Types Of Support Calculation And
Reaction
Kush Bhatt 130460119010Kush Bhatt 130460119010
Siddhant Bhavsar 130460119011 Siddhant Bhavsar 130460119011
Jayesh Bhojwani 130460119012Jayesh Bhojwani 130460119012
UNIVERSAL COLLEGE OF UNIVERSAL COLLEGE OF ENGINEERING AND ENGINEERING AND
THECHNOLOGY THECHNOLOGY
NEED FOR SUPPORT
THE LOAD CARRYING STRUCTURES NEED SUPPORTS TO AVOID
-DEFORMATION
-BENDING-INSTABILITY
POINT LOAD
UDL
Length = lLength = L
UNIFORMLY VARYING LOAD
COMBINED UDL AND UVL
=
W= 1500N/m
TYPES OF SUPPORT
SUPPORTS
SIMPLE ROLLER HINGED
• 2 (USUALLY ONE) ROLLER SUPPORTS
• SUPPORTS ALLOW FREE EXPANSION
•TAKES VERTICAL LOADS NORMAL TO ROLLER PLANE
• 2 OR MORE VERTICAL SUPPORTS
• JUST PIVOTS
•TAKES ONLY VERTICAL LOADS
•2 (USUALLY ONE) HINGED SUPPORTS
• SUPPORTS TAKE VERTICAL AND HORI…LOAD
• USUALLY DESIGNED WITH A ROLLER SUPPORT FOR FREE EXPANSION OF ONE END
• VERTICAL AND HORI… LOADS DETERMINE REACTION AND LINE OF ACTION
Types of SupportTypes of Support
In order for loaded parts to remain in In order for loaded parts to remain in equilibrium, the balancing forces are equilibrium, the balancing forces are the reaction forces at the supportsthe reaction forces at the supports
Most real life products have support Most real life products have support geometries which differ from the geometries which differ from the idealized caseidealized case
Designer must select the Designer must select the conservative caseconservative case
Types of SupportTypes of Support
Guided is support at the end of the beams Guided is support at the end of the beams that prevent rotation, but permits that prevent rotation, but permits longitudinal and transverse displacementlongitudinal and transverse displacement
Free or unsupported is when the beam is Free or unsupported is when the beam is totally free to rotate in any directiontotally free to rotate in any direction
Held is support at the end of the beam Held is support at the end of the beam that prevents longitudinal and transverse that prevents longitudinal and transverse displacement but permits rotationdisplacement but permits rotation
Types of SupportTypes of Support
Simply Supported is support at the Simply Supported is support at the end of the beam that prevents end of the beam that prevents transverse displacement, but permits transverse displacement, but permits rotation and longitudinal displacementrotation and longitudinal displacement
Fixed is support at the ends of the Fixed is support at the ends of the beam that prevents rotation and beam that prevents rotation and transverse displacement, but permits transverse displacement, but permits longitudinal displacementlongitudinal displacement
Idealized SupportsIdealized Supports
Idealized SupportsIdealized Supports
SIMPLE SUPPORT
ROLLER SUPPORT
LOCATION OF ROLLER BEARING TO SUPPORT JET ENGINE ROTOR
HINGED SUPPORT
KNEE HINGE
COMBINED SUPPORT
HINGED SUPPORT
ROLLER SUPPORT
DISTRITIBUTED LOAD = w
Concentrated and Distributed Concentrated and Distributed LoadsLoads
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 ΣH & ΣV is the sum of horizontal and vertical component of the forces ,The supported beam is in equilibrium, hence
ΣH = ΣV = 0 RH = RBH = 0 RBH = 0 ...(i) ΣV = RBV –50 –5 – RDV = 0 RBV + RDV = 55 ...(ii)
Taking moment about point B
50 × 0.5 – RBV × 0 – RDV × 5 + 5 × 7 = 0RDV =12 KN .......ANS
Putting the value of RBV in equation (ii)
RBV = 43KN .......ANS
Hence RBH = 0, RDV = 12KN, RBV = 43KN
Types of loadsTypes of loads
• Concentrated loadsConcentrated loads (eg. P (eg. P11, P, P22, P, P33, P, P44 ) )
• When a load is spread along the axis When a load is spread along the axis of a beam is a of a beam is a distributed loaddistributed load. . Distributed loads are measured by Distributed loads are measured by their their intensity q (force per unit intensity q (force per unit distance)distance)
• Uniformly distributed load Uniformly distributed load hashas constant intensity q (fig 4-2a)constant intensity q (fig 4-2a)
• A varying load has an intensity q A varying load has an intensity q that changes with distance along the that changes with distance along the axis. axis. Linearly varying load from qLinearly varying load from q11 - - qq22 (fig 4-2b) (fig 4-2b)
• Another kind of load is a Another kind of load is a couple of couple of moment moment MM11 acting on the acting on the overhanging beam (fig 4-2c)overhanging beam (fig 4-2c)
FIG. 4-2FIG. 4-2Types of beams:Types of beams:(a) simple beam,(a) simple beam,
(b) cantilever (b) cantilever beam,beam,
and (c) beam with and (c) beam with an overhangan overhang
Distributed LoadDistributed Load
2222
For calculation purposes, distributed load can be represented as a single load acting on the center point of the distributed area.
Total force = area of distributed load (W : height and L: length)Point of action: center point of the area
ExampleExample
2323
ExampleExample
2424
Deflection CalculationDeflection Calculation
0.15” at base with 1draft angle for ribs
0.5”
4.0”
0.125”
Force=100lbs distributed
inchesy
ininlb
ininlb
y
IE
Lwy
inL
inlbsw
inI
psiEpe
0174.0
0192.0*000,250*384
)4(*25*5
**384
**5
4
4/100
0192.0
000,250
max
42
4
max
4
max
4
Type of BeamsType of BeamsStatically Determinate Statically Determinate
2626
Simply Supported Beam
Overhanging Beam
Cantilever Beam
Type of BeamsType of BeamsStatically Indeterminate Statically Indeterminate
2727
Continuous Beam
Propped Cantilever Beam
Fixed Beam
2828
Example 1Example 1
Equilibrium equation for 0 x 3m:
A B
* internal V and M should be assumed +ve
kNV
VF
Fy
9
0
0
)(9
0
0
kNmxM
MVx
M
M
VF
x
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