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 â€“ end load :

-3

: Total beam deflection by superposition

: Beam Deflections by Singularity Functions

-5

:Strain energy â€“ 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€™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