Physics

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Q2_2: QUIZ 2, PROBLEM #2

The composite beam AB, of length L=2m, is free at A (x=0) and fixed at B (x=L) and is composed of a round cylindrical core of constant radius R0=1cm bonded inside a sleeve of thickness R0 (outer radius 2R0=2cm). The beam is loaded, as indicated, by a downward linearly varying distributed load per unit length of magnitude
q(x)=q0xL,with
q0=2.76kN/m.
The material moduli are:

For the core, EC=70GPa=E0
For the sleeve, ES=210GPa=3E0

Q2_2_1 : 60.0 POINTS

Obtain a symbolic expression for the internal bending moment resultant in terms of L, q0 (enter as q_0), and x:

M(x)= ................

Q2_2_2 : 60.0 POINTS

Obtain a symbolic expression for the effective section stiffness of the beam (EI)eff in terms of R0 and E0 (enter these as R_0 and E_0, leave rationals as fractions, and enter π as pi):

(EI)eff= ...............

Q2_2_3 : 60.0 POINTS

Obtain symbolic expressions for the curvature at the neutral axis 1ρ(x) and the slope ϑ(x) of the beam in terms of L, q0, R0, E0, and x (again, leave rationals as fractions and enter π as pi):

1ρ(x)= ........
Ï‘(x)= .........

Q2_2_4 : 70.0 POINTS

Obtain the numerical value (in cm) for the displacement at the free end, vA=v(x=0):

vA= ....cm

Q2_2_5 : 70.0 POINTS

Obtain the numerical values in MPa for the maximum tensile stresses in the core (σmax,C) and in the sleeve (σmax,S):

σmax,C= MPa
σmax,S= MPa

  • Physics -

    Is it correct ?

    Q2_2_4

    vA=-5.82 cm ??

  • Physics -

    Q2_2_2
    23/2*R_0^4*E_0*pi

    Q_2_2$
    -5,82 cm

  • Physics -

    Q2_2_5

    STRESS CORE=9 MPa

    stress sleve= 73 MPa

    Is it correct ?

  • Physics -

    Q 2_2_1?
    Q 2_2_3?
    Q 2_2_4?
    please reply

  • Physics -

    Q2_2_5 is incorrect

  • Physics -

    Q 2_2_1
    q_0*x^3/(6*L)

    Q 2_2_3
    q_0*x^3/(6*L)/(23/2*R_0^4*E_0*pi)

    Q 2_2_4
    -5.82

  • Physics -

    2_2_1 & 2_2_3 are incorrect!

  • Physics -

    2_1_1,
    1_2,
    1_3,
    1_4
    please?

  • Physics -

    2_1_1 -3/4*t*L
    2_1_2 (t*L)/(pi*G*R^4)
    (t*(3*L-2*x))/(2*pi*G*R^4)
    3/4*L
    2_1_3 (3/2*t*L)/(pi*R^3)
    R
    3/2L

  • Physics -

    Q2_2_1 : 60.0 POINTS

    Obtain a symbolic expression for the internal bending moment resultant in terms of L, q0 (enter as q_0), and x:

    M(x)= ................

  • Physics -

    2_1_3 is wrong

  • Physics -

    Anyone have any idea for

    q2_2_1
    Q2_2_3
    Q2_2_5

    Appreciate your help. Thanks :)

  • Physics -

    M(x) = -q_0*x^3/(6*L)

  • Physics -

    thanks simon76 :)

  • Physics -

    Q2_2_3

    1/rho_x = -(q_0*x^3/(6*L))/(46/4*E_0*pi*R_0^4)

    because

    Q2_2_2

    EI_eff = (46/4*E_0*pi*R_0^4)

  • Physics -

    Q2_2_3

    Just try this for the slope:

    (q_0*(L^4-x^4)/(24*L))/(46/4*E_0*pi*R_0^4)

    but I'm not sure

  • Physics -

    Q2_2_3

    Just try this for the slope:

    (q_0*(L^4-x^4))/(24*L))/(46/4*E_0*pi*R_0^4)

    but I'm not sure

  • Physics -

    any one Q2_2_5

  • Physics -

    2_2_5

    50.9
    305.6

  • Physics -

    please any one
    2_1_1
    and
    2_2_3
    v(x)

    Thanks!!

  • Physics -

    2_2_1

    -q_0*x^3/(6*L)

    Q2_2_2

    23/2*R_0^4*E_0*pi

    Q2_2_3

    -(q_0*x^3/(6*L))/(46/4*E_0*pi*R_0^4)

    V(x)????

    Q2_2_4

    -5.82

    Q2_2_5

    50.9
    305.6

  • Physics -

    2_2_3

    v(x)= (q_0*(L^4-x^4)/(24*L))/(46/4*E_0*pi*R_0^4)

  • Physics -

    2_1_1,
    1_2,
    1_3,
    1_4
    please?

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