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
Calculation for Stress-strain carves:   After reaching point D, if bar is strained further, a local reduction in cross section occurs in gauge length (that is, formati

V iolatio n of K-P Statement: A HE produce work 'W' by exchanging the heat with one reservoir at temp. T 1 only. The K-P statement is violated.   H.P. is extract

work done by an impulse turbine

Industrial applications of ultrasonics-cleaning, welding, soldering, drilling


Drill Bit: This is a drilling tool used in drilling machines. The application of this tool is to make holes. Figure shows drill bit. Figure: Drill Bit

A semi circular frame of flexural rigidity EI is built at A and caries a vertical load W at B. calculate the magnitude of the vertical and horizontal deflection at B and hence the

Deflection at the centre - maximum deflection: A simply supported beam of span 6 m is subjected to Udl of 24 kN/m for a length of 2 m from left support. Discover the deflectio


Types of Registration Provisional Registration Certificate ( PRC ) This is given for the pre-operative period and enables the units to obtain the term loans and worki