Question1.3:
A square prismatic bar of 1300-sq.mm cross-sectional area is composed of
two pieces of wood glued together along the x’ plane, which makes an angle
θ
with the
axial direction. The normal and the shearing stresses acting simultaneously on the joint
are limited to 20 and 10 Mpa, respectively, and on the bar itself, to 56 and 28 Mpa
respectively. Determine the maximum allowable axial load that the bar can carry and the
corresponding value of angle
θ
.
Y
Solution
Y’
X’
X
θ
P
P
Let us denote the axial force applied by “P”, the cross-sectional area of the bar by “A”,
σ
,
σ
’,
τ
,
τ
’ be the normal and shear stresses on the normal cross-section of the bar and the
joint respectively.
Cross-section of the joint,
)
cos(
A
A'
q
=
……………….
by geometry.
Now the stresses developed on the joint are
'
joint
on the
force
Normal
'
A
=
s
'
joint
on the
force
shear
'
A
=
t
Since the axial load on the bar is P, the normal and shear components of this load onto

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