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    Chapter 1 (1-2)

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    Gnabry
    1. Hooke's law states that stress is directly proportional to strain within the elastic limit of a material. Young's modulus (E) represents the ratio of stress to strain. 2. A tensile test measures properties like elasticity, yield strength, maximum tensile strength, and breaking point by applying an axial pulling force to a material sample. 3. The stress-strain diagram plots stress on the y-axis against strain on the x-axis, showing properties like proportional limit, elastic limit, yield point, and breaking point. The slope of the linear portion is Young's modulus.

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    Chapter 1 (1-2)

    Uploaded by

    Gnabry
    10 views27 pages
    1. Hooke's law states that stress is directly proportional to strain within the elastic limit of a material. Young's modulus (E) represents the ratio of stress to strain. 2. A tensile test measures properties like elasticity, yield strength, maximum tensile strength, and breaking point by applying an axial pulling force to a material sample. 3. The stress-strain diagram plots stress on the y-axis against strain on the x-axis, showing properties like proportional limit, elastic limit, yield point, and breaking point. The slope of the linear portion is Young's modulus.

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    CHAPTER 1(1-2)

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    1. Hooke's law states that stress is directly proportional to strain within the elastic limit of a material. Young's modulus (E) represents the ratio of stress to strain. 2. A tensile test measures properties like elasticity, yield strength, maximum tensile strength, and breaking point by applying an axial pulling force to a material sample. 3. The stress-strain diagram plots stress on the y-axis against strain on the x-axis, showing properties like proportional limit, elastic limit, yield point, and breaking point. The slope of the linear portion is Young's modulus.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    10 views27 pages

    Chapter 1 (1-2)

    Uploaded by

    Gnabry
    1. Hooke's law states that stress is directly proportional to strain within the elastic limit of a material. Young's modulus (E) represents the ratio of stress to strain. 2. A tensile test measures properties like elasticity, yield strength, maximum tensile strength, and breaking point by applying an axial pulling force to a material sample. 3. The stress-strain diagram plots stress on the y-axis against strain on the x-axis, showing properties like proportional limit, elastic limit, yield point, and breaking point. The slope of the linear portion is Young's modulus.

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    © All Rights Reserved
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    Download as pdf or txt
    of 27

    Edited By

    Muhd Nasae Bin Mahyuddin


    Lecturer
    Politeknik Tuanku Sultanah Bahiyah
    OUTLINE
    0 Hooke’s Law
    0 Young Modulus, E
    0 Tensile test
    0 Stress-strain diagram
    Refresh the memory back..
    0 Stress O Modulus of
    elasticity
    σ
    E= ε
    0 Strain

    PL
    E = A∆L
    What is Hooke’s Law?
    0 Stress applied to the material is directly proportional
    to the strain provided the elastic limit of the material
    is not exceeded.
    0 Applied to all elastic material including steel.
    0 E.g. bungee jumping rope.
    Young Modulus, E
    0 The ratio of linear stress to the linear strain.
    0 Also known as elasticity modulus.
    0 Elastic value of the material.
    0 Value of E differ depending on the material type.
    0 E , strength of the material
    0 e.g. E steel higher than aluminum.
    σ, stress
    E
    steel
    aluminum

    Δσ

    Δε

    ε, strain
    Example of E
    STRESS VS STRAIN Based on the graph, find
    the value of Elasticity
    GRAPH
    modulus.
    100
    Stress, σ (kN/m2)

    80
    60
    40
    20
    0
    0.2 0.4 0.6 0.8
    Strain, ε
    #2
    Example of E Got the answer?

    Find the slope!! 100 kN/m2

    STRESS VS STRAIN Based on the graph, find


    the value of Elasticity
    GRAPH
    modulus.
    100
    Stress, σ (kN/m2)

    80
    we know:
    60
    40
    20
    So? What to do next?
    0
    0.2 0.4 0.6 0.8
    Strain, ε #1
    Make sure it is a STRESS VS
    STRAIN GRAPH!!
    What if the graph is NOT stress versus
    strain?

