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    PCD Example

    Uploaded by

    Denice Castro
    The document provides an example problem of determining an appropriate rectangular cross-section for a simply supported beam carrying various loads. It calculates the moments at transfer and service and checks the section modulus requirements at the top and bottom fibers. Adopting trial dimensions, it determines that a 250 mm width x 609 mm depth section satisfies the section modulus requirement and should be used for the beam.

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    © All Rights Reserved
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    PCD Example

    Uploaded by

    Denice Castro
    123 views3 pages
    The document provides an example problem of determining an appropriate rectangular cross-section for a simply supported beam carrying various loads. It calculates the moments at transfer and service and checks the section modulus requirements at the top and bottom fibers. Adopting trial dimensions, it determines that a 250 mm width x 609 mm depth section satisfies the section modulus requirement and should be used for the beam.

    Original Description:

    Original Title

    PCD EXAMPLE

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    The document provides an example problem of determining an appropriate rectangular cross-section for a simply supported beam carrying various loads. It calculates the moments at transfer and service and checks the section modulus requirements at the top and bottom fibers. Adopting trial dimensions, it determines that a 250 mm width x 609 mm depth section satisfies the section modulus requirement and should be used for the beam.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    123 views3 pages

    PCD Example

    Uploaded by

    Denice Castro
    The document provides an example problem of determining an appropriate rectangular cross-section for a simply supported beam carrying various loads. It calculates the moments at transfer and service and checks the section modulus requirements at the top and bottom fibers. Adopting trial dimensions, it determines that a 250 mm width x 609 mm depth section satisfies the section modulus requirement and should be used for the beam.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Civil Engineering Design (1)

    Example

    Problem
    The single-span, simply-supported beam shown below carried the loads as shown.
    Taking the losses to be 25% and:
    • permissible tensile stresses are 2.5 N/mm2 at transfer and 2.0 N/mm2 in
    service;
    • permissible compressive stresses are 20 N/mm2 at transfer and at service.
    Determine an appropriate rectangular section for the member taking the density of
    prestressed concrete to be 25 kN/m3.

    Solution
    We will check the requirements at the critical section which is at mid-span. To
    determine an approximate initial transfer moment, M t , we estimate the section depth
    based on a span depth ratio of, say, 15:

    9000
    dtrial 600 mm
    15

    Try this with a width of 250 mm, which is a practical minimum. Hence, the sefl
    weight load is:

    34 Dr. C. Caprani
    Civil Engineering Design (1)

    wsw 25 0.6 u 0.25 3.75 kN/m

    At transfer only self weight is present. Therefore:

    wL2 3.75 u 92
    Mt 38 kNm
    8 8

    At service the moment is:

    Ms
    wL2 >3.75  5  20@ u 9 2

    291 kNm
    8 8

    Check the section modulus at the top fibre:

    Ms DMt
    Zt t
    f sc  D f tt
    291  0.75 u 38
    Zt t
    20  0.75 2.5
    Z t t 12.0 u 106 mm3

    And at the bottom:

    Ms DMt
    Zb t
    D ftc  f st
    291  0.75 u 38
    Zb t
    0.75 20  2.0
    Z b t 15.4 u 106 mm3

    35 Dr. C. Caprani
    Civil Engineering Design (1)

    If the section is to be rectangular, then Z b Z t and so the requirement for Z b


    governs:

    bh 2
    Z t 15.4 u 106
    6

    Keeping the 250 mm width:

    250h 2
    t 15.4 u 106
    6
    6 15.4 u 106
    ht
    250
    h t 609 mm

    Thus adopt a 250 mm × 650 mm section.

    Note that this changes the self weight and so the calculations need to be performed
    again to verify that the section is adequate. However, the increase in self weight is
    offset by the larger section depth and hence larger section modulii which helps reduce
    stresses. These two effects just about cancel each other out.
    Verify This

    36 Dr. C. Caprani

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