Manufacturing Processes for Engineering Materials (6th Edition)
Manufacturing Processes for Engineering Materials (6th Edition)
6th Edition
ISBN: 9780134290553
Author: Serope Kalpakjian, Steven Schmid
Publisher: PEARSON
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Chapter 2, Problem 2.94P
To determine

The compressive load applied in the z-direction according to Tresca yield criteria

Expert Solution & Answer
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Answer to Problem 2.94P

Compressive load applied in the z-direction is 60kN .

Explanation of Solution

Given data:

  Area of the face of the metal cube, A=5cm2Shear yield strength of the metal, k=140MPa,Compressive load applied on the metal, Fx=40kN,Fy=80kN.

Calculation:

Calculating the compressive stress due to applied load,

  σx=FxAσx=40×10005×104σx=80MPa,σy=FyAσy=80×10005×104σy=160MPa.

Writing the formula for principal stresses,

  σ1/2=σx+σy2±(σxσy2)2+τxy2Here, τxy=0,Pugging the value of σx&σyσ1/2=801602±(80(160)2)2+02σ1/2=2402±(80+1602)2σ1/2=2402±802σ1/2=120±40σ1=120+40σ1=80MPa,σ2=120140σ2=160MPa

Let the stress in the z-direction be σ3=σz

Now according to Tresca yield criteria,

  τmax=|(σ1σ22),(σ3σ32),(σ3σ12)|k=|(σ1σ22),(σ2σ32),(σ3σ12)|Plugging the value of k,σ1&σ2140=|(160(80)2),(80(σz)2),(σz(160)2)|140=|(160+802),(80+σz2),(σz+1602)|140=|(802),(80+σz2),(σz+1602)|

Now taking the above values as shown below,

  140=|(802),(80+σz2),(σz+1602)|140=|80+σz2|140=80+σz280+σz=140×280+σz=280σz=280+80σz=360MPa,140=|σz+1602|σz+1602=140σz+160=140×2σz+160=280σz=280160σz=120σz=120MPa

Since, we have taken stress in the z-direction as negative for compressive load and out of two values from above one is positive and one is negative.

Hence, the compressive stress in z-direction would be σz=120MPa

Now calculating the compressive load in the z-direction,

  σz=FzA120×106=Fz5×104Fz=120×106×5×104Fz=600×102Fz=60kN

Hence the compressive load applied in the z-direction according to Trescas criteria would be 60kN .

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Chapter 2 Solutions

Manufacturing Processes for Engineering Materials (6th Edition)

Ch. 2 - Prob. 2.11QCh. 2 - Prob. 2.12QCh. 2 - Prob. 2.13QCh. 2 - Prob. 2.14QCh. 2 - Prob. 2.15QCh. 2 - Prob. 2.16QCh. 2 - Prob. 2.17QCh. 2 - Prob. 2.18QCh. 2 - Prob. 2.19QCh. 2 - Prob. 2.20QCh. 2 - Prob. 2.21QCh. 2 - Prob. 2.22QCh. 2 - Prob. 2.23QCh. 2 - Prob. 2.24QCh. 2 - Prob. 2.25QCh. 2 - Prob. 2.26QCh. 2 - Prob. 2.27QCh. 2 - Prob. 2.28QCh. 2 - Prob. 2.29QCh. 2 - Prob. 2.30QCh. 2 - Prob. 2.31QCh. 2 - Prob. 2.32QCh. 2 - Prob. 2.33QCh. 2 - Prob. 2.34QCh. 2 - Prob. 2.35QCh. 2 - Prob. 2.36QCh. 2 - Prob. 2.37QCh. 2 - Prob. 2.38QCh. 2 - Prob. 2.39QCh. 2 - Prob. 2.40QCh. 2 - Prob. 2.41QCh. 2 - Prob. 2.42QCh. 2 - Prob. 2.43QCh. 2 - Prob. 2.44QCh. 2 - Prob. 2.45QCh. 2 - Prob. 2.46QCh. 2 - Prob. 2.47QCh. 2 - Prob. 2.48QCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Prob. 2.55PCh. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 2 - Prob. 2.59PCh. 2 - Prob. 2.60PCh. 2 - Prob. 2.61PCh. 2 - Prob. 2.62PCh. 2 - Prob. 2.63PCh. 2 - Prob. 2.64PCh. 2 - Prob. 2.65PCh. 2 - Prob. 2.66PCh. 2 - Prob. 2.67PCh. 2 - Prob. 2.68PCh. 2 - Prob. 2.69PCh. 2 - Prob. 2.70PCh. 2 - Prob. 2.71PCh. 2 - Prob. 2.72PCh. 2 - Prob. 2.73PCh. 2 - Prob. 2.74PCh. 2 - Prob. 2.75PCh. 2 - Prob. 2.76PCh. 2 - Prob. 2.78PCh. 2 - Prob. 2.79PCh. 2 - Prob. 2.80PCh. 2 - Prob. 2.81PCh. 2 - Prob. 2.82PCh. 2 - Prob. 2.83PCh. 2 - Prob. 2.84PCh. 2 - Prob. 2.85PCh. 2 - Prob. 2.86PCh. 2 - Prob. 2.87PCh. 2 - Prob. 2.88PCh. 2 - Prob. 2.89PCh. 2 - Prob. 2.90PCh. 2 - Prob. 2.91PCh. 2 - Prob. 2.92PCh. 2 - Prob. 2.93PCh. 2 - Prob. 2.94PCh. 2 - Prob. 2.95PCh. 2 - Prob. 2.96PCh. 2 - Prob. 2.97PCh. 2 - Prob. 2.98PCh. 2 - Prob. 2.99PCh. 2 - Prob. 2.100PCh. 2 - Prob. 2.101P
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