Evaluate the point of contraflexure, Mechanical Engineering

Evaluate the point of contraflexure:

An overhanging beam of 15 m span is carrying a consistently distributed load of 1 kN/m over the length of 10 m at a distance 5 m from the left free end and point loads 7 kN and 4 kN, at free end and at a distance 2 m from the free end, respectively. Sketch the BMD and SFD for the beam. Situate the point of contraflexure.

Solution

Taking moments around B and equating to zero,

R A   × 10 - (7 × 15) - (4 × 13) - (1 × 10 × (10/2) ) = 0

RA = 20.7 kN

and      RB = 7 + 4 + (1 × 10) - 20.7 = 0.3 kN

Shear Force (beginning from the left end C)

SF just right of C, FC = - 7 kN

SF just left of D, FD = - 7 kN

SF just right of D, FD = - 7 - 4 = - 11 kN

SF just left of A, FA = - 11 kN

SF just right of A, FA = - 11 + 20.7 = 9.7 kN

SF just left of B, FB = + 9.7 - (1 ×10) = - 0.3 kN = Reaction at the support B.

Bending Moment      

BM at B, MB = 0

 BM at A, MA

= (0.3 × 10) - (1 × 10 × (10/2))  = - 47 kN m

BM at D, MD = - (7 × 2) = - 14 kN m

BM at C, MC  = 0

let a section XX at a distance x from the end B as illustrated in Figure.

Shear force at section XX,

Fx = - 0.3 + 1(x)

For maximum bending moment, shear force will be zero.

- 0.3 + x = 0

x = 0.3 m

We have,

Mx = + 0.3(x) - 1 × (x) ×(x/2) = 0.3x - x 2 /2

Mmax = 0.3 × (0.3) - ((0.3)2 /2) = + 0.045 kN m

1024_Evaluate the point of contraflexure.png

Figure

This is seen that the maximum negative bending moment take place at A and maximum positive bending moment take place at a distance 0.3 m from the right end B.

Mmax (positive) = + 0.045 kN m

Mmax (negative) = - 47 kN m

Point of Contraflexure

This is observed that the BM changes sign among A and B,

BM at any section XX,

Mx = 0.3 x - x 2 / 2

Equating this to zero,

0.3 x - x2/2      = 0

0.6 x - x2    = 0

∴          x = 0.6 m

Thus, the point of contraflexure is at a distance of 0.6 m from the right end B.

Posted Date: 1/22/2013 12:54:59 AM | Location : United States







Related Discussions:- Evaluate the point of contraflexure, Assignment Help, Ask Question on Evaluate the point of contraflexure, Get Answer, Expert's Help, Evaluate the point of contraflexure Discussions

Write discussion on Evaluate the point of contraflexure
Your posts are moderated
Related Questions
Draw the P-h and T-S diagram for the vapour compression cycle when the vapour after compression is : (i) wet region (ii) dry saturated

Incompletely Constrained Motion: While a connection among the elements, building a pair is such that the constrained motion is not done by itself, but by some other means. Such a

Q. CSCC in Gas Streams? Due to process upset of FWKO or Treater, there may be chance of chloride carry over into the gas lines. Depending on the chloride contents of formation

Creating 3-d solid models Two basic approaches to create solid models are :    (i)  Constructive solid geometry (CSG or c-rep), and (ii)  Boundary representation (b-rep).

a) Illustrate with neat and clean diagram the measurement of brake power by prony brake Dynamiter OR Belt transmission type Dynamiter. b) A torsion dynamometer is fixed to a pro

Calculate the vertical deflection: Calculate the vertical deflection at the tip of the cantilever shown in Figure Figure Solution Measuring the distance x f



Find out ratio of strain-energy: A circular rod of diameter d and length l is fixed at one end and a torque T applied at the other. Now, if any close coiled helical spring is

procedure for measuring area of square by planimeter