    How are we going to find the E value?


    Hurmmm….
    Tensile Test
    0 Test to measure:
    0 Elasticity point
    0 Maximum tension strength
    0 Yield point
    0 Break point
    0 Different material different value.
    Tensile Test
    Stress-strain diagram
    P = ratio limit
    A = elasticity limit
    Y = yield point
    S = max tension strength
    B = break point

    *credits to substech.com
    Tensile Test
    before

    after

    neck

    before

    after
    Compressive Test
    Tensile Test
    What should you know?
    1. Yield stress
    2. Max tension stress
    3. % elongation
    4. % area reduction
    Stress-strain diagram
    P = ratio limit
    A = elasticity limit
    Y = yield point
    S = max tension strength
    B = break point

    *credits to substech.com
    E value without strain VS stress
    graph..
    LOAD VERSUS
    LENGTH GRAPH
    100
    Load,P (kN)

    80
    60
    40
    20
    0

    Length, L (mm)
    E value without strain VS stress
    graph..
    LOAD VERSUS
    LENGTH GRAPH
    100 we know:
    Load,P (kN)

    80
    60
    40
    20
    0

    Length, L (mm)

    What happen if we find the Can we find these values in


    slope? the graph?
    E value without strain VS stress
    graph..
    LOAD VERSUS
    LENGTH GRAPH
    100 we know:
    Load,P (kN)

    80
    60
    40
    20
    0

    Length, L (mm)

    What happen if we find the


    slope?
    E value without strain VS stress
    graph..
    LOAD VERSUS
    LENGTH GRAPH
    100 we know:
    Load,P (kN)

    80
    60
    40
    20
    0

    Length, L (mm)

    What happen if we find the


    slope?
    Force Elongation Diagram
    A= proportional
    limit
    B= elastic limit
    C= upper yield point
    D= lower yield point
    E= maximum force
    F= break point
    Formula
    0 Yield stress
    𝑢𝑝𝑝𝑒𝑟 𝑦𝑖𝑒𝑙𝑑 𝑝𝑜𝑖𝑛𝑡
    𝜎𝑦 =
    𝑜𝑟𝑖𝑔𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
    0 Max tension stress
    𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑓𝑜𝑟𝑐𝑒
    𝜎𝑚𝑎𝑥 =
    𝑜𝑟𝑖𝑔𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
    0 % elongation
    ∆𝐿
    = × 100%
    𝐿𝑜
    0 % area reduction
    ∆𝐷
    = × 100%
    𝐷𝑜
    Let’s try it out
    #1
    A tensile test towards a steel rod with diameter of 14.35mm and
    original length of 56mm being conducted. These are the results
    recorded:
    Load, kN 0 20 40 60 80
    Length Increment, mm 0 0.031 0.061 0.092 0.122
    Final length of rod = 65.6mm
    Final Diameter of rod = 11.45mm
    i. Draw a load versus length increment graph and find the slope
    value.
    ii. Calculate:
    a. E value
    b. % elongation
    c. % area reduction
    What else should you know??
    0 working stress.
    𝑃𝑟𝑜𝑜𝑓 𝑆𝑡𝑟𝑒𝑠𝑠
    𝜎𝑤 =
    𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
    0 proof stress.
    𝑝𝑜𝑛𝑡 𝑛𝑒𝑎𝑟 𝑢𝑝𝑝𝑒𝑟 𝑦𝑖𝑒𝑙𝑑 𝑝𝑜𝑖𝑛𝑡
    𝜎𝑝 =
    𝑜𝑟𝑖𝑔𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
    0 factor of safety.
    𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑡𝑟𝑒𝑠𝑠
    𝑆. 𝐹 =
    𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠
    0 Poisson’s ratio.

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