MEKTEKDAS - 04 Frame Analysis

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Topic 4

Frame AnalysisMeriam & Kraige:

Chapter 4.6



Fakutas Teknik Mesin dan DirgantaraInstitute Teknologi Bandung

MS2121 Mekanika Teknik DasarDr. M.A. Kariem © 2013

Analysis of Frames

• Frames and machines are structures with at least one multi-

force member. Frames are designed to support loads andare usually stationary. Machines contain moving parts and

are designed to transmit and modify forces.

• A free body diagram of the complete frame is used to

determine the external forces acting on the frame.

• Internal forces are determined by dismembering the frame

and creating free-body diagrams for each component.

• Forces between connected components are equal, have

the same line of action, and opposite sense.

• Forces on two force members have known lines of action

but unknown magnitude and sense.

• Forces on multi-force members have unknownmagnitude and line of action. They must be represented

with two unknown components.

2





Frames Which Cease to be Rigid when Detached from Their

Supports

• Some frames may collapse if removed from theirsupports. Such frames can not be treated as rigid

bodies.

• A free-body diagram of the complete frame

indicates four unknown force components which

can not be determined from the three equilibriumconditions.

• The frame must be considered as two distinct, but

related, rigid bodies.

• With equal and opposite reactions at the contactpoint between members, the two free-body

diagrams indicate 6 unknown force components.

• Equilibrium requirements for the two rigid

bodies yield 6 independent equations.

3





Sample Problem 6.4

Members ACE and BCD are

connected by a pin at C and by the

link DE . For the loading shown,determine the force in link DE and

the components of the force exerted

at C on member BCD.

SOLUTION:

• Create a free-body diagram for thecomplete frame and solve for the

support reactions.

• Define a free-body diagram for

member BCD. The force exerted by the

link DE has a known line of action butunknown magnitude. It is determined

by summing moments about C .

• With the force on the link DE known,

the sum of forces in the x and y

directions may be used to find theforce components at C .

• With member ACE as a free-body,

check the solution by summing

moments about A.

4





Sample Problem 6.4

5

SOLUTION:

• Create a free-body diagram for the completeframe and solve for the support reactions.

N4800 y y A F N480 y A

mm160mm100 N4800 B M A N300 B

x x A B F 0 N300 x A

07.28tan

150

801

Note:





Sample Problem 6.4

• Define a free-body diagram for member

BCD. The force exerted by the link DE hasa known line of action but unknown

magnitude. It is determined by summing

moments about C .

N561

mm100 N480mm06 N300mm250sin0

DE

DE C

F

F M

C F DE N561

• Sum of forces in the x and y directions may be used to find the force

components at C .

N300cos N5610

N300cos0

x

DE x x

C

F C F

N795 xC

N480sin N5610

N480sin0

y

DE y y

C

F C F

N216 yC

6





Sample Problem 6.4

• With member ACE as a free-body, check

the solution by summing moments about

A.

0mm220795mm100sin561mm300cos561

mm220mm100sinmm300cos

x DE DE A C F F M

(checks)

7





Machines

• Machines are structures designed to

transmit and modify forces. Their mainpurpose is to transform input forces into

output forces.

• Given the magnitude of P , determine the

magnitude of Q.

• Create a free-body diagram of thecomplete machine, including the reaction

that the wire exerts.

• The machine is a nonrigid structure. Use

one of the components as a free-body.

• Taking moments about A,

P b

aQbQaP M A 0

8





Sample problem 4.6

The frame supports the 400-kg load in themanner shown. Neglect the weights of the

members compared with the forces induced

by the load and compute the horizontal and

vertical components of all forces acting on

each of the members.

SOLUTION

9





Solution

10





Sample problem 4.7

Neglect the weight of the frame and compute the

forces acting on all of its members.

11





Solution Sample Problem 4.7

12

Draw FBD: Number of Unknown: 4

Number of Equations: 3

12





Solution Sample Problem 4.7 (Cont’d)

G

D

E

50 lbE

D

13






= 50 lb

14






= 100 lb

15 lb =

= -20 lb

15





Sample Problem 4.8

The machine shown is designed as an overload protection device which

releases the load when it exceeds a predetermined value T . A soft metalshear pin S is inserted in a hole in the lower half and is acted on by the upper

half. When the total force on the pin exceeds its strength, it will break. The

two halves then rotate about A under the action of the tensions in BD and CD,

as shown in the second sketch, and rollers E and F release the eye bolt.

Determine the maximum allowable tension T if the pin S will shear when the

total force on it is 800 N . Also compute the corresponding force on the hinge

pin A.

16





Solution Sample Problem 4.8

Draw FBD:

17






18





Sample Problem 4.10

In the particular position shown, the excavator applies a 20-kN force parallel to the

ground. There are two hydraulic cylinders AC to control the arm OAB and a singlecylinder DE to control arm EBIF .

(a) Determine the force in the hydraulic cylinders AC and the pressure p AC against

their pistons, which have an effective diameter of 95 mm.

(b) Also determine the force in hydraulic cylinder DE and the pressure pDE against its

105-mm-diameter piston.

Neglect the weights of the members compared with the effects of the 20-kN force.

19





a) Draw FBD:

20





b) Draw FBD:

21

MEKTEKDAS - 04 Frame Analysis

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