1. Tutorial 7_Review MECH 101 Liang Tengfei tfliang@ust.hk Office phone : 2358-8811 Mobile : 6497-0191 Office hour : 14:00-15:00 Fri 1

2. A chance to show what you have learned: Statics structure in Equilibrium → the forces atcing on it Mechanics of material the force → stress and strain in each point → deformation & break or not

3. Statics Free bodyFree body diagram force equation + moment equation The force you want Question choose solve build draw

4. Which free body should I choose? remember which force you want let the target force appear in you F.D.B external force will appear in the F.B.D Specify your free body Solve the force from the pin C acting on the member DC and AB

5. How to draw F.B.D? Only external force will appear in the F.B.D Search around the F.B. every thing contacting the F.B. will give it force. How about gravity?? Draw all the force in F.B.D if you known the direction → draw the real direction. otherwise → assume a direction.

6. Build up equilibrium equations Build up the equation base on the F.B.D the sign of the force and moment is base on the direction of the force in F.B.D usually force : same with the coordinate : + moment : counterclockwise : +

7. solve the force Clarify the real direction of the force. Use your intuition to check the answer.

8. The 100N weight of the rectangular plate acts at its midpoint. Determine the reactions exerted on the plate at B and C. B A C 100N 45 O Solution: Notice AB is a two-force member, so the reaction at B must be directed along the line between A and B. 4m Example

9. B C 100N 45 O Apply the equilibrium equation: 4m Solution

10. Other things in statics Replace the distributed load Two force member

11. Mechanics of material Internal force stress deformationstrain statics observation Equilibrium equation Equation of compatibility Hook’s law

12. Normal Stress and Normal Strain Normal stress: force per unit area Normal strain: elongation per unit length This equation is valid only if the stress is uniformly distributed over the cross section of the bar. A P P P L A P Remind strain is a dimensionless quantity

13. Hook’s Law and Poisson’s Ratio Hook’s law Poisson’s ratio Poisson’s ratio is also a constant, a property of the material, and dimensionless P P Note: A permanent strain exists in the specimen after unloading from the plastic region. Dashed means the original shape with out P

14. Composite A-36 steel bar shown made from two segments AB and BD. Area A AB = 600 mm 2 and A BD = 1200 mm 2. E st = 210 GPa Determine the vertical displacement of end A and displacement of B relative to C. δ =δ = PL AE  Elongation → +δ, Contraction → -δ Tension → + P, Compression → - PExample

15. δ A = δ A/B + δ B/C + δ C/D = P AB L AB A AB E P BC L BC A BC E + P CD L CD A CD E + +75kN x 1m x 10 6 600mm 2 (210)(10 3 )kN/m 2 +35kN x 0.75m x 10 6 1200mm 2 (210)(10 3 )kN/m 2 + -45kN x 0.5m x 10 6 1200mm 2 (210)(10 3 )kN/m 2 + = = 0.61 mm Displacement of B relative to C ( δ BC ) = +35kN x 0.75m x 10 6 1200mm 2 (210)(10 3 )kN/m 2 = 0.104 mmExample

16. Shear Stress - single shear Shear stress: Bearing stress:

17. Shear Stress and Bearing Stress Shear stress acts tangential to the surface of the material. Average shear stress: Average bearing stress: Where n V m q V p a L n m d

18. Shear Strain and Hooke’s law in Shear Shear strain : change in the shape of the element is smallWhen Hook’s law in shear

19. Stress on inclined Plane

20. Thermal effect

21. The 100N weight of the rectangular plate acts at its midpoint. Determine the reactions exerted on the plate at B and C. if the pin at C is connected by a double shear pin. Pin’s lenghth is 2.5cm (0.5, 1.5, 0.5), The shear and bearing stress limit of the pin is 100MPa & 150MPa, if the safe factor is 1.5, what the minimum diameter of the pin? B A C 100N 45 O 4m Example

22. 2. the bar AB has a rectangular cross-section. Its area is 10 mm 2. AB is glued together at pq, theta = 30 degree. the shear stress limit on this surface is 50MPa, will this bar break?