Fundamentals andpreliminary sizing ofpreliminary sizing ofsections and joints

ObjectivesObjectives

• Overview of section and joint structuralOverview of section and joint structural behaviour in a design context.

• To outline the design and sizing approach for• To outline the design and sizing approach for sections and joints.

Characteristics of thin walled structures

• manufactured with more than one componentmanufactured with more than one component and joined together by spot welds, seam welds or by an adhesivewelds or by an adhesive.

• Two types:O th thi h t t l i f d ith– Open ‐ the thin sheet metal is formed with a discontinuityClosed the section forms a complete loop– Closed ‐ the section forms a complete loop

Open SectionsOpen Sections• Some open sections:

– Angle section– Z section– Channel– Lipped channel– Hat section

• Major limitations:Major limitations:– lack of Torsional stiffness due 

to their very low polar second moment of area.

– Wharping : under torsion transverse sections do not remain plane, there is axial displacement at various pointsdisplacement at various points on the section 

Angle SectionAngle Section• Not a suitable structural member

when considered alone.• The principal axes U–U and V–V

are inclined to the faces of theangle and if bending is appliedabout either Y–Y or Z–Z bendingwill occur about both axes.

• Stress distribution is veryasymmetric and results in largeparts of the section being under‐

dstressed.• inefficient use of material

Z sectionZ section• Similar undesirable

characteristics and henceis not suitable as a sectionon its own.

• Principal axes of the Zsection are inclined.

• Angle of the principalAngle of the principalaxes U –U and V –Vrelative to the Y –Y axiswill depend on thewill depend on therelative lengths of b1, b2and d.

Channel ‐1/2Channel  1/2• Suitable structural section

and used in commercialvehicle chassis and bodystructures.

• Suitable for bending loadscausing moments aboutthe Z–Z axis.

• Care must be taken toensure that the flangewidth ‘b’ is not excessivewidth b is not excessiveas this can lead toreduced allowablecompressive stressp

Channel‐2/2Channel 2/2

• Less satisfactory forLess satisfactory forbending about the Y –Yaxis because it is lessstiff (has lower value forIyy than Izz) and has an

t i tasymmetric stressdistribution.

Lipped channelLipped channel

• The wide flange resultsThe wide flange results in a low stress at which buckling occurs.

• Improvement in buckling stress can be achieved by adding a lip to the channel

Hat sectionHat section

• Has good bendingHas good bendingproperties about bothY–Y and Z–Z axesprovided the value of2b2 is approximately

l t bequal to b1.

Open SectionsOpen Sections

• Polar moments of Inertia of sections JxPolar moments of Inertia of sections Jx– Angle  = (a + b)*t3/3– Z section  = (b1 + b2 + d)*t3/3( 1 2 ) /– Channel  = (2b + d)*t3/3– Lip Channel  = (2d1 + d + 2b)*t3/3p ( 1 ) /– Hat (e)  = (b1 + 2b2 + 2d)*t3/3

• t is small hence Jx will be smallerx

• Hence larger twist angle θ=TL/GJxθ TL/GJx

Closed SectionsClosed Sections

Closed SectionsClosed Sections

• Two Z sections withTwo Z sections with unequal length flanges joined to form a closed rectangular section.

• Second moments of area about the Y –Y and Z–Z axes are much increased over the openincreased over the open section

Closed SectionsClosed Sections

• Combination of twoCombination of two channels, one with wide and one with narrow flanges.

• This combination avoids inclined principal axes and still has substantial second moments ofsecond moments of area about Y –Y and Z–Z axes.axes.

Closed SectionsClosed Sections

Two hat sections are combined, both of these form ff ti t t l b ith d b dieffective structural members with good bending properties about Y –Y and Z–Z axes.

