Overview • Stressing of welded joints: – Bending analysis of welds – Stress Concentration – Fati Fatigu guee of we weld lded ed joi joint ntss
Bending Analysis of Welds • Bending analysis of welded structures follows on closely from analysis of torsional loading: – rea!ing t"e a##lied loads down into direct $#rimary% loads $tension and&or s"ear loads% and $secondary% ending moment – analysing t"e #rimary stresses due to t"e direct loads as force&area – analysing t"e secondary stresses due to t"e ending moment' unit second moment of area ( u
Stressing of welds in comined ending&s"earing • For a cantilever wit" fillet welds along its to# and ottom faces: F
l
Stressing of welds in comined ending&s"earing • )e#lace a##lied load F wit" V and M :
V
M
Stressing of welds in comined ending&s"earing
'
τ =
V A
=
F A
A = 2 × 0.707 hl = 1.414hl
Stressing of welds in comined ending&s"earing • *"e moment + #roduces ending stresses σ in t"e welds • (t is usual to assume t"at t"is stress acts normal to t"e t"roat area • *rue de#t" of t"e weld is usually small com#ared to ot"er dimensions • By treating t"e welds as lines we can use t"e unit second moment of area for bending
Stressing of welds in comined ending&s"earing • (n t"is case: A = 1.414hb x
=
y
=
b
b
0.707h
d
2 d 2
2
I u
=
bd 2
Stressing of welds in comined ending&s"earing • ,nit -nd moment of area aout "ori.ontal a/is is: bd 2
I u
=
2
• Second moment of area is: I = 0.707hI u
• 0ormal stress $at a distance y from t"e neutral a/is% is: Ty σ =
I
Stressing of welds in comined ending&s"earing If there is no shear loading: • Assume t"at t"e ma/imum s"ear stress in t"e weld is e1ual to t"e nominal tensile $or com#ressive% stress we "ave calculated ased on t"e t"roat area • Assess t"e strengt" of t"e weld y com#aring t"is nominal s"ear stress wit" t"e allowale s"ear stress in t"e material2
Comining t"e s"ear and ending stresses • S"igley et al use vectorial comination of stresses • A etter a##roac" is to use +o"r3s circle $for or 4 dimensional stresses%
2θ
σ +τ
5/am#le • 5stimate t"e safety factor in t"e rac!et if t"e ma/imum allowale stress is 6-7 +8a 120
6
F = 7.5 kN
120
6
6 60
5/am#le • ,se t"e relations"i#s from row 9 of t"e tale in a##endi/ A A = 0.707h( b + 2d ) b x = 2
5/am#le: Secondary Stress • *"e vertical centroid distance is: y
d 2
=
b + 2d
=
0.12 2 0.06 + 2(0.12)
=
48 mm
• *"e unit second moment of area is: I u
=
=
=
2d 3 3
−
2d 2 y + ( b + 2d ) y 2
2(0.12) 3 3
−
2(0.12) 2 × 48 ×10
460.8 ×10 6 m 3 −
−3
+
(0.06 + 2(0.12))( 48 ×10
−3
)
2
5/am#le: Secondary Stress • *"e ma/imal secondary stress occurs furt"est from t"e neutral a/is $ma/imum y' A;A c < =- mm% I = 0.707hI u
=
= 1.954 × 10
σ =
=
My I XX
=
0.707 × 6 × 10
−6
7.5 × 10
m 3
× 460.8 × 10
−6
4
× 72 × 10
1.954 × 10
33.16 MPa
−3
−6
−3
120 72
5/am#le: total stress • Comine t"e #rimary and secondary stresses using +o"r3s circle: (0, 5.89)
2θ = 19.6°
34.175 MPa
σ
(33.16, 5.89) +τ
5/am#le: Secondary Stress • *"e ma/imal stress is 4>26=9 +8a' ?2@ off t"e "ori.ontal and acting on t"e toe of t"e vertical weld • *"is re#resents a safety factor $under static loading of a ductile material% of
n=
120 34.175
=
3.5
Stress Concentrations F
• For elastic materials nominal stress is σ nom =
F
t b
bt
• Saintenant3s 8rinci#le says t"is is so eyond a c"aracteristic lengt" $% from a stress raiser
F
Stress Concentrations • +a/imum stresses may e muc" larger t"an t"e nominal • Stress concentration factor is:
K
=
F t b
σ m a x σ n o m
F
Stress Concentration • Stress concentration factors are found em#irically $loo! for t"em in tales% • Stress concentrations are geometry and surface finis" stress concentration in a flat ar of de#endent2 reducing section – note t"e lend radii
Stress Concentration • (n ductile materials stress concentrations are usually ignored due to material flow • Stress concentrations must e accounted for in designs involving: – rittle materials $w"ic" are very sensitive% – Fatigue loading – (m#act loading 8"otoelastic and F5A determination of stress concentrations in t"e flat ar of reducing section
Stress concentrations in welds • Stress concentration is 62- on a reinforced utt weld • )educes to 6 if weld is DdressedE
Stress concentrations in welds • Stress concentration at t"e end of a #arallel fillet weld is -2=
Stress concentrations in welds • Fatigue Stress concentration factors $; fs % for weld and #arent metal: • • • •
)einforced utt weld 62*oe of transverse fillet 629 5nd of #arallel fillet -2= * weld wit" s"ar# corners -27
Fatigue oading • +any materials e/"iit a fatigue limitG elow t"is limit fatigue failure is unli!ely2 • For steel t"e fatigue limit is around 97H of t"e ,*S for static loading • For aluminium it3s #oorly defined ut around -9H of ,*S
Fatigue limit is s"own on t"e S0 $endurance% diagram
σ s s e rt s e r ul i a F
Fati%ue liit Nuber !" #$#les t! "ailure
Welding I Fatigue )esources • "tt#:&&www2roymec"2co2u!&,seful*ales&Fatig – *ales of stress concentration factors K design guide
• "tt#:&&www2gowelding2com& – all manner of information
