Tutorial 7_Review MECH 101

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1

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

Statics

Question

0F

0M

choose

solve build

draw

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

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.

Build up equilibrium equationsBuild 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 : +

solve the force

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

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

45O

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

B C

100N

45O

BFCYF

CXF

Apply the equilibrium equation:

045cos CXo

BX FFF

010045sin CYo

BY FFF

021004 CYB FM

NFCY 50

NFCX 50

NFB 7.70

4m

Solution

Other things in staticsReplace the

distributed load

Two force member

0

L

F f x dx 0

( )L

f x xdx

dF

Mechanics of material

Internal force stress

deformation strain

statics

observation

Equilibrium equation

Equation of compatibility

Hook’s law

Normal Stress and Normal StrainNormal Stress and Normal Strain

A

P

L

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

PP

P

L

A

P

Remind strain is a dimensionless quantity

Hook’s Law and Poisson’s RatioHook’s Law and Poisson’s Ratio

E

strain axial

strain lateral

Hook’s law

Poisson’s ratio

Poisson’s ratio is also a constant, a property of the material, and dimensionless

PP

Note: A permanent strain exists in the specimen after unloading from the plastic region.

Dashed means the original shape with out P

Composite A-36 steel bar shown made from two segments AB and BD. Area AAB = 600 mm2 and

ABD = 1200 mm2.

Est = 210 GPa

Determine the vertical displacement of end A and displacement of B relative to C.

δ =PL

AE

Elongation → +δ, Contraction → -δ Tension → + P, Compression → - P

ExampleExample

δA = δA/B + δB/C + δC/D = PABLAB

AABE PBCLBC

ABCE + PCDLCD

ACDE +

+75kN x 1m x 106

600mm2(210)(103)kN/m2 +35kN x 0.75m x 106

1200mm2(210)(103)kN/m2 +

-45kN x 0.5m x 106

1200mm2(210)(103)kN/m2 +

=

= 0.61 mm

Displacement of B relative to C (δBC) = +35kN x 0.75m x 106

1200mm2(210)(103)kN/m2 = 0.104 mm

ExampleExample

Shear Stress - single shear

22

4, is the diameter of the bolt

14

V P Pd

A dd

Shear stress:

Bearing stress: , is the thickness of the bar or flangebb

b

F Ph

A d h

Shear Stress and Bearing StressShear Stress and Bearing Stress

A

Vaver

b

bb A

F PaLFb dLAb

Shear stress acts tangential to the surface of the material.

Average shear stress:

Average bearing stress: Where

22

PaLV

4

2dA

Where

n

V

m

q

V

p

aLnm

d

4

2dA

Shear Strain and Hooke’s law in ShearShear Strain and Hooke’s law in Shear

G

Shear strain : change in the shape of the element

is smallWhen

Hook’s law in shear

Stress on inclined Plane

)2cos1(2

1cos2 )2(sin

2

1cossin

Thermal effect

T T

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

100N45

O

4m

Example

NFCY 50

NFCX 50

NFB 7.70

2. the bar AB has a rectangular cross-section. Its area is 10 mm2 . AB is glued together at pq, theta = 30 degree. the shear stress limit on this surface is 50MPa, will this bar break?