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Deflection : Spring Rates -1

: Tension, Compression, and Torsion-2

: Round bar subjected to a twisting moment T


: Deflection Due to Bending-3

,

,

Ď is the radius of curvature

:Beam Deflections by Superposition -4 : Translation due to compression of spring Kt

-1

: Rotation of the spring Kr

-2

[(Elastic deformation [from table A-9 (cantilever – end load :

-3


: Total beam deflection by superposition

: Beam Deflections by Singularity Functions

-5


:Strain energy – 6


-7

,

.The transverse shear

strain energy

generally considered negligible for l/d > 10

torsion

: Deflection of Curved Members -8


, R/ H <10

, For thick curved members where

, (a

. U1 : due to the bending moment M

. U2 : axial component due to normal force Fϴ

: U3 : moment component due to normal force Fϴ

:

U4 :

transverse shear energy due to Fr

Where C is the correction factor


: Total strain energy

: Total defflection

:

R/ H >10

For thin curved members where

: Buckling of Columns -9

(a


. C is end-condition constant

K=radius of gyration

: Euler equation

(a

: parabolic or Johnsonâ&#x20AC;&#x2122;s formula

(b

Pcr = critical force

:Columns with Eccentric Loading *

Deflection at any x


Deflection at x=L/2

Compressive stress . where I = AK² ;

p Mc σ c= + A A K2

(Compressive stress at midspan (Mmax

:Struts or Short Compression Members

For differentiating between a “secant column” and a strut, : or short compression member



Deflecton note book