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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