STRUCTURAL SURFACES & FLOOR GRILLAGESarahim/structural surface.pdf · Planar structural...
Transcript of STRUCTURAL SURFACES & FLOOR GRILLAGESarahim/structural surface.pdf · Planar structural...
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STRUCTURAL SURFACES & FLOOR GRILLAGES
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INTRODUCTIONIntegral car bodies are 3D structures largely composed of approximately subassemblies- SSS
Planar structural subassemblies can be grouped into two categories based on their functions:a) SSS- carry in-plane loads-example:sideframeb) Grillage structures – carry out-of-plane loads-example:compartment floor
The floor carries both types of load but the two functions can be treated separately:a) Grillage- out-of-plane stiffness comes from attached beamb) Torsion-box- in-plane stiffness comes from very thin panel to carry almost all shear load
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In-plane loads and SSS•Structures which are flexible in-plane are not considered as SSSand tend to cause unsatisfactory break in load paths. Examples arediscontinuous frames, missing edges, unreinforced cut-outs, open ring frame with pin-jointed or flexible-jointed corners.
• Typical effective SSS are:a) Thin walled panelsb) triangulated planar trussesc) stiff jointed framesd) combination of the above
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Shear Panels• One role of SSS is to effectively carrying shear forces Q
Shear flow and shear stress• shear flow is shear force per unit length, q = Q/L (N/m)• The average shear stress is shear force per unit area,τavg = Q/A=Q/Dt
Thus, q = tτ
Q2
Q1Q1
Q2
Q1B=Q2D
B
D
D
t
τ
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Stiffness of Shear Panel• Shear stress = shear modulus x shear strain
τ = Gγ
∆
Q2
Q1
Q2
Q1
τ= Q1/Dtγ= ∆ /BQ1/Dt = G ∆/BQ1=K ∆=GtD ∆/B
Shear stiffnessK=GtD/B
γ
B
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Shear panel as part of of an assembly• The edge shear forces Q1 and Q2 will have to be reacted by
adjacent structural elements. These may be: a) other shear panels b) edge booms or flanges
i) Shear panel assemblies-torsion box (Transmission tunnel)
Q1
Q1 QC1
QC1
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ii) Boom- panel structures
- to represent a cantilever structure
- assumption made to a beam composed by of booms and panel:
a) Bending moment is reacted by by the axial forces in the boom
b) The shear panel carries all the shear force Q1
P
P
Q2
Q2Q1 Q1
Pxx
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Triangulated truss/bay• This is composed of pin-ended members connected in a
triangulated arrangement• The individual members experience only tension and compression
Q1
Q2
P3θ
Q1=P3cos θQ2 = P3 sin θ
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Q
∆
1 3
4
2
5θ
Shear stiffness of triangulated bay
Strain energy method:
A = Cross-sectional areaL= LengthE = Young modulus
∑=AE
LPU2
2
Assumed that the shear force Q is carried by member 3
θ
θ
23
3
32
32
33
23
3
cos2
2/
2cos2
EA
QLQU
EA
LQEA
LPU
=∂∂=∆
==3
23 /cos/ LEAQKeq θ=∆=
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Single or multiple open ring frames• A rectangular open ring with stiff edge members and stiff cornerjoints
• more flexible in overall shear than a continuous panel because stiffness is derived from its local bending in the edge members
Q2
Q1
B
D
BM Mmax = Q1B/4= Q2D/4
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Shear stiffness of single bay symmetric open ring
x
QQ1
P1M1
)//(/)24(,stiffnessShear
)24/()//(/
)48/()//(
4EnergyStrain Total
22
)2/(2/;2/
212
212
1
2122
1
4/1
2/
0 2
222/
0 1
124/1
12211
IDIBBEK
EIDIBBQQU
EIDIBBQU
U
dYEI
MdXEI
MU
DBYQYQMXQMDB
+=
+=∂∂=∆
+=
=
+=
===
∫∫
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EXAMPLE:Cross – section beam 100x100x2mmWidth 500mmDepth 500 mmYoung modulus 210 000 N/mm2
Shear modulus 80 000 N/mm2
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Simple structural surface with additional external loads• some panels experience extra external forces as well as edge loads• example: front bulkhead
boom
• panels A & B are purely in complementary shear
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In-plane forces in sideframes• comprises of multiple ring frames• such frames are statically indeterminate, determination of shear forces and bending moment in each pillar is complicated
• Finite element method can be used to predict those parameters• or simplified rough estimation can be performed:a) Pillar with rigid end joints
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∑
∑
=
∆=
=∆=∆=∆=∆
=⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
=∆
=
)(/)(
)12(
......321
123
)2
(2,
,2
33
3
3
max
i
i
j
jtotal
i
itotal
H
I
H
IQQj
H
IEQ
pillarpillarpillar
EIQH
EI
HQdeflection
HQMb) Poor joint at one end
EIQH
QHM
3
max3
=∆
=
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c) Mixture of joint conditions• stiff joints at B- and C- pillars and a poor joint at A-pillar
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Loads normal to surfaces: floor structures• floors are subjected to loads normal to their plane• the floor is stiffened against out-of-plane load by added beam member called a grillage
• a true grillage is a flat frame loaded normal to its plane andthe active forces are normal force, bending moment and torsion• The grillage members consist of:
a) members integral to the floor panel, e.g. transmission tunnelb) added members e.g. separate beams welded onto the floorc) bulkhead
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Load distributions in floor member• the share of forces in the different floor members influences the shear force and bending moments in the sideframei) Perfect joints
- the distribution of forces will be in proportion to the stiffnessof the members
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Effect of joints flexibility on load distribution• the joints between the members has great influence on loaddistribution
• Example: transmission tunnel is continuous and cross-memberis attached to it
• The effect was if F is loaded to the central joint, all the loadwill transfer along the tunnel. However, seat loads appliedpart-way along the tunnel and the rocker panels
• Corrective measures:
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