Calculate the magnitude of maximum bending moment, Mechanical Engineering

Calculate the magnitude of maximum bending moment:

The shear force diagram for the overhanging beam is illustrated in Figure. Draw the loading diagram & bending moment diagram. Determine the magnitude of maximum bending moment & situated the point of contraflexure.

2366_Calculate the magnitude of maximum bending moment.png

Solution

Let us analyse the shear force diagram specified in Figure .

At A

The shear force diagram suddenly reduces from 0 to - 400 N. It denotes that there is a downward point load of 400 N at point A.

Between A and B

The shear force diagram is an inclined straight line and reduces from - 400 N to - 560 N. It denote that there is a consistently distributed load of (560 - 400 = 160) ⇒ 160 × 1 = 160 kN/m among A and B.

At B

There is a sudden enhances from - 560 N to + 440 N at B. It denotes that there is a support reaction of 1000 N at B.

Between B and C

As the shear force diagram varies linearly from + 440 N to - 520 N among B & C. It denote that a u.d.l. of (440 + 520 = 960) 960 /6= 160 kN/m is acting between B and C.

At C

At C, the shear force diagram enhance suddenly from - 520 kN to 480 N. It denote that there is a support reaction of 1000 N (520 + 480) at C.

Between C and D

The shear force diagram is an inclined straight line which denote that there is a uniform ally distributed load of 480/3 = 160 kN/m from C to D.

Bending Moment

BM at A and D, MA = MD = 0.

 BM at B, M B =- (400 × 1) - (160 × 1 × (½) ) =- 480 N m

BM at C, M C = - (160 × 3 × (3/2)) =- 720 N m

Maximum Bending Moment

SF at any section XX among B and C,

Fx = +1000 - 400 - 160x

For maximum bending moment, Fx must be equal to zero.

600 - 160x = 0

∴          x = 3.75 m

∴ M max            = (1000 × 2.75) - (400 × 3.75) - (160 × 3.75 × (3.75/2)

                            = + 125 N m

Maximum positive bending moment take places at a distance of 3.75 m from the end A, where SF changes sign.

Maximum negative bending moment takes place at a support C where SF changes sign.

∴          Mmax (negative) = - 720 N m

Points of Contraflexure

Let M1 and M2 be the points of contraflexure, where BM is zero. However at any section XX among B and C at a distance x from the end A.

M x   = 1000 ( x - 1) - 400x - (160 × x × (x/2) )

or         1000x - 1000 - 400x - 80x2 = 0

80x2 - 600x + 1000 = 0

8x2 - 60x + 100 = 0

2x2 - 15x + 25 = 0

(2x - 5) (x - 5) = 0

Therefore,        x = 2.5 m  and   5 m.

Posted Date: 1/22/2013 1:05:53 AM | Location : United States







Related Discussions:- Calculate the magnitude of maximum bending moment, Assignment Help, Ask Question on Calculate the magnitude of maximum bending moment, Get Answer, Expert's Help, Calculate the magnitude of maximum bending moment Discussions

Write discussion on Calculate the magnitude of maximum bending moment
Your posts are moderated
Related Questions
A machine having a mass of 100 Kg and supported on springs of total stiffness 7.84 x 105 n/m has an unbalanced rotating element which results in a disturbing force of 400 N at a sp


Explain the Advantages of Automation 1. There is an increase in productivity. 2. The unit cost is reduced as larger number of components can be manufactured in shorter time

Motor shall operate successfully at rated load with a voltage variation of plus or minus ten percent and frequency variation of plus or minus five percent, or combined variation of

in the torsion equation the term j/r is called

A three phase squirrel cage induction motor has the nameplate data shown in Table I below  Table I : Induction Motor Nameplate Data. a)  Calculate the induction motor ef

The purpose of this section of your assignment is to familiarise yourself with the basic FE theory and relate it to the fundamental concepts of stress and strain calculations in en

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

Fuel Feed System: Fuel feed system is provided to serve the air fuel mixture to the engine in an appropriate ratio so that it can burn efficiently and transmit power to crank shaf