Physics
posted by Harm .
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 Ï€ as pi):
(EI)eff= ...............
Q2_2_3 : 60.0 POINTS
Obtain symbolic expressions for the curvature at the neutral axis 1Ï(x) and the slope Ï‘(x) of the beam in terms of L, q0, R0, E0, and x (again, leave rationals as fractions and enter Ï€ as pi):
1Ï(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 (Ïƒmax,C) and in the sleeve (Ïƒmax,S):
Ïƒmax,C= MPa
Ïƒmax,S= MPa

Is it correct ?
Q2_2_4
vA=5.82 cm ?? 
Q2_2_2
23/2*R_0^4*E_0*pi
Q_2_2$
5,82 cm 
Q2_2_5
STRESS CORE=9 MPa
stress sleve= 73 MPa
Is it correct ? 
Q 2_2_1?
Q 2_2_3?
Q 2_2_4?
please reply 
Q2_2_5 is incorrect

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 
2_2_1 & 2_2_3 are incorrect!

2_1_1,
1_2,
1_3,
1_4
please? 
2_1_1 3/4*t*L
2_1_2 (t*L)/(pi*G*R^4)
(t*(3*L2*x))/(2*pi*G*R^4)
3/4*L
2_1_3 (3/2*t*L)/(pi*R^3)
R
3/2L 
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)= ................ 
2_1_3 is wrong

Anyone have any idea for
q2_2_1
Q2_2_3
Q2_2_5
Appreciate your help. Thanks :) 
M(x) = q_0*x^3/(6*L)

thanks simon76 :)

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) 
Q2_2_3
Just try this for the slope:
(q_0*(L^4x^4)/(24*L))/(46/4*E_0*pi*R_0^4)
but I'm not sure 
Q2_2_3
Just try this for the slope:
(q_0*(L^4x^4))/(24*L))/(46/4*E_0*pi*R_0^4)
but I'm not sure 
any one Q2_2_5

2_2_5
50.9
305.6 
please any one
2_1_1
and
2_2_3
v(x)
Thanks!! 
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 
2_2_3
v(x)= (q_0*(L^4x^4)/(24*L))/(46/4*E_0*pi*R_0^4) 
2_1_1,
1_2,
1_3,
1_4
please?