Sunday

September 25, 2016
Posted by **Harm** on Saturday, July 27, 2013 at 11:26am.

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)= ........

ϑ(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 -
**ElementarySchoolStudent**, Saturday, July 27, 2013 at 2:16pmIs it correct ?

Q2_2_4

vA=-5.82 cm ?? - Physics -
**Montenegro**, Saturday, July 27, 2013 at 4:46pmQ2_2_2

23/2*R_0^4*E_0*pi

Q_2_2$

-5,82 cm - Physics -
**11YearsOldMITStudent**, Saturday, July 27, 2013 at 9:11pmQ2_2_5

STRESS CORE=9 MPa

stress sleve= 73 MPa

Is it correct ? - Physics -
**anonymous**, Sunday, July 28, 2013 at 1:20amQ 2_2_1?

Q 2_2_3?

Q 2_2_4?

please reply - Physics -
**jason**, Sunday, July 28, 2013 at 2:01amQ2_2_5 is incorrect

- Physics -
**Anonymous**, Sunday, July 28, 2013 at 3:51amQ 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 -
**anonymous**, Sunday, July 28, 2013 at 5:15am2_2_1 & 2_2_3 are incorrect!

- Physics -
**Ash**, Sunday, July 28, 2013 at 5:19am2_1_1,

1_2,

1_3,

1_4

please? - Physics -
**SimonaSay**, Sunday, July 28, 2013 at 5:50am2_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 -
**Peter**, Sunday, July 28, 2013 at 10:40amQ2_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 -
**jason**, Sunday, July 28, 2013 at 12:38pm2_1_3 is wrong

- Physics -
**jason**, Sunday, July 28, 2013 at 12:40pmAnyone have any idea for

q2_2_1

Q2_2_3

Q2_2_5

Appreciate your help. Thanks :) - Physics -
**Simon76**, Sunday, July 28, 2013 at 1:02pmM(x) = -q_0*x^3/(6*L)

- Physics -
**jason**, Sunday, July 28, 2013 at 1:10pmthanks simon76 :)

- Physics -
**Simon76**, Sunday, July 28, 2013 at 1:23pmQ2_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 -
**Simon76**, Sunday, July 28, 2013 at 1:28pmQ2_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 -
**Simon76**, Sunday, July 28, 2013 at 1:28pmQ2_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 -
**abcd**, Sunday, July 28, 2013 at 1:50pmany one Q2_2_5

- Physics -
**Unknonsense**, Sunday, July 28, 2013 at 2:20pm2_2_5

50.9

305.6 - Physics -
**Jon**, Sunday, July 28, 2013 at 2:56pmplease any one

2_1_1

and

2_2_3

v(x)

Thanks!! - Physics -
**Jon**, Sunday, July 28, 2013 at 3:07pm2_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 -
**Jon**, Sunday, July 28, 2013 at 3:12pm2_2_3

v(x)= (q_0*(L^4-x^4)/(24*L))/(46/4*E_0*pi*R_0^4) - Physics -
**Ash**, Monday, July 29, 2013 at 1:13am2_1_1,

1_2,

1_3,

1_4

please?