Determine the loading on the beam:

Shear force diagram for a loaded beam is illustrated in Figure. Determine the loading on the beam & therefore, draw the bending moment diagram. Situate the point of contraflexure, if any.

Solution

Let us analyse the shear force diagram specified in given Figure .

At A

The shear force diagram enhance suddenly from 0 to 6.875 kN in upward direction, at A. This denote that there is support at A, along magnitude of reaction 6.875 kN.

Between A and C

The SF diagram is an inclined straight line among A and C. It denotes that there is a uniformly distributed load among A and C. The load enhance from 6.875 kN to 3.875 kN (6.875 kN - 3.875 kN = 3 kN). Therefore, the beam carries a uniformly distributed load of   3/1.5= 2 kN/m among A and C.

At C

The shear force diagram suddenly reduces from 3.875 kN to 1.875 kN. It denote that there is a point load of 2 kN (3.875 kN - 1.875 kN) working in downward direction at C.

Figure

Between C and D

As the shear force diagram is horizontal among C and D, there is no load among C and D.

Between D and E

The SF diagram is an inclined straight line among D and E. It denotes that there is a uniformly distributed load. Load reduction from + 1.875 kN to - 1.125 kN. Thus, the beam carries a uniformly distributed load of (+1.875 + 1.125 = 3 kN) ⇒ 3/1.5= 2 kN/m between D and E.

At E

 The shear force diagram has sudden reduce from - 1.125 kN to - 6.125 kN. It denotes that there is a point load of 5 kN (↓) at E.

Between E and B

The SFD reduce from - 6.125 kN to - 9.125 kN by an inclined straight line, that shows that the beam carries a u.d.l. of   3 /1.5 = 2 kN/m among E and B.

At B

As there is a sudden enhance from - 9.125 kN to 0 at B, there is a support at B of reaction 9.125 kN.

Bending Moment

BM at A,         M_A = 0

BM at C,           M _C    = (6.875 × 1.5) - (2 × 1.5 × (1.5/2) )  = 8.06 kN^-m

BM at D ,  M _D  = (6.875 × 3) - 2 × 1.5 × 2.25 = (- 2 × 1.5) = 10.875 kN-m

BM at E,  M _E  = (9.125 × 1.5) - ( 2 × 1.5 × (1.5/2)   = 11.44 kN-m

Maximum Bending Moment

Let a section XX among D and E at a distance x from the end B. SF at section XX,

F_x  =- 9.125 + 5 + 2 x - 4.125 + 2 x = 0

∴ x = 2.0625 m  (for maximum BM)

∴ M _max            = (9.125 × 2.0625) - 5 × (2.0625 - 1.5) - ( 2 × 2.0625 × (2.0625/2) )

= 11.75 kN-m

Posted Date: 1/22/2013 1:03:39 AM | Location : United States

Ask an Expert

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

Write discussion on Determine the loading on the beam
Your posts are moderated

Write your message here..

Related Questions

What is enthalpy, Enthalpy defines as heat content of a chemical system. Enthalpy defines as heat content of a chemical system.

Magnitude of the centripetal acceleration of the car, A car travels at a co... A car travels at a constant speed around a circular track whose radius is 2.2 km. The car goes once around the track in 400 s. What is the magnitude of the centripetal acceleration

Determine the maximum stress in the beam, For the beam shown below, we need... For the beam shown below, we need to determine: (i) The support reactions R L and R R                                                                            (ii) The s

Stepped pulley, Definition of stepped pulley Definition of stepped pulley

Determine the centroidal moment of inertia, Determine the centroidal moment... Determine the centroidal moment of inertia: Determine the centroidal moment of inertia of a thin flat disc shown in Figure which is having a mass m kg. By using the parallel a

Angle of repose, Angle of Repose(α): It is the maximum angle of inclin... Angle of Repose(α): It is the maximum angle of inclined plane on which body tends to move down the plane because of its own weight. Consider the equilibrium of body when body

SIMPLE VAPOUR COMPRESSION REFRIGERATION SYSTEM, p-h chart p-h chart

Quasistatic loading, • For the ASTM dogbone specimens, the ¾ inch hole spec... • For the ASTM dogbone specimens, the ¾ inch hole specimens, and the notched specimen tabulate the failure load, in pounds. • Show plots of stress and strain for all specimens w

Types of holons, Types of Holons The four major types of holons are: ... Types of Holons The four major types of holons are: Order holons Product holons Resource holons Staff holons Considering the cooperative aspect of the

Boiler efficiency, what is equivalent evaporation what is equivalent evaporation