   # Repeat Problem 8.5-22 but replace the square tube column with a circular tube having a wall thickness r = 5 mm and the same cross-sectional area (3900 mm 2 ) as that of the square tube in figure b in Problem 8.5-22. Also, add force P. = 120 N at B (a) Find the state of plane stress at C. (b) Find maximum normal stresses and show them on a sketch of a properly oriented element. (c) Find maximum shear stresses and show them on a sketch of a properly oriented element. ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

#### Solutions

Chapter
Section ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 8, Problem 8.5.24P
Textbook Problem
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## Repeat Problem 8.5-22 but replace the square tube column with a circular tube having a wall thickness r = 5 mm and the same cross-sectional area (3900 mm2) as that of the square tube in figure b in Problem 8.5-22. Also, add force P. = 120 N at B(a) Find the state of plane stress at C. (b) Find maximum normal stresses and show them on a sketch of a properly oriented element. (c) Find maximum shear stresses and show them on a sketch of a properly oriented element. (a)

To determine

The state of plane stress on an element C.

### Explanation of Solution

Given information:

The cross-section of the bicycle rack tubing is circular.

The weight of the bicycle = 14 kg is represented as point load applied at B on a plane frame model of the rack.

A force in z direction has also been added Pz= 120 N

Weight density of the steel γ=77kN/m3

Calculation:

From the figure, let us consider horizontal portion of the cycle rack. The weight of the cycle is considered as the point load and this load produces a moment and a direct compressive load in the beam along Y-direction.

Also, a load Pzhas been added in z direction. This load will produce bending moment in the horizontal beam and twisting moment in the vertical portion of the beam.

The cross-sectional area of the beam is given by

A=3900mm2=3.9×103m2

A=π4(d2(dt)2)3900=π4(d2(d5)2)

d=499.06mm

The moment in the vertical beam =

M=14×9.81×1M=137.34Nm

The moment in the horizontal beam due to load Pz= Mz=Pz×1m

Mz=120×1=120Nm

Total moment Me=137.34+120=257.34Nm

The load Pzwill produce twisting moment equal to Mz. This twisting moment will produce the shear stress at the base of rack.

From the properties of the cross-section, the moment of inertia is

I=πd464π(dt)464

I=π×(499

(b)

To determine

The maximum normal stress and the sketch of properly oriented element.

(c)

To determine

The maximum shear stress and the sketch of properly oriented element.

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