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
Aggregate Production Planning: This unit provides the definition and physical significance of aggregate production planning. Further, this is illustrated that how the internal

Compare otto cycle with Diesel cycle: Sol.: These two cycles can be compared on the basis of either the same compression ratio or the same maximum pressure and temperature.

The processing of payroll for the 10,000 workers in a large rm can either be done using 1 hour of computer time (signed by K) and no clerks or with 10 hours of clerical time (sign

Rockwel l Hardness Test: The specimen is subjected to a major load for about 15 seconds after the initial load. ASTM says 13 scales for testing of wide range of materials. Th

The extent of a hazardous area depends on the rate of release, ventilation conditions, and fluid properties and is defined by the relevant regional or country standards. The pot

A jet of water moving at 8 m/sec. impinges on a concave-shaped vane to deflect the jet through 120 o when stationary. If the vane is moving at 5 m/sec., calculate the angle of jet

Resistance welding electrodes and holders Requisites For Electrodes : The resistance welding electrodes are meant for the following functions: Conducting electricity

SERVICE INDUSTRY GROWTH: The service industry is growing very fast in today's world market scenario. In Indian context, we can see the impact of service sector growth upon (GDP) g

Process Selection and Sequencing In this, some factors, which have an influence in all processes, are discussed. The factors include size, shape complexity, tolerances and produ

Evaluation Phase of Radial drilling machine Steps: 1. To judge the ideas generated in the creation phase for ability to meet the required criteria. 2. To refine, develop