Structural Member Stress Analysis: Eccentric Loading

_______________________________________________________________________
PROBLEM (9.46) A structural member is loaded as illustrated in Fig. P9.46. Determine the
maximum tensile and compressive stresses for two cases:
(a) The eccentricity is a = 2h.
(b) The eccentricity is a = h/4.
SOLUTION
P
A
B
C
2Pa/3
P
b
P
a/L
P
a/L 312Ibh=
h
P
-Pa/3
2L/3
Abh
=
x
P
x
M
L/
3
Just to the
left of C (i.e., 32PaM
=
), at the bottom & top edges, respectively:
22
44
,
bot top
PMc P Pa P Pa
A I bh bh bh bh
σσ =+ = + = −
Just to the right of C (i.e., 32PaM
=
):
22
22
,
bot top
M
cPa McPa
I
bh I bh
σσ =− =− = =−
(a) To the left of C, for a :2h=
..
() 9 () 7
bot tens top comp
PA pA
σ
σ ==−
(b) To the left of C, for :4ha =
.
() 2
bot tems PA
σ
=
To the right of C, for :4ha =
.
() 0.5
bot comp PA
σ
=−
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