Lightweight Electric/Hybrid Vehicle Design

204 Lightweight Electric/Hybrid Vehicle Design
Peery 2 uses the assumption of constant shear flow in the web, for the generalized curved section
of a beam, (b), to show that twice the area enclosed by the curved web [A] divided by the ‘chord’
of the curve gives the moment arm of the resultant of shear flow in the web. This is helpful, for
example, in finding the ‘shear’ centre of an asymmetric section beam, or that distance offset from
the section that a shear force can be applied without causing any twist of the section. For a beam
section such as that in Fig. 8.1(d), but with corner booms, area A f , only and no central stringers, for
section depth d and breadth b, with corresponding symmetrical wall thicknesses t d and t b , this
would be idealized by a four boom box beam having boom section areas A f + (bt f /2) + (dt b /6). The
analysis technique is to make an imaginary cut which makes the closed section momentarily open,
and finding ‘open-section’ shear flows. The next stage is to apply an opposite sense shear flow q o
on all elements (between booms) which equals the ‘resultant shear flow’ q* on the cut element.
The final stage is to balance moments of the combined shear flows against the moment arm of the
externally applied load, the q o flows being assumed to set up torque T = q o 2[A]. Because, in this
case, the beam is subjected to bending loads only, and not external torque, the twist per unit length
can be equated to zero in σq*(s/t) = 0.
P
S
M S
P+δP
σ c=o
δz
S S
P 2=σ vtdz
T..t.dz 45°
P+δP
M+
δM
δP
δP
S
S
(a)
δP
(b)
(c)
P
P 1=σ 1.t.dz/√2
q
s
qL
c
A
B
δx
(a)
P
Flange
Web
ft fc
fc ft
Flange
Fig. 8.3 Thin-walled structural idealizations: (a) flat shear panels and end-load bars; (b) shear
flow in curved section beam; (c) tension field in sidewall to examine shear buckling.
δs
r
δy
δA
O
ft
qδs
(b)
A
L
B
fc
P