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Beam One: [Flange = Timber, Web = Timber] The first beam to consider is a fully-timber beam. Note the whole cross-section is a single material and linear elastic. T The dimensions are as given earlier. The neutral axis of the beam is located at the centroid. What is the position of the centroid measured from the base? y = mm What is the second moment of area of the cross-section about the neutral axis? Izz = mm Tinger Timber What is the second moment of area of the cross-section about the neutral axis? Izz mm4 What is the stress at the top fibre of the beam? MPa Ebot O top What is the stress at the bottom fibre of the beam? MPa O bot By using Hooke's Law, what is the value of normal strain at the top and bottom fibres of the beam? Etop For values of stresses and strains, assume tension is positive and include a negative sign in your entry if in compression.

Beam One: [Flange = Timber, Web = Timber] The first beam to consider is a fully-timber beam. Note the whole cross-section is a single material and linear elastic. T The dimensions are as given earlier. The neutral axis of the beam is located at the centroid. What is the position of the centroid measured from the base? y = mm What is the second moment of area of the cross-section about the neutral axis? Izz = mm Tinger Timber What is the second moment of area of the cross-section about the neutral axis? Izz mm4 What is the stress at the top fibre of the beam? MPa Ebot O top What is the stress at the bottom fibre of the beam? MPa O bot By using Hooke's Law, what is the value of normal strain at the top and bottom fibres of the beam? Etop For values of stresses and strains, assume tension is positive and include a negative sign in your entry if in compression.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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An engineer is designing a beam to support a flooring system above it, as well as two walls. The beam will be a T-section, though the engineer is considering the idea of combining timber and steel to create a composite member for the application. The dimensions of the T-section beam are shown below: The dimensions of the T-section beam are shown below: d b₁ Flange (horizontal section of cross-section): .by = 340 mm • ty = 15 mm Web (vertical section of cross-section): . • d = 340 mm • t = 15 mm 1₁ The loading of the beam can be modelled as the following free-body diagram, where P = 20 kN represents the dead load of each wall, and to = 4 kN/m represents the dead load of the flooring uniformly distributed over the span of the beam W Walls L Flooring Beam B The length of the beam is L = 8 m. The engineer will consider the stresses developed at the mid-span of the beam. The following beams will be considered: 1. all timber (flange + web), 2. a composite beam consisting of a steel flange and timber web, and 3. a composite beam consisting of a timber flange and steel web. The Young's moduli of each material may be given by: • Steel: E, 200 GPa • Timber: E, = 25 GPa In all cases, assume both materials remain linear elastic under the loading.
Transcribed Image Text:An engineer is designing a beam to support a flooring system above it, as well as two walls. The beam will be a T-section, though the engineer is considering the idea of combining timber and steel to create a composite member for the application. The dimensions of the T-section beam are shown below: The dimensions of the T-section beam are shown below: d b₁ Flange (horizontal section of cross-section): .by = 340 mm • ty = 15 mm Web (vertical section of cross-section): . • d = 340 mm • t = 15 mm 1₁ The loading of the beam can be modelled as the following free-body diagram, where P = 20 kN represents the dead load of each wall, and to = 4 kN/m represents the dead load of the flooring uniformly distributed over the span of the beam W Walls L Flooring Beam B The length of the beam is L = 8 m. The engineer will consider the stresses developed at the mid-span of the beam. The following beams will be considered: 1. all timber (flange + web), 2. a composite beam consisting of a steel flange and timber web, and 3. a composite beam consisting of a timber flange and steel web. The Young's moduli of each material may be given by: • Steel: E, 200 GPa • Timber: E, = 25 GPa In all cases, assume both materials remain linear elastic under the loading.
Beam One: [Flange = Timber, Web = Timber] The first beam to consider is a fully-timber beam. Note the whole cross-section is a single material and linear elastic. T Tingger Timber The dimensions are as given earlier. The neutral axis of the beam is located at the centroid. What is the position of the centroid measured from the base? y = mm What is the second moment of area of the cross-section about the neutral axis? Izz = mm¹ What is the second moment of area of the cross-section about the neutral axis? Izz = mm ¹ What is the stress at the top fibre of the beam? MPa top What is the stress at the bottom fibre of the beam? Ebot = MPa bot By using Hooke's Law, what is the value of normal strain at the top and bottom fibres of the beam? Etop For values of stresses and strains, assume tension is positive and include a negative sign in your entry if in compression.
Transcribed Image Text:Beam One: [Flange = Timber, Web = Timber] The first beam to consider is a fully-timber beam. Note the whole cross-section is a single material and linear elastic. T Tingger Timber The dimensions are as given earlier. The neutral axis of the beam is located at the centroid. What is the position of the centroid measured from the base? y = mm What is the second moment of area of the cross-section about the neutral axis? Izz = mm¹ What is the second moment of area of the cross-section about the neutral axis? Izz = mm ¹ What is the stress at the top fibre of the beam? MPa top What is the stress at the bottom fibre of the beam? Ebot = MPa bot By using Hooke's Law, what is the value of normal strain at the top and bottom fibres of the beam? Etop For values of stresses and strains, assume tension is positive and include a negative sign in your entry if in compression.
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