Determine reactions at supports, Mechanical Engineering

Determine reactions at supports:

Determine reactions at supports of supported beam of 6m span carrying increasing load of 1500N/m to 4500N/m from one end to another end. 

1592_Determine reactions at supports.png

Sol.: As Beam is simply supported that is, at point A and point B only point load is acting. At first change UDL and UVL in point load. As shown in the given figure. Let ∑H & ∑V is the sum of horizontal and vertical component of Resultant forces, the supported beam is in equilibrium, therefore resultant force is zero.

Draw the free body diagram of the beam as shown in the given figure

Divided the diagram ACBE in to two parts A triangle CDE and a rectangle ABCE. Point load of Triangle CDE =1/2 × CD × DE = 1/2 × 6 × (4.5 -1.5)= 9KN

act at a distance 1/3 of CD (i.e., 2.0m )from point D

Point load of Rectangle ABCD = AB × AC = 6 × 1.5 = 9KN

act at a distance 1/2 of AB (i.e., 3m )from point B

Now apply condition of equilibrium:

∑H = 0;

RAH = 0                                         .......ANS

∑V = 0;

RA  -1500 × 6 - 3000 × 3 + RB = 0

RA  + RB = 18000 N                                                                                   ...(i)

Now taking moment about 'A'

- RB  × 6 + 9000 × 3 9000 × 4 = 0

RB = 10500 Nm                       .......ANS

Putting the value of RB  in the equation (i)

RA = 7500 Nm                         .......ANS

Posted Date: 10/17/2012 5:37:32 AM | Location : United States







Related Discussions:- Determine reactions at supports, Assignment Help, Ask Question on Determine reactions at supports, Get Answer, Expert's Help, Determine reactions at supports Discussions

Write discussion on Determine reactions at supports
Your posts are moderated
Related Questions
What are the Constructional Aspects of Well Foundations  There are several aspects which require careful consideration during sinking of well foundations. They are i)  Prepa

Derive the shape functions N1...N10 for a 10 node triangular element in terms of area coordinates L 1 , L 2 , L 3 .  Nodes are equally spaced on the edges and node 10 is at the cen

(a) Illustrate all the laws of mechanics? (b) What ate the two limits of limitation on Newtonian mechanic?

(a) What is the importance of safety at workshop? (b) What problems may arise, if we do not take safety precautions in the workshop?

Calculate the magnitude of maximum bending moment: The shear force diagram for the overhanging beam is illustrated in Figure. Draw the loading diagram & bending moment diagram

Find modulus of elasticity of the composite under isostrain: A composite is made of alternate layers of 60% E-glass and 40% epoxy resin. If modulii of elasticity of E-glass an

‘coefficient of insensitiveness’ of governors

Environments can cause deterioration of foundation. Can you explain this in the following cases? a) A column footing which was stable for a number of years suddenly gave way. T

Design Problem:  Design a pipeline and pump station to pump 100 MGD of water to the Mississippi river.  To reduce the required horsepower of the pumps, the flow will be pressurized

(a) Show following complex numbers in Rectangular forms : (i) 5e 0.927j (ii) 10e 4.068j (b) Show the periodic functions by Fourier series (Harmonic series).