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    Advanced Mechanics

    Uploaded by

    Ivan Mono
    This document contains a multi-part question about analyzing stresses and deflections in beams and columns. It provides dimensional parameters and material properties, and asks the student to calculate things like stresses, strains, loads, and deflections based on the given information. Calculations are required to determine yields loads, stresses at specific points, buckling loads, shear and normal stresses, and bending radii and deflections. The questions cover basic structural analysis and mechanics of materials concepts.

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    © All Rights Reserved
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    Advanced Mechanics

    Uploaded by

    Ivan Mono
    26 views9 pages
    This document contains a multi-part question about analyzing stresses and deflections in beams and columns. It provides dimensional parameters and material properties, and asks the student to calculate things like stresses, strains, loads, and deflections based on the given information. Calculations are required to determine yields loads, stresses at specific points, buckling loads, shear and normal stresses, and bending radii and deflections. The questions cover basic structural analysis and mechanics of materials concepts.

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    advanced mechanics

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    This document contains a multi-part question about analyzing stresses and deflections in beams and columns. It provides dimensional parameters and material properties, and asks the student to calculate things like stresses, strains, loads, and deflections based on the given information. Calculations are required to determine yields loads, stresses at specific points, buckling loads, shear and normal stresses, and bending radii and deflections. The questions cover basic structural analysis and mechanics of materials concepts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    26 views9 pages

    Advanced Mechanics

    Uploaded by

    Ivan Mono
    This document contains a multi-part question about analyzing stresses and deflections in beams and columns. It provides dimensional parameters and material properties, and asks the student to calculate things like stresses, strains, loads, and deflections based on the given information. Calculations are required to determine yields loads, stresses at specific points, buckling loads, shear and normal stresses, and bending radii and deflections. The questions cover basic structural analysis and mechanics of materials concepts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 9

    Student Name: Student number:

    Question 1 (10 points): The rigid beam is supported by the three


    posts A, B , and C of equal length. Posts A and C have a cross-
    sectional area of 4400+MN ( in mm2 ) and are made of a material for
    which E = 70 GPa and Y = 20 MPa. Post B has a cross-section of
    300+MN ( in mm2 ) and is made of a material for which E1 = 100 GPa
    and Y1 = 590 MPa.

    Here MN are the last two digits of your student number.

    Determine the smallest magnitude of P so that


    (a)only rods A and C yield and
    (b)all the posts yield.
    This page is for you to answer question 1, if you need more space
    Question 2 (15 points): A cantilever beam with dimension shown is
    carrying a load P in the y-z plane at the centroid of the beam cross-
    section ( = 75). The value of P is given in Newton by P = 1000 + 48 mm
    MN, where MN are last two digits of your student number. For each
    point of A and B at the fixed end of the beam where the bending .
    A
    moment is maximum, find
    1. The normal stress, 240 mm .
    B
    y
    P

    2. The shear stress.



    z
    Note: The locations of points A and B are: o
    2m
    A: y = 120 mm, z = 24 mm
    B: y =  60 mm, z = 24 mm.
    This page is for you to answer question 2, if you need more space
    Question 3 (15 points): A long slender column ABC is pinned at ends A
    and C and compressed by an axial force P (see figure). At the midpoint
    B, lateral support is provided to prevent deflection in the y direction. The
    column is a steel rectangular section with dimensions 5 mm and 12 mm

    12 mm
    and Young’s modulus E = 208 GPa. The distance between lateral supports
    is given in millimeter by L = 2000 + MN, where MN are last two digits 5 mm
    of your student number. Calculate the allowable load P, taking into
    account the possibility of buckling about either principal centroidal axis z
    (i.e., axis y and axis z). y

    x
    This page is for you to answer question 3, if you need more space
    y
    Question 4 (15 points): A beam of web-flange shape is subjected to a
    bending moment M z = 27,000 + MN ( in N.m ) and a vertical shear force V
    = 45000 + MN ( in Newton ), where MN are last two digits of your student z
    A . h1 =
    h=
    0.32 m 0.29 m
    number. The cross-sectional dimensions of the beam are b = 0.165 m, t = t = 0.0075 m
    0.0075 m, h = 0.32 m, and h1 = 0.29 m. Point A is in the web just below the
    flange. Point O is at the centroid of the cross-section.
    b=
    Determine: 0.165 m
    1. The shear stress at point A.
    2. The shear stress at point O.
    3. The normal stress at point A (due to bending moment) .
    4. The maximum in-plane (x-y plane) shear stress at point A.
    5. The maximum absolute shear stress at point A.
    This page is for you to answer question 4, if you need more space
    Question 5 (10 points): A couple M0 acts on the end of a slender cantilever beam as shown below. For this
    beam, we have L = 15 + N ( in mm, N is the last digit of your student number ) and c = 0.5 mm.
    a) Determine the radius of curvature () if the outer fiber of the beam is at the tensile yield strain of the material,
    εy = 0.01.
    b) Determine the tip deflection δmax at this loading.

     M0

    max
    2c
    x
    2c
    c
    y L

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