1. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 1 Supplementary problem 5 A force P is applied as shown. Calculate the reaction force (x-direction) on the block, using the principle of virtual work ? P A C B θθ l l Z X Y Sliding block

2. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 2 Supplementary problem 5 1. In this machine, we know it is definitely fixed at A and will not lift up at B P A C B θθ l l Z X Y Sliding block 2. We are interested in a virtual displacement at B and C

3. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 3 Supplementary problem 5 3. Assign reactions at A and B P A C B θθ l l Z X Y AxAx AzAz BxBx BzBz

4. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 4 Supplementary problem 5 4. Create a displacement for point B and thereby for point C P.δz + B x.δx = 0 5. Use the principle of virtual work : F i.δ i = 0 Pδz Cos0 + B x δx Cos180 = 0 δz = δ (-l Cosθ) = l Sinθ δθ δx = δ (2l Sinθ) = 2l Cosθ δθ P (l Sinθ δθ) Cos0 + B x (2l Cosθ) δθ Cos180 = 0 B x = (P/2) Tanθ δzδz BxBx BzBz z = -l Cosθ B AxAx AzAz δxδx θ δθ x = 2l Sinθ C X Z

5. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 5 Supplementary problem 6 P M A C B E D F Find the couple M required to maintain the mechanism in equilibrium ! AC = EC = CB = DB = DF = l

6. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 6 Supplementary problem 6 P M A C B E D F 1. Assign reactions AxAx ExEx EzEz X Z AC = EC = CB = DB = DF = l

7. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 7 Supplementary problem 6 P M A C B E D F 1. Create a virtual displacement for point D AxAx ExEx EzEz X Z AC = EC = CB = DB = DF = l

8. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 8 Supplementary problem 6 P M A C B E D F 1. Create a virtual displacement for point D AxAx ExEx EzEz X Z θ δθ δxδx x = 3l Sinθ δx = 3l Cosθ δθ D A B F C

9. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 9 Supplementary problem 6 P M A C B E D F 2. Apply the principle of virtual work AxAx ExEx EzEz X Z D A θ δθ δxδx x = 3l Sinθ δx = 3l Cos θ δθ P(+δx) + M(-δθ) = 0 P(3l Cosθ δθ ) + M(-δθ) = 0 M = 3Pl Cosθ B F C AC = EC = CB = DB = DF = l

10. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Problem 5 Micromechanics – WS 2011/2012/ Exercise 1 / sheet 10 Calculate the internal force variables and plot the trend curves

11. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Problem 5 Micromechanics – WS 2011/2012/ Exercise 1 / sheet 11 1. Divide the beam into two sectors and calculate IFVs in each sector Sector II Sector I

12. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Problem 5 Micromechanics – WS 2011/2012/ Exercise 1 / sheet 12 2. Plot IFVs along beam axis

13. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 13 Supplementary problem 7 P F A C B E D F Find the force F required to maintain the mechanism in equilibrium !

14. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Micromechanics – WS 2011/2012/ Exercise 3 / sheet 14 Supplementary problem 8 A force P is applied as shown. Find the angle θ for which the mechanism is in an equilibrium position ? Find the tension in the spring as well. The spring has a spring constant k. The unstretched length of the spring is h. P A C B θθ l l Sliding block

15. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Problem 5 Micromechanics – WS 2011/2012/ Exercise 1 / sheet 15 Find the reactions at A and B.

16. IMTEK Lehrstuhl Konstruktion von Mikrosystemen Problem 6 Micromechanics – WS 2011/2012/ Exercise 1 / sheet 16 Calculate the internal force variables and plot the tend curves