A rectangular beam with two notches (with radius r = 2.5 mm) is shown in Figure 1.1. The beam has dimensions w = 55 mm and d = 50 mm. The beam is subjected to a bending moment of M = 1.3 kNm and the maximum allowable bending stress in the material is 400 MPa. Determine the smallest thickness, tmin, in mm that this beam should be designed for. Stress concentration graph is provided in Figure 1.2.

A rectangular beam with two notches (with radius r = 2.5 mm) is shown in Figure 1.1. The beam has dimensions w = 55 mm and d = 50 mm. The beam is subjected to a bending moment of M = 1.3 kNm and the maximum allowable bending stress in the material is 400 MPa. Determine the smallest thickness, tmin, in mm that this beam should be designed for. Stress concentration graph is provided in Figure 1.2.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A rectangular beam with two notches (with radius r = 2.5 mm) is shown in
Figure 1.1. The beam has dimensions w = 55 mm and d = 50 mm. The beam
is subjected to a bending moment of M = 1.3 kNm and the maximum
allowable bending stress in the material is 400 MPa. Determine the smallest
thickness, tmin, in mm that this beam should be designed for. Stress
concentration graph is provided in Figure 1.2.
K₁
M
3.0
2.6
2.2
1.8
1.4
16
1.0
0
1.10
1.05
1.02
0.05
wld = ∞
W
1.5
0.10
Figure 1.1.
0.15
rld
Figure 1.2.
Inom
0.20
6M
td²
0.25
M
M
0.30

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