ASEN 3112 - Structures
Rec #1 - Problem 1 - Bar Internal Force via FBD
FBD:
B
cut
F=?
P
P
D
A
L
C
L
D
A
L
C
L
a) Draw FBD diagram (right figure) on the board. Does it
matter where the cut is made in member AB?
b) Show that F = − P/2. What is the secret to do this quickly?
c) What is the meaning of the minus sign in F = − P/2?
d) Is member AB in tension or compression? Explain why.
e) Does it matter how one draws the direction of
the internal force in the FBD on the right?
ASEN 3112 Recitation 1 – Slide 1
ASEN 3112 - Structures
Rec #1 - Problem 2 Avg Stresses In Truss of Problem 1
B
B
Side
view
P= 2400 N
A
D
A
L
C
Top view
L
A
D
All pins have diameter of 10 mm
Cross sections 20 mm
of bars AB
and AD
5 mm
Find the following average stresses expressed in MPa:
avg
a) Average normal stress σAB
in bar AB away from ends
pinB
b) Average normal stress σAB
in bar AB at pin B (deduct hole)
C
c) Average shear stress τAD
in bar AD at C just to the right of P
pinA
d) Average shear stress τAD
in bar AD at pin D (deduct hole)
ASEN 3112 Recitation 1 – Slide 2
ASEN 3112 - Structures
Rec #1 - Problem 3A - Pull-out Test
P
Fiber
;;;
;;;
;;;
L
Resin
D
P
L
A fiber pull-out test is to be conducted to
determine the shear strength of the interface
between the fiber and the resin matrix in a
composite material (top Figure).
Assuming a uniform shear stress τ
avg
at the interface, derive a formula for
the shear stress in terms of the applied
force P, the length of fiber L and the fiber
diameter D. Use the FBD sketched in
the bottom Figure.
τavg
D
ASEN 3112 Recitation 1 – Slide 3
ASEN 3112 - Structures
Rec #1 - Problem 3B - Torque-Slip Test
;;;
;;;
;;;
Fiber
T
L
Resin
D
T
L
A second interface shear strength test
applies a torque T to the fiber (top Figure).
Assuming a uniform shear stress τavg
at the interface, derive a formula for
the shear stress in terms of the torque
T, the length of fiber L and the fiber
diameter D. Use the FBD sketched in
the bottom Figure.
τavg
D
ASEN 3112 Recitation 1 – Slide 4
ASEN 3112 - Structures
Rec #1 - Problem 4 - Stresses in a Skew Bar Cut
P
P
FBD:
P
skew cut
P
F=P
θ
F=P
N
P
Blow up of
left skew cut
Aθ = area
of skew cross
section cut
θ
skew cut
θ is + CCW
θ
F=P
V
cut
a) Draw FBD diagram (yellow BG) on board, marking skewangle θ
made wrt normal cut
b) Ask students: why is this FBD correct for any skewangle θ? Hint:
move F (on left) up & down or rotate it, and ask why it is wrong
c) Ask students to derive N = F cos θ = P cos θ and V = F sin θ =
P sin θ using statics, and A = A/cos θ using trigonometry
d) Ask students to derive σ θ = N/A θ and τθ = V/A θ as
functions of P, A, and θ. [ Ans: (P/A) cos2 θ, (P/A) sin θ cos θ]
e) If P/A is fixed, for which angles θ are: σθ max, | τθ | max?
Sketch the variation of both stresses as functions of skewangle.
ASEN 3112 Recitation 1 – Slide 5
ASEN 3112 - Structures
Rec #1 - Problem 4 - Solution to Item (e)
1
0.8
0.6
0.4
σθ
P/A
0.2
0
0.4
−0.2
0.2
0
−90
τθ
P/A
−0.4
0
θ
90
−90
−45
ASEN 3112 Recitation 1 – Slide 6
0
−45
90