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
What are main important terms included in the footings? Term included in the footings: a. described different types of footings and the process of selecting each type, b.

A simple band brake performs on a drum of 600mm in diameter that is running at 200 r.p.m. The coefficient of friction is 0.25. The brake band has a contact at 270 o one end is fas

State the need for demand forecasting?

A paint manufacturing company has a manufacter function Q = K+ √L. For this manufacter function MPK = 1 and MPL = 1=(2√L). The rm faces a price of labor w that equivalent $1 per u

Find out the smallest force: A block weighing 800 N is raised up with the help of two 6o wedges B and C of negligible weights as illustrated in Figure. If the coefficient of s

Determine the distance of application of the load: A rigid bar of negligible weight transmits a load W to a combination of 3 springs as illustrated in Figure. The three spring

CLASSIFIC A TIO N: 1.     In accordance to number of strokes per cycle: (a) Two stroke          (b) Four stroke. 2.     In accordance to the fuel being used: (a)

Find out diameter of steel wire: Q: A load of 5 KN is to be raised with help of steel wire. Find out diameter of steel wire, if maximum stress does not to exceed 100 MNm 2

equivalent evaporation of boiler..?

What is couple