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 ideaof 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:db₁Flange (horizontal section of cross-section):.by = 340 mm• ty = 15 mmWeb (vertical section of cross-section):.• d = 340 mm• t = 15 mm1₁The 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 theflooring uniformly distributed over the span of the beamWWallsLFlooringBeamBThe 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 compositebeam 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 GPaIn 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.TTinggerTimberThe 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 =mmWhat is the second moment of area of the cross-section about the neutral axis?Izz =mm¹What is the second moment of area of the cross-section about the neutral axis?Izz =mm ¹What is the stress at the top fibre of the beam?MPatopWhat is the stress at the bottom fibre of the beam?Ebot =MPabotBy using Hooke's Law, what is the value of normal strain at the top and bottom fibres of the beam?EtopFor values of stresses and strains, assume tension is positive and include a negative sign in your entry if in compression.

To find the Depth of Neutral axis, Moment of Inertia and stresses and strains for the Beam One.

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

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Bars

In civil engineering, bars refer to steel reinforcement bars or rebars. These are structural members primarily used for reinforcement purposes in masonry works. A bar is characterized by its cross-sectional area, which is negligible compared to its length. Bars are usually manufactured by steel which is uniform throughout the length, or by meshing multiple steel wires. Other materials of the bar include carbon steel, glass fiber, carbon fiber, and basalt fiber. The reinforcing bars are coated with epoxy resins and other materials to enhance some of their properties including corrosion resistance.

Question

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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.

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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