The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit will be denoted as ξ . If the shaft shown in the figure is to have a uniform diameter d except in the locality of the bearing mounting, it can be approximated as a uniform beam with simple supports. Show that the minimum diameters to meet the slope constraints at the left and right bearings are, respectively, d L = | 32 F b ( l 2 − b 2 ) 3 π E l ξ | 1 / 4 d R = | 32 F b ( l 2 − a 2 ) 3 π E l ξ | 1 / 4 Problem 4–45
The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit will be denoted as ξ . If the shaft shown in the figure is to have a uniform diameter d except in the locality of the bearing mounting, it can be approximated as a uniform beam with simple supports. Show that the minimum diameters to meet the slope constraints at the left and right bearings are, respectively, d L = | 32 F b ( l 2 − b 2 ) 3 π E l ξ | 1 / 4 d R = | 32 F b ( l 2 − a 2 ) 3 π E l ξ | 1 / 4 Problem 4–45
Solution Summary: The author explains the minimum diameter to meet the slope constraints at the left and right bearings, and the expression for the deflection in the shaft.
The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit will be denoted as ξ. If the shaft shown in the figure is to have a uniform diameter d except in the locality of the bearing mounting, it can be approximated as a uniform beam with simple supports. Show that the minimum diameters to meet the slope constraints at the left and right bearings are, respectively,
d
L
=
|
32
F
b
(
l
2
−
b
2
)
3
π
E
l
ξ
|
1
/
4
d
R
=
|
32
F
b
(
l
2
−
a
2
)
3
π
E
l
ξ
|
1
/
4
I need handwritten solution with sketches for each
Given answers to be: i) 14.65 kN; 6.16 kN; 8.46 kN ii) 8.63 kN; 9.88 kN iii) Bearing 6315 for B1 & B2, or Bearing 6215 for B1
(b)
A steel 'hot rolled structural hollow section' column of length 5.75 m, has
the cross-section shown in Figure Q.5(b) and supports a load of 750 kN.
During service, it is subjected to axial compression loading where one end
of the column is effectively restrained in position and direction (fixed) and
the other is effectively held in position but not in direction (pinned).
i)
Given that the steel has a design strength of 275 MN/m², determine
the load factor for the structural member based upon the BS5950
design approach using Datasheet Q.5(b).
[11]
ii)
Determine the axial load that can be supported by the column
using the Rankine-Gordon formula, given that the yield strength of
the material is 280 MN/m² and the constant *a* is 1/30000.
[6]
300
600
2-300 mm
wide x 5 mm
thick plates.
Figure Q.5(b)
L=5.75m
Pinned
Fixed
Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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