Determine the point of contraflexure - overhanging beam, Mechanical Engineering

Assignment Help:

Determine the point of contraflexure:

Draw the shear force & bending moment diagram for 10 m span overhanging beam along overhanging part of 4 m subjected to a system of loads as illustrated in Figure . Determine the maximum bending moment and also situated the point of contraflexure.

Solution

Taking moments around A and equating it to zero,

R B   × 6 - (8 × 10) - 3 × 4 × ( 6 + (4/2)   - (20 × 4) - (10 × 2) = 0

RB = 46 kN

RA = 10 + 20 + (3 × 4) + 8 - RB = 50 - 46 = 4 kN

1211_Determine the point of contraflexure.png

Figure

Shear Force (beginning from the end A)

SF at A, FA = + 4 kN

SF just left of D, FD = + 4 kN

SF just right of D, FD = + 4 - 10 = - 6 kN

 SF just left of E, FE = - 6 kN

SF just right of E, FE = - 6 - 20 = - 26 kN

 SF just left of B, FB = - 26 kN

SF just right of B, FB = - 26 + 46 = + 20 kN

SF just left of C, FC = + 20 kN = Load at C

Bending Moment

BM at C, MC  = 0

BM at B, M A= (0.3 × 10) - (1 × 10 × (10/2) )  = - 47 kN m

BM at E, ME = + (4 × 4) - (10 × 2) = - 4 kN m

BM at D, MD = + (4 × 2) = + 8 kN m

Maximum Bending Moment

As SF changes sign at D & B, the maximum positive bending moment shall occur at D and maximum -ve bending moment shall take place at B.

Mmax (positive) = + 8 kN m

Mmax (negative) = - 56 kN m

Point of Contraflexure

BM changes sign among D & E. Thus, consider a section XX at distance x from the end A.

BM at section XX,

Mx = + 4 x - 10 (x - 2)

 Equating this to zero, we obtain

4 x - 10 (x - 2) = 0

4 x - 10x + 20 = 0

- 6x + 20 = 0

∴          x = 3.333 m

The point of contraflexure is at any distance of 3.333 m from the left end of A.


Related Discussions:- Determine the point of contraflexure - overhanging beam

Air standard cycles - thermodynamics, AIR STANDARD CYCLES - thermodynamics:...

AIR STANDARD CYCLES - thermodynamics: Most of the power plant operates in the thermodynamic cycle that is the working fluid undergoes a series of processes and returns to its

Ionization of inert gases, inert gas is ionizing in tig and mig,plasma arc ...

inert gas is ionizing in tig and mig,plasma arc welding processe.but it is impossible to react with inert gas

What are the principles of location of drilling jig, a) Define the degree o...

a) Define the degree of freedom of a work piece in space. What are the basic principles of location of drilling jig.

What is one way shear, What is one way shear? Explain with a suitable demon...

What is one way shear? Explain with a suitable demonstration. One Way Shear This worked out seen a similar case is the case of wall footings. For square footings also the cr

Arc welding power sources-arc characteristics, ARC CHARACTERISTICS In ...

ARC CHARACTERISTICS In order to understand the different output characteristics that are required by the welding power source it is necessary to understand the load which is f

Performance criterion of a steam power plant, Performance criterion of a st...

Performance criterion of a steam power plant: Sol. :   The design of power plant can be determined largely by the consideration of capital cost and operating cost; the forme

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