Determine the value of maximum bending moment, Mechanical Engineering

Determine the value of maximum bending moment:

Draw the shear force & bending moment diagrams for the beam overhanging on both of sides as illustrated in Figure. Determine the magnitude of maximum positive and maximum negative bending moment and also situate the point of contraflexure, if any exist.

Solution

Letting right side, take moments around A,

MA = RB × 12 - 2 × 12 × 10

MA = 12 RB - 240

Considering left side, take moments about A,

MA = - 6 × 4 = - 24 kN m

Equating these two values, we get the reaction at the support B,

12 RB - 240 = - 24

RB = 18 kN

RA = 6 + (2 × 12) - RB = 30 - 18 = 12 kN

Shear Force (Starting from the left end C)

SF at C, FC = - 6 kN

SF just left of A, FA = - 66 kN

SF just right of A, FA = - 6 + 12 = + 6 kN

SF at D, FD = + 6 kN

SF just left of B, FB = + 6 - (2 × 8) = - 10 kN

SF just right of B, FB = - 10 + 18 = + 8 kN

SF at E, FE = + 8 - (2 × 4) = 0.

1357_Determine the value of maximum bending moment.png

Figure

BM at C and E, MC  = ME = 0

BM at B, MB = - ( 2 × 4 × (4/2) )  = - 16 kN m

BM at D, MD =+ (18 × 8) - ( 2 × 12 × (12/2)  = 0

BM at A, MA = - (6 × 4)  = - 24 kN m

Maximum Bending Moment

Let a section XX at a distance 'x' from the end E. SF at section XX,

Fx = - 18 + 2x

For maximum bending moment, Fx must be zero.

- 18 + 2x = 0

∴          x = 9 m

BM at any section XX among D and B,

Mx = 18 (x - 4) - 2x ×(x/2)

= 18 (x - 4) - x2

Mmax = 18 (9 - 4) - 92  = 9 kN m

Maximum negative bending moment = -24 kN m

Maximum positive bending moment = + 9 kN m

 

Points of Contraflexure

Assume M and D is the points of contraflexure where the BM changes sign.

To determine the position of M, equate the moment equation among D and B to zero.      

                        18 (x - 4) - x2 = 0

                        - x2 + 18x - 72 = 0

or,                     x2 - 18x + 72 = 0

We obtain,       x = 6 m and x = 9 m.

There are two points of contraflexure, one of at a distance of 6 m & the other at a distance of 9 m from the end E.

Posted Date: 1/22/2013 1:02:26 AM | Location : United States







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

Write discussion on Determine the value of maximum bending moment
Your posts are moderated
Related Questions
Rubber Rubber is a plastic that is largely derived from natural sources and utilized in a modified form. For automobile tyres, Rubber is well identified as material. Rubber re

What are wall footings? Explain in short. Generally wall footings are required to support direct concentric loads. However, an exception is the wall footings for retaining wall

Plant level - Safety Organization This level works at plant level and would directly report to general manager safety. There must be four plant safety managers as recognized

(a) Illustrate why a rich mixture is required for the following (i) idling (ii) sudden acceleration (iii) Maximum power (b) A simple jet carburetor is required to supply 5Kg

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

Q. What is Tantalum? Tantalum is one of the most corrosion-resistant metals known. However, the high cost of tantalum has limited its commercial use as an all-purpose corrosio

Determine the magnitude and nature of the stresses: A thin spherical hollow steel shell of 400 mm diameter & 5 mm thickness is immersed into a liquid container pressurized to

determine the minimum no of teeth required on pinion in order to avoid interference which is to gear with 1 a wheel to give a gear ratio of 3 to 1 solution in detail

We shutdown our furnace and always encountered crack on our piping at the weld joints. I investigated that upon shutdown the furnace cracking, our maintenance immediately remove th

What is differential approach (differential formulation) in fluid mechanics? What are velocity and acceleration fields, give examples. Find, study and write down the differential f