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

Assignment Help:

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 ( ↓ )


Related Discussions:- Evaluate the deflection at the free end of the cantilever

Force on string - mechanics, Force on String: A string ABCD , attach...

Force on String: A string ABCD , attached to the two fixed points A and D has two weight of 1000N each attached to it at points B and C . The weights rest with portio

Strength of material, how will you apply principle of superposition in a st...

how will you apply principle of superposition in a stepped bar?

Two wheeler engines, Two Wheeler Engines: Engine is a unit of motorcycle t...

Two Wheeler Engines: Engine is a unit of motorcycle that runs the motorcycle by converting fuel energy to mechanical power. This power comes from the burning of fuel inside the cy

Blade tips with burrs, Industrial had been producing various types of medic...

Industrial had been producing various types of medical products. One of the manufacture lines is Blade Department. Recently we had received a complained from Headquarter regarding

Classification of internal combustion models of engine, CLASSIFIC A TIO ...

CLASSIFIC A TIO N: 1.     In accordance to number of strokes per cycle: (a) Two stroke          (b) Four stroke. 2.     In accordance to the fuel being used: (a)

Solid modeling and design, You are an engineer for WhyShopHere Toys. You ha...

You are an engineer for WhyShopHere Toys. You have been tasked with the following: Design a child's toy to provide food for fish in an aquarium. The toy should take the fo

Scope of materials for sulfuric acid service, Q. Scope of Materials for sul...

Q. Scope of Materials for sulfuric acid service? This Engineering Practice presents materials of construction commonly used in Sulfuric Acid service. The corrosiveness of sulfu

Insulation for personnel protection, Q. Insulation for personnel protection...

Q. Insulation for personnel protection? Insulation for personnel protection shall be provided as follows on all piping and equipment adjacent to work platforms or other operati

Economic order quantity, Economic Order Quantity: Assume an economic o...

Economic Order Quantity: Assume an economic order quantity case where annual demand D = 500 units, economic order quantity Q = 100 units, the wanted probability of not stockin

Complaints of engine starting by repairing of motorcycle , Complaints of En...

Complaints of Engine Starting: If there is a problem related to the starting of the bike, it can be due to mechanical as well as electrical reasons. The possible reasons could be

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd