Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 64 views

    Finite Dif Tut B

    Uploaded by

    romelramarack1858
    The flexural rigidity of the beam is EI. Find the slope and deflection at mid-span of the beam. Use four divisions and five nodes. Compare your answer with the exact value: 3PL3 / 16EI.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd

    Finite Dif Tut B

    Uploaded by

    romelramarack1858
    64 views2 pages
    The flexural rigidity of the beam is EI. Find the slope and deflection at mid-span of the beam. Use four divisions and five nodes. Compare your answer with the exact value: 3PL3 / 16EI.

    Original Description:

    Original Title

    finite_dif_tut_B

    Copyright

    © Attribution Non-Commercial (BY-NC)

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    The flexural rigidity of the beam is EI. Find the slope and deflection at mid-span of the beam. Use four divisions and five nodes. Compare your answer with the exact value: 3PL3 / 16EI.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    64 views2 pages

    Finite Dif Tut B

    Uploaded by

    romelramarack1858
    The flexural rigidity of the beam is EI. Find the slope and deflection at mid-span of the beam. Use four divisions and five nodes. Compare your answer with the exact value: 3PL3 / 16EI.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    Problems : Finite difference method

    1.
    For the beam shown in Fig. 1 find the slope and deflection at mid-span of the beam. Use four divisions
    and five nodes. The flexural rigidity of the beam is EI.

    Ans. Deflection = 0.0198pL4/EI Slope = 0.003pL3/EI

    2p
    p
    Fig. 1

    2.
    The stepped cantilever beam in Fig. 2 is of length L. Find the deflection of the free end using four
    divisions and five nodes. Compare your answer with the exact value: 3PL3/16EI.

    NOTE At an abrupt change of cross-section the effective flexural rigidity (EI)eff is given by
    1/(EI)eff = 0.5{1/(EI)left + 1/(EI)right}. This is because the curvature 1/R = M/EI must be the same. Using
    the average flexural rigidity 0.5{(EI)left + (EI)right} does not guarantee this.

    P
    2EI EI
    Fig. 2

    3.
    Determine the deflection, bending moment and end support reactions for the beam of fexural rigidity
    EI below. The beam sits on an elastic foundation beteen simple supports. The foundation modulus k is
    equal to 0.1024EI/4 where  = L/4. Use four equal divisions and symmetry to reduce the amount of
    work.

    Ans. The mid-span deflection and bending moment are 0.0102qL4/EI and 0.0978qL2 respectively. The
    end reaction is 0.414qL.

    q per unit length


     Fig. 3

    4.
    Find the deflection upward of the simply-supported beam of flexural rigidity EI shown below. Use five
    equal divisions. Compare your answer with the exact values: y 1 = 0 y2 = 320L2/EI y 3 = 560L2/EI
    y 4 = 640L2/EI y5 = 480L2/EI y6 = 0 all multiplied by 10-4.

    1
    Fig.4

    L
    5.
    Find the rotation at end A of the beam of flexural rigidity EI shown below. Use four equal divisions.
    Compare your answer with the exact value L/4EI.

    1
    A B Fig.5

    6.
    Find the deflection and bending moment at midspan of the beam-column of flexural rigidity EI shown
    below. The magnitude of the axial load P is 0.3PE where PE is the critical buckling load. Use six equal
    divisions. Compare your answer with the exact values: y3 = 1.420WL3/(48EI) M3 = 1.350WL/(4EI)

    W
    P = = P Fig.6

    7.
    Using four equal divisions find the end-moment at B in the beam-column shown in Fig. & below.

    Ans. MB = 0.342PL

    9EI A B
    P= Fig.7
    L2 EI 1.5EI

    L/2 L/2

    Ian Khan-Kernahan September 2010

    You might also like