Evaluate the deflection at the free end of the cantilever, Mechanical Engineering

Evaluate the deflection at the free end of the cantilever:

Discover the slope and deflection at the free end of the cantilever illustrated in Figure . Take EI = 200 × 106 N-m2.

Solution

Apply Udl in both the upward and downward directions in the portion CB.

1275_Evaluate the deflection at the free end of the cantilever.png

 Figure

477_Evaluate the deflection at the free end of the cantilever1.png

 Figure

M = - 24 x . (x/2) + 24 ( x - 1) (( x - 1)/2) - 30 [ x - 2]

= - 12 x2  + 12 [ x - 1]2  - 30 [ x - 2] --------- (1)

EI (d 2 y /dx2 )= M = - 12 x 2  + 12 [ x - 1]2 - 30 [ x - 2]        ----------- (2)

EI dy/ dx = - 4 x3 + 4 [ x - 1]3 - 15 [ x - 2] 2+ C1        --------- (3)

EIy =- x + [ x - 1] - 5 [ x - 2] + C1 x + C2            --------------- (4)

The boundary conditions are :

 At B, x = 4 m, dy/ dx  = 0         -------- (5)

At B, x = 4 m,  y = 0                       ----------- (6)

From Eqs. (3) and (5)

0 = - 4 × 4 3+ 4 (4 - 1) 3- 15 (4 - 2)3 + C1

∴          C1 = 208                   ----------- (7)

 From Eqs. (4), (6) and (7)

0 =- 4 4+ (4 - 1)4 - 5 (4 - 2) 3+ 208 × 4 + C2

∴          C2  = - 617                  --------- (8)

∴          EI (dy / dx )=- 4 x3  + 4 [ x - 1]3  - 15 [ x - 2]2  + 208         ---------- (9)

EIy =- x4  + [ x - 1]4  - 5 [ x - 2]3  + 208 x - 617-------- (10)

At free end A, x = 0, From Eq. (9)

 θ A = + 208 /EI = + 208 × 10/200 × 106 = + 1.04 × 10- 3  radians

From Eq. (10)

yA  =     617/EI = - 617 × 103 × 103 / 200 × 106 = - 3.085 mm ( ↓ )

Posted Date: 1/21/2013 5:55:56 AM | Location : United States







Related Discussions:- Evaluate the deflection at the free end of the cantilever, Assignment Help, Ask Question on Evaluate the deflection at the free end of the cantilever, Get Answer, Expert's Help, Evaluate the deflection at the free end of the cantilever Discussions

Write discussion on Evaluate the deflection at the free end of the cantilever
Your posts are moderated
Related Questions
The two-storey  frame shown in Figure Q4 is such  that  the self-mass may be considered to be located at the beam levels and the beams may be presumed to be rigid.  The self-mass (

what do you understand by dynamically equivalent mass system

Evaluate the chebyshev Spacing for a function y = 2 x 2 - x for the range 0 ≤ x ≤ 2 where four precision point are required. For these precision points, determine φ 2 , φ 3 , φ 4

Cylinder : As the name implies it is a cylindrical vessel or space in which the piston makes a reciprocating motion (forward and backward). The varying volume created in the cylin

Example: Order Quantity and Reorder Point: Daily demand for a particular product manufactured by ABC company is distributed normally with a mean of 30 and standard deviation o

The input-output curve of a 60 MW power station is provided by : I = 10 6 [8 + 8L + 0.4L 2 ] Kcl/hour where I is the input in the Kcal/hour and L is the load in MW. (a) Ev

Engine oil : Check engine oil level and viscosity.

Relation between stress and strain: The relation between stress and strain is generally shown by plotting a stress-strain (σ -e) diagram. Stress can be plotted on ordinate (ve

wire-frame entities-representing ellipse and parabolas

WHAT IS SPECIFIC HEAT