Analyse the beam, Mechanical Engineering

Analyse the beam:

Analyse the beam illustrated in Figure and draw the SFD, BND & thrust diagram. Situated the point of contraflexure, if any.

1146_Analyse the beam.png

Figure

Solution

Vertical component of 4 kN at C, = 4 × cos 60o = 2 kN ( ↓ )

Horizontal component of 4 kN at C, = 4 × sin 60o = 3.464 kN ( ← )

Vertical component of 2 kN at D, = 2 × cos 30o = 1.732 kN ( ↓ )

Horizontal component of 2 kN at D, = 2 × sin 30o = 1 kN ( → )

Taking moment around A,

R B   × 8 - (3 × 10) - 2 × 4 × (4 + (4/2)) - (1.732 × 3) - (2 × 1) = 0

RB  = 10.6495 kN

RA  = 2 + 1.732 + (2 × 4) + 3 - RB  = 14.732 - 10.6495 = 4.0825 kN

Shear Force (beginning from the Left End A)

SF at A, FA  = + 4.0825 kN

SF just left of C, FC  = + 4.0825 kN

SF just right of C, FC  = + 4.0825 - 2 = + 2.0825 kN

SF just left of D, FD  = + 2.0825 kN

SF just right of D,  FD  = + 2.0825 - 1.732 = + 0.3505 kN

SF at E, FE  = + 0.3505 kN

SF just left of B, FB  = + 0.3505 - (2 × 4) = - 7.6495 kN

SF just right of B, FB  = - 7.6495 + 10.6495 = + 3 kN

SF just left of F, FF  = + 3 kN = load at the end F.

Bending Moment (beginning from the F)

BM at F,          MF   = 0

BM at B,  M B  = - (3 × 2) = - 6 kN-m

BM at E, M E  =+ (10.46 95 × 4) - (3 × 6) - ( 2 × 4 ×( 4/2))   =+ 8.599 kN-m

BM at D, BM at C,

M D  = + (4.0825 × 3) - (2 × 2) = + 8.2475 kN-m

M C  = + (4.0825 × 1) = + 4.0825 kN-m

 BM at A,        MA = 0

Maximum Bending Moment

Maximum bending moment shall occur at B and among B and E. Consider a section XX at a distance x from the end F.

Fx  = - 10.6495 + 3 + 2 ( x - 2)

For maximum bending moment, Fx must be equal to zero.

- 10.6495 + 3 + 2x - 4 = 0

x = 5.82475 m ≈ 5.825 m

BM at section XX,

∴          M x = + 10.6495 ( x - 2) - 3x - 2 ( x - 2) × (( x - 2)/2)

                   = 10.6495 ( x - 2) - 3x - ( x - 2)2

M max  = 10.6495 (5.825 - 2) - 3 (5.825) - (5.825 - 2)2

=+ 8.629 kN-m

Maximum positive bending moment = + 8.629 kN-m

Maximum negative bending moment = - 6 kN-m.

Point of Contraflexure

Equating the BM at section XX, to zero.

10.6495 ( x - 2) - 3x - ( x - 2)2  = 0

or         10.6495 x - 21.299 - 3x - x2  + 4 x - 4 = 0

or         x2  + 11.6495x - 25.299 = 0

or         x2  - 11.6495x + 25.299 = 0

Solving out by trial and error, we obtain x = 2.9 m.

Point of contraflexure is at a distance of 2.9 m from the end F.

Thrust Diagram

Horizontal reaction at A,

+ H A  + 3.464 - 1 = 0

+ H A  + 2.464 = 0

∴ H A  =- 2.464 kN

 ('-' denote that the reaction is towards right)

The portion AC is subjected to a compressive force of 2.464 kN. The part CD is subjected to a tensile force of 1 kN (that means3.464 - 2.464 = 1).

Posted Date: 1/22/2013 1:16:31 AM | Location : United States







Related Discussions:- Analyse the beam, Assignment Help, Ask Question on Analyse the beam, Get Answer, Expert's Help, Analyse the beam Discussions

Write discussion on Analyse the beam
Your posts are moderated
Related Questions
Define term transfer of stress to footing. Transfer of Stress to Footing:  The column transfers the load to the top of the footing by bearing. The magnitude of the pressure

Copper Alloys Some alloys of copper are employed in industry for varying causes. Copper forms alloys along with zinc or the brasses, tin or the bronzes, along with tin and pho

Engine Oil Replacement and Top-up :   The engine oil has to be changed at a periodic interval because after some point of time it loses its viscosity and cooling, anti rust, and se

Phase 1 Initially ALL Valves A, B, C, D, E and F are closed.  ALL Tanks A, B, C, D, E are separated and each sealed from the atmosphere. Tank E initially has 2' of air @

Q.  A supported rectangular beam with the symmetrical section 200mm in depth is having moment of inertia of 2.26 x 10 -5 m 4 about  its neutral axis. Find out longest span over w

A shaft is hinghed by two bearings placed 1.0 m apart. A 600mm diameter pulley is mounted at a distance of 300 mm to the right of left hand bearing and this operates a pulley direc

Describe carburetion. What are the basic different air-fuel mixture on which an engine can be operated ? Write a short note on sterling cycle. In an engine working on inlet pres

Find speed for two hours with HSS tools Find speed for two hours tool life for dry machining of free cutting mild steel with HSS tool. Solution From Table 3, a value o

write the conservation of mass for steady flow throught a streamtube with asingal one dimensional inlet 1and exit 2

hi how much torque required to move 100kg in a skate board with a wheel diameter of 1.8 inch