Closed SectionsClosed Sections

• Hat section with a flatHat section with a flat closing plate

Closed SectionsClosed Sections

• At (a) the enclosed area is:shown at (b) :

A = (b1 − 2b2)d + 4(b2 − b3)t• And the periphery:

shown at (b) :A = (b1 − 2b2)dAnd s = 2(b1 − 2b2) + 2d

s = 2(b1 − 2b3) + 2d + 4(b2 − b3)1 2

Some passenger car sections 1/2Some passenger car sections 1/2

OneOne Shallow hat

h llTwo Shallow hat

Some passenger car sections 2/2Some passenger car sections 2/2Two Shallow hat + shallow  Two shallow 

hat + flatflat hat + flat 

Hat+ plate+ Z

Two hat + angle + roof

Floor Cross‐BeamFloor Cross Beam

Hat section on fl lfloor panel

Floor Cross‐BeamFloor Cross Beam

• LoadsLoads– Ffp = Load from passenger/seatK = Load from engine rail– K1 = Load from engine rail

– K2 = simple supports reaction with no fixing supportssupports

• Loading condition on the cross‐beam is bending and shearbending and shear.

Floor Cross‐BeamFloor Cross Beam

• Bending moment e d g o e tM = K2l1 − Ffpl2

values of K2 and Ffp must be based on the staticvalues of K2 and Ffp must be based on the static loads multiplied by any load factor necessary to allow for dynamic effects.

• Designing for strength use the standard engineer’s bending theory to obtain the stress in th b d t th b di tthe beam due to the bending moment:

f = My/I

Floor Cross‐BeamFloor Cross Beam

• Section properties to be evaluated including a p p gwidth of approximately 20t of the floor panel either side of the hat section 

b b + 2b + 40tb3 = b1 + 2b2 + 40t• Safety factor – 1.5• For shear non linear shear stress theory:• For shear ‐ non‐linear shear stress theory:

τ = K2Ay/zI (y is moment of area, z is widthz is width, I is second moment of inertia)

τ ≈ K2/2dt (as stress in b1 abd b3 is low)2/ ( )

‘A’ PillarA  Pillar

‘A’ PillarA  Pillar

• Large bending loads when theLarge bending loads when the structure is loaded in torsion

• From the roof loads the shear force between the top of the windscreen frame and along the cantrail can be bt i dobtained.– Q1 = across the frontQ = across the sides– Q2 = across the sides

– proportion ‘n’ of the side frame load Q2 is that taken by the ‘A’‐pillar

‘A’ PillarA  Pillar• Assuming the joint at the top of the ‘A’‐pillar to the 

i d h d il/ t il d th j i t t thwindscreen header rail/cantrail and the joint to the dash/wing are “fixed supports”

• Bending moments and stresses areM Q h/4Mx = Q1h/4fbx = Mxb/2Ixx

2 sin * / 2*cosyM nQ hα α=

• Direct compression stressf Q / (2b 2d)

y

2y

byyy

M df

I=

fc = nQ2 cos α / (2b + 2d) t• where (2b + 2d)t is approximately the cross‐sectional 

area

‘A’ PillarA  Pillar• Stress plots show

– At A, the bending stresses are tensile but the direct stress is again compressive so giving a reducedso giving a reduced resultant stress

• Design criteria described are based on the torsionare based on the torsion load condition.

• For the ‘A’‐pillar section, critical case can be thecritical case  can be the in‐roof crush test SAE J374

Engine longitudinal railEngine longitudinal rail

Engine longitudinal railEngine longitudinal rail

• Shear forces and bending moments.g• Shared Loads:

– Bumper FB,– Radiator FR,– Power‐train FPT– Reaction from the front suspension R LReaction from the front suspension RFL.

• Factors for Dynamic loads• The engine rail is supported in the structure byg pp ythe dash panel and by the floor cross‐beamsituated under the front seats.

Engine longitudinal railEngine longitudinal rail

• Solving for forces on K1 and K2Solving for forces on K1 and K2• Resolve vertically:

/2 /2 2( / ) 0FB /2+  FR /2+ 2( FPT/4) + K1 − K2 − RFL = 0• Moments about K1:FBl1/2 +  FRl2/2 + FPTl3/4 + FPTl5/4 + K2l6 − RFLl4 = 0

Engine longitudinal railEngine longitudinal rail

• Plots show high shear between the suspensionPlots show high shear between the suspensionreaction and the dash panel and the maximummoment is at the dash panel : need for a deepersection

• Design governed by bending strength requirement atth d h l h ll d th ‘d’ h ld b lthe dash panel, hence overall depth ‘d’ should be large.

