Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

There are still two unknowns in this equation; consequently, another equation is necessary
to obtain a solution. Let F 1 equal the force corresponding to the allowable stress s allow,1 in
member (1), and solve for the applied load P. (Note: The negative sign attached to F 1 can
be omitted here since we are interested only in the magnitude of load P.) First, we have
⎡
⎤
s ⎢ + ⎥
⎣
⎦
=
⎡⎛
⎞
⎝
⎜
⎠
⎟ ⎛ ⎝ ⎜
⎞
⎠
⎟ ⎛ ⎝ ⎜ ⎞ ⎤
A
L 1 A2
E2
2 2
1.8 2,000 70
allow,1 1
1 (160 N/mm )(3,600 mm ) ⎢
⎠
⎟ + 1
L A E
⎥
2 1 1
⎣ 1.4 3,600 200 ⎦
= (576,000 N)[1.25] = 720,000 N = 720 kN ≥ P
Next, repeat this process for member (2). Then solve Equation (e) for F 1 :
F
F L 2 A1
E1
=− (f)
L A E
1 2
Now substitute Equation (f) into Equation (a) to obtain
1
2
2
F
F L 2 A1
E1
⎡
+ = F2
1 +
L1
A2
E
⎢
2 ⎣
2 2
L
L
2
1
A
A
1
2
E1
⎤
E
⎥
2 ⎦
=
P
Finally, let F 2 equal the allowable force and solve for the corresponding applied force P:
⎡ L2
A1
E1
⎤
s ⎢ + ⎥
⎣
⎦
= 2 2
⎡
+ ⎛ ⎝ ⎜ 1.4⎞
⎠
⎟ ⎛ ⎝ ⎜
3,600 ⎞
A 1 (120 N/mm )(2,000 mm )1 ⎢
⎠
⎟ ⎛ allow,2 2
L A E
⎣ 1.8 2,000 ⎝ ⎜
1 2 2
= (240,000 N)[5.0] = 1,200,000 N = 1,200 kN ≥ P
Therefore, the maximum load P that can be applied to the flange at B is P = 720 kN.
Ans.
200
70
⎞ ⎤
⎠
⎟ ⎥
⎦
mecmovies
ExAmpLES
m5.5 A steel rod (1) is attached
to a steel post (2) at flange B. A
downward load of 110 kN is applied
to flange B. Rod (1) and post
(2) are attached to rigid supports
at A and C, respectively. Rod (1)
has a cross-sectional area of 800
mm 2 and an elastic modulus of
200 GPa. Post (2) has a crosssectional
area of 1,600 mm 2 and
an elastic modulus of 200 GPa.
(a) Compute the normal stress in
rod (1) and post (2).
(b) Compute the deflection of
flange B.
m5.6 An aluminum tube
(1) encases a brass core
(2). The two components
are bonded together to
form an axial member that
is subjected to a downward
force of 30 kN.
Tube (1) has an outer diameter
D = 30 mm and an
inner diameter d = 22 mm.
The elastic modulus of
the aluminum is 70 GPa.
The brass core (2) has a
diameter d = 22 mm and an
elastic modulus of 105 GPa. Compute the
normal stresses in tube (1) and core (2).
110