Draw shear force diagrams for the overhanging beam, Mechanical Engineering

Draw shear force diagrams for the overhanging beam:

Draw shear force & bending moment diagrams for the overhanging beam illustrated in Figure

673_Draw shear force diagrams for the overhanging beam.png

Figure

 Solution

Taking moments around A & equating to zero,

 

RB   × 6 - (6 × 8) - 0.8 × 3 × ( 3 +(3/2))  - (5 × 2) = 0

RB = 11.47 kN and RA = 5 + (0.8 × 3) + 6 - 11.47 = 25 - 11.5 = 1.93 kN

Shear Force (beginning from the left end A)

SF at A, FA = + 1.93 kN

SF just left of D, FD = + 1.93 kN

SF just right of D, FD = + 1.93 - 5 = - 3.07 kN

SF at E, FE = - 3.07 kN

SF just left of B, FB = - 3.07 - (0.8 × 3) = - 5.47 kN

 SF just right of B, FB = - 5.47 + 11.47 = + 6 kN

SF just left of C, FC = + 6 kN = Load at E

Bending Moment

BM at C, MC  = 0

BM at B, MB = - 6 × 2 = - 12 kN m

 BM at E, M E =+ (11.46 × 3) - (6 × 5) -( 0.8 × 3 × (3/2) )=+ 0.81 kN m

BM at D, MD = + 1.93 × 2 = + 3.86 kN m

BM at A, MA = 0

Maximum Bending Moment

Maximum positive bending moment take place at D and maximum negative bending moment take place at B.

Mmax (positive) = + 3.86 kN m

Mmax (negative) = - 12 kN m

Point of Contraflexure

As the bending moment changes sign among E and B, let a section XX among E and B at a distance x from C.

BM at section XX,

Mx = - 6x + 11.47 (x - 2) - 0.8 (x - 2) ((x - 2)/2)

= - 6x + 11.47x - 22.94 - 0.4 (x - 2)2

= - 0.4x2 + 7.07x - 24.54

By equating this equation to zero, we achieved the point of contraflexure,

- 0.4x2 + 7.07x - 24.54 = 0

x2 - 17.67x + 61.35 = 0

Solving out by trial and error,

x = 4    Value of (x2 - 17.675x + 61.35) = 6.65

x = 4.9 Value of (x2 - 17.675x + 61.35) = - 1.2475

x = 4.8  Value of (x2 - 17.675x + 61.35) = - 0.45

x = 4.7 Value of (x2 - 17.675x + 61.35) = 0.3675

 x = 4.75 Value of (x2 - 17.675x + 61.35) = - 0.04375        

x = 4.745 Value of (x2 - 17.675x + 61.35) = - 0.00285

Point of contraflexure is at distance of 4.745 m from the end of C.

Posted Date: 1/22/2013 12:50:43 AM | Location : United States







Related Discussions:- Draw shear force diagrams for the overhanging beam, Assignment Help, Ask Question on Draw shear force diagrams for the overhanging beam, Get Answer, Expert's Help, Draw shear force diagrams for the overhanging beam Discussions

Write discussion on Draw shear force diagrams for the overhanging beam
Your posts are moderated
Related Questions
Calculate the feed in Drilling Operation Calculate the feed in m/min if a drill makes 200 revolutions per minute and penetrates to a distance of 3 mm per revolution. Solut

show that the avogadro constant is the number of atoms in 0.072kg of carbon-12

General Phase of Value Engineering: Steps- 1. Prepare a strong foundation for the value study. Extension of auger in screw conveyer in hydraulic paver machine is to be do

Evaluate the reactions at hinge and roller support: Q: A Force P = 5000N is applied at centre C of beam AB of length 5m as shown in figure given below. Find the reactio

Q. Requirements for vessels with thickness? The following additional requirements are applicable, as specified,  to Carbon Steel and Low Alloy steel pressure vessels with main

Diesel Cycle - Thermodynamics: Diesel cycle is also called as the constant pressure cycle as all addition of heat takes place at constant pressure. The cycle of operation is s

Venturi Tube: A venturi is basically an air passage that has a shape similar to that shown in Figure that is narrower at the middle known as venturi tube. As air travels thro

Find out the effort required to run this machine: The efficiency of a machine is 75% while an effort of 20 N is required to lift a load of 160 N. Compute the velocity ratio an

(a) Illustrate Fourier Series and calculate the constant coefficients. (b) A Harmonic motion is provided by x(t) = 10sin(30t -π/3) where t in seconds and phase angle in radians.