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
Wet saturated steam -  thermodynamics: we t saturated steam Wet steam is a 2-phase mixture comprising of boiling water particles and dry steam in equilibrium state. Its for

Illustrate the Centrifugal Clutch in Detail with neat sketch ? Illustrate the Electromagnetic Clutch in Detail with neat sketch ? Illustrate the Diaphragm spring Clutch in

draw the projection of hexagonal prism of base side 20mm & axis length 50mm. when it is lying on the ground on one of its rectangular phase and axis is inclained 35 degree to vp. s

Define the following : (a) Boot Strap Air Evaporative System (b) Simple VCR System (c) Advantage and disadvantage of VCR system over Air Refrigeration System (d) Reduce

Working of a Four-stroke Engine: To understand the working of a four-stroke motorcycle engine, the whole operation can be divided into four parts, known as strokes. The strokes ar

a) state Newton's Law of Viscosity and also define the various unit of Viscosity. Also describe how viscosity changes with temperature. b) a uniform body of size 3m long x 3m wi

What do you mean by thermodynamic equilibrium? Compare irreversible process with reversible process. Give some examples of irreversible process.

Q. Corrosive properties of caustic? Sodium hydroxide, more commonly known as Caustic Soda or simply ‘Caustic', is widely used in the petrochemical industry to neutralize acidic

Q. Define Zirconium and its alloys? Zirconium and its alloys were developed primarily for the nuclear industry, but have found many industrial corrosion-resistant applications

Currency Bull Spread and Bear Spread: A currency bull spread is constructed by buying a call option for a particular underlying currency and simultaneously writing a call opti