• Stiffness may also be important and the deflection ofthe beam calculatedthe beam calculated.

• This member will also be designed to absorb energy infrontal impactsfrontal impacts

Sheet metal JointSheet metal Joint

Shear flow around the section shows thatas the spot welds are spaced further from the beam centre and hence the load will be reduced

Sheet metal jointSheet metal joint

• If a moment M is applied, tension in top of hat a o e t s app ed, te s o top o atand compression in closing plate.

• Vertical shear force is carried by the side flanges, y glike curved shear panels – The top and bottom flanges will not carry any 

i ifi t ti l fsignificant vertical force.– Side flanges: load is applied normal to their plane they will be ineffective in resisting the forceg

• When horizontal shear forces are applied the opposite will result.

Sheet metal JointSheet metal Joint

Sheet metal jointSheet metal joint

• Spot weld jointsSpot weld joints• No fixing moment while providing only a shear   connectionconnection

• From the analysis of this joint we can learn i l f d i i j itwo important rules for designing joints:

– Avoid out‐of‐plane bending on thin sections.– Load thin sections with in‐plane bending and shear.

Spot welds LoadingSpot welds Loading

• A centre core which has the microstructure similar to a casting

• There is some working of• There is some working of the metal due to the pressure of the electrodes

• Surrounding the core is a heat‐affected zone that has reduced strengthhas reduced strength compared to the base material

Spot welds LoadingSpot welds Loading

• The spot weld nuggetThe spot weld nugget has peeled away from the base material.

• Parent metal is subject to out‐of‐plane bending which again is unsatisfactory causing yielding at very lowyielding at very low loads

Spot weld LoadingSpot weld Loading

• The small area cannot resist a large twisting moment caused by the long moment arm

Spot weld patternsSpot weld patterns• Position of centroid

• Force divided equally n 

1 2

1 2

(3 3 ) / 8

(2 3 ) / 8

y y y

x x x

= +

= +

all rivets• Additional shear force for offset torque

Spot welds along a closed sectionsSpot welds along a closed sections

q T Tτ1 22 2 ( 2 )

qt At d b b t

τ = = =−

s

qLNF

=

Shear Panels – Roof panelShear Panels  Roof panel

• The largest panel in a passenger car and underThe largest panel in a passenger car and under the torsion load case this may buckle due to shearshear.

• ESDU 02.03.18/19 data sheet can be used to i ti t thi hinvestigate this phenomenon.

• These data is not ideal because they consider plates with curvature in one direction, but the roof panel has curvature in two directions.

Shear Panels – Roof panelShear Panels  Roof panel

• Buckling stressBuckling stressτ = KE(t/b)2

K = Buckling stress co‐efficeintgE = modulus of elasticityT = panel thicknessB = length of curved side

• The coefficient K is presented as a function of thel h h d f h h k f hlength a, the radius of curvature R, the thickness of thepanel t and the ratio a/b (the ratio of the lengths of thepanelsides)panelsides).

Shear panels –Roof panelShear panels  Roof panel

• Investigations made into a roof panel 980mmInvestigations made into a roof panel 980mm wide by 1250mm long, 1mm thick and radius of curvature of 2425mm resulted in stress toof curvature of 2425mm resulted in stress to cause buckling of 13.8N/mm2which is four times larger than the applied shear stresstimes larger than the applied shear stress.

• Other approaches areESDU 71005 fl t l– ESDU 71005 : flat panels 

– ESDU 75030 : design for vibrations

Shear panels – Inner fenderShear panels  Inner fender

• ESDU 71005• For typical dimensions, applied stress levels may exceed by a factor 

of 5, hence there is need to provide stiffeners to prevent buckling.This panel in practice has considerable curvature is restrained at the– This panel in practice has considerable curvature, is restrained at the edges by adjacent parts and also the model is a very simplified representation of the structure. In practice the load will be shared between the engine rail the fender– In practice the load will be shared between the engine rail, the fender top rail as well as the panel. 

• All these factors will tend to reduce the risk of panel buckling but thi d ill t t th d t dd tiff d i thithis does illustrate the need to add stiffeners and swages in this part of the structure.