The picture shows a simplified schematic of a hoist system designed to move heavy things
around. The design is composed of 5 1020-steel tubes, with rectangular cross-sections, labeled
from A through E. Notice how the joints are also labeled, but from 1 through 9. Consider
that a regular operational regime consists of moving a 200 kg element around while going
over bumps and ramps which can introduce cyclic loads of up to 2g's of vertical acceleration.
Assume that in a normal day of operations the hoist experiences 300 of such loading cycles.
Here is what we know about this hoist design:
9
Simplified Model
0-2g
E
Z
500mm
6
8
A
B
300mm 300mm
D
800mm
1,700mm
Junction 3
100mm
Ho
1020 Steel
Bo
T
Figure 1: Hoist System
Side view of relevant member
F
500mm
Junction 3
1,700mm
1. 1020 rectangular thin-walled steel construction;
2. Outer height Ho = 80 mm, outer width B. = 60 mm, and thickness is T = 5 mm;
3. Required overall design factor of safety FOS = 2;
4. Fatigue knockdown factor (all together) K = 0.678;
8
5. Young's Modulus (E = 200 GPa);
6. Yield Strength (Sy = 350 MPa);
7. Ultimate Tensile Strength (Su = 700 MPa). A) The mean and alternating compressive stresses (mean-c) and (alt-c) without
any factors.
B) The factor of safety for large scale yielding in compression (Sy/max-c).
C) The equivalent completely reversed stress in compression (eq-CR-C) for fa-
tigue, including the fatigue stress concentration factor (KF).
D) The factor of safety in fatigue in compression (SF/eq-CR-C).
E) The mean and alternating tensile stresses (mean-t) and (alt-t) without any
factors.
F) The factor of safety for large scale yielding in tension (Sy/max-c).
G) The equivalent completely reversed stress in tension (eq-CR-T) for fatigue,
including the fatigue stress concentration factor (KF).
H) The factor of safety in fatigue in tension (SF/Oeq-CR-C).
I) The hoist service life in years (construct a S-N chart for the problem).
Use the following charts to estimate the necessary coefficients for your calculations:
• Stress concentration factor: Assume junction No. 3 can be approximated as a cross-
section reduction and a fillet joint. For this case, use H/h = 1.5 and r/h = 0.05.
• Notch sensitivity factor (q) for bending: Use the appropriate bending curves.
K₁
Evaluate Junction No. 3 and determine:
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0
0.05
0.10
M
0.15
r/h
o nom
H
Mc 6M
I bh²
0.20
0.25
M
0.30
H/h=6
-2
1.2
1.05
1.01
(a) Bending Stress Concentration factor chart
Notch sensitivity index, q
1.0
0.9
0.8
0.7
0.5
0.4
0.3
0.2
0.1
0
0
200 (400 Bhn) 180 (360 Bhn)
140 (280 Bhn) 120 (240 Bhn)-
100 (200 Bhn) 80 (160 Bhn)
80 (160 Bhn)60 (120 Bhn)
60 (120 Bhn)
50 (100 Bhn)
0.02
S for bending or axial loading, ksi
S for torsional loading (tentative), ksi
0.04
0.08 0.10
Notch radius r, in.
(b) Notch sensitivity factor chart
Aluminum alloy (based on 2024-T6 data)
0.06
0.12
Steel
0.14
0.16
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