Force method - Compendium of solutions for beam displacements Load case ii displ. at midspan (f)

displ. at end (δ) ij

11 3

lEJ 2

16Mlf EJ 21 6

lEJ

21,0 16

FlEJ 3

48Flf EJ

31,0 24

p lEJ 45

384p lf EJ

1,0 24

M lEJ

11 2

lEJ 2

8Mlf EJ

1,0

l Th

2,0l Th

3

3FlEJ 2

2FlEJ

2

2M lEJ U M l

M EJ

4

8p lEJ

Ex: 1 11 1 12 2 10M M

F

p

p

Bolt connections Bolt geometry data (according to the standard UNI 4535-64)

Allowable stresses for the assessment of bolts:

Allowable stresses for the assessment of plates:

Shear joint assessment Bolt Shear (if only tangential stress) ∙

∙ If combined stress on bolt

2 2

, ,1

b adm b adm

Hole plastic deformation ∙

Tearing ∙

Friction joint assessment , f ∙ ∙ 0,8 ∙ , ∙

Beam profiles

Axis yy Axis xx Linear mass Profile identification

Axis-symmetric elastic problems (disks) General stress solution

Solid disk with external pressure pe

Hollow disk with external and internal pressure pe and pi

222

2222

22222

2222

22

1)(

1)(

rrrrrpp

rrrprp

rrrrrpp

rrrprp

ieeiie

ieeeii

ieeiie

ieeeiir

Rotating solid disk at constant speed = cost – No pressure

2222

222

831

83

)(83

rrrr

e

er

Rotating hollow disk at constant speed = cost – No pressure

)331(8

3)(8

3

22

22222

22

22222

rrrrrr

rrrrrrieei

ieeir

TBN The maximum value of is reached for

r F 'r C1 C2

r 2 38 2r 3

dF 'dr Frr C1 C2

r 2 1 38 2r 2

2

Stress solution for infinite plate with hole

Plate with hole subject to biaxial stresses

Plate with hole subject to internal pressure

Plate with hole subjected to uniaxial load

Theoretical solutions for Kt

Coefficients for fatigue assessment Solution for coefficient to calculate the Notch sensitivity index.

Dimensional coefficient md

Surface finish coefficient ms

Finite Elements