
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= 2.8 kN at midspan, see figure below. L/2 If b₁ = 86 mm and b₂ = 36 mm determine: a) the modular ratio n. Enter your answer to 4 decimal places. B L/2 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. c) moment of inertia about the horizontal centroidal axis for timber. Enter your answer in mm² to 1 decimal place. d) moment of inertia about the horizontal centroidal axis for transformed CFRP. Enter your answer in mm² to 2 decimal places. e) moment of inertia about the horizontal centroidal axis for the whole section. Enter your answer in mm² to 2 decimal places.
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= 2.8 kN at midspan, see figure below. L/2 If b₁ = 86 mm and b₂ = 36 mm determine: a) the modular ratio n. Enter your answer to 4 decimal places. B L/2 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. c) moment of inertia about the horizontal centroidal axis for timber. Enter your answer in mm² to 1 decimal place. d) moment of inertia about the horizontal centroidal axis for transformed CFRP. Enter your answer in mm² to 2 decimal places. e) moment of inertia about the horizontal centroidal axis for the whole section. Enter your answer in mm² to 2 decimal places.
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