SUPPORT REACTIONS

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SUPPORT REACTIONS

• BY
• GP CAPT NC CHATTOPADHYAY

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NEED FOR SUPPORT

• THE LOAD CARRYING STRUCTURES NEED SUPPORTS TO
  AVOID
• -DEFORMATION
• -BENDING
• -INSTABILITY

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Types of loads

• Several types of loads can act on beams, such as
  concentrated loads, distributed loads, varying
  loads and couples.
• Concentrated loads are idealized from loads
  applied on a very small area.
• Magnitudes are known .
• Distributed loads are spread along the axes of
  beams. For example, the weight of the beam can be
  assumed as a distributed force.
• Distributed loads are converted into equivalent
  forces to make the solution process easier. For
  vertical loads, the equivalent force is through
  the centroid of the distributed load. Thus, if
  the distributed load is a basic shape, the
  centroid is easy to determine without
  integration.
•   
•  Couples are moments applied on the beam. Do not
  contribute to force .
•   
• Uniform varying Load    
• In this case the load varies uniformly along the
  length (gradual increase, gradual decrease)

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POINT LOAD
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UDL
Length l
Length L
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UNIFORMLY VARYING LOAD
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COMBINED UDL AND UVL
W 1500N/m

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TYPES OF SUPPORT

• 2 (USUALLY ONE) HINGED SUPPORTS
• SUPPORTS TAKE VERTICAL AND HORILOAD
• USUALLY DESIGNED WITH A ROLLER SUPPORT FOR
  FREE EXPANSION OF ONE END
• VERTICAL AND HORI LOADS DETERMINE REACTION
  AND LINE OF ACTION

• 2 OR MORE VERTICAL SUPPORTS
• JUST PIVOTS
• TAKES ONLY VERTICAL LOADS

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SIMPLE SUPPORT
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ROLLER SUPPORT
LOCATION OF ROLLER BEARING TO SUPPORT JET ENGINE
ROTOR
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HINGED SUPPORT
KNEE HINGE
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COMBINED SUPPORT
DISTRITIBUTED LOAD w
HINGED SUPPORT
ROLLER SUPPORT
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I THINK. I CAN THINK.
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Calculate the support reactions

•    Solution First change UDL in to point
  load.Resolved all the forces in horizontal and
  vertical direction. Since roller at B (only one
  vertical reaction) and hinged at point B (one
  vertical and one horizontal reaction).Let
  reaction at hinged i.e., point B is RBH and RBV,
  and reaction at roller support i.e. point D is
  RDV Let SH SV is the sum of horizontal and
  vertical component of the forces ,The supported
  beam is in equilibrium, hence     SH SV
  0    RH RBH 0    RBH 0                    
                     ...(i)    SV RBV 50 5
  RDV 0 RBV RDV 55                        
           ...(ii)Taking moment about point B50
  0.5 RBV 0 RDV 5 5 7 0RDV 12
  KN                               
  .......ANSPutting the value of RBV in equation
  (ii)RBV 43KN                                
  .......ANSHence RBH 0, RDV 12KN, RBV 43KN

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NUMERICAL

• A 9m long beam ABCD is supported on a hinge at
  A and a roller support at an angle of 45o at
  D. The beam has a clockwise moment of 9 kNm at
  B and a point load of 6 kN at C. If the
  points are equidistant, find the support
  reactions.