Supplementary notes to statics of rigid bodies mech 400
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Tips to remember when reviewing for the exams.

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Supplementary notes to statics of rigid bodies mech 400

Supplementary Notes to Statics of Rigid BodiesMECH 400

ACCA


Points to ponder for mech 400 prelims

REACTIONS

  • Always start by taking the sum of the moments at the SUPPORTS

  • It is usually advisable to convert the force(s) into its x- and y- components so that it will be easier to obtain the perpendicular distance(s)

  • Remember that the directions of the reactions are only ASSUMED at the beginning


Reactions

6”

W

D

C

8”

B

4”

F

G

4”

E

A

9”

9”

Reactions

D and B are both pin-connected or pin-supported. The reactions at these two (2) joints are only internal.

Therefore, when you take the moment at any point while considering the whole system, the only reactions will be Av and Ev plus the external load W.

Av

Ev

Figure 1


Reactions1
Reactions

Only when isolating the member does the internal reactions of a pin-supported joint become exposed.

Notice that the reaction at C is only vertical. This is due to the normal contact between the two members meeting at point C.

C

Bh

B

F

FG

A

ISOLATED MEMBER ABC

Av

Cv

Bv


Normal reactions
Normal Reactions

D

B

A

A

C

B

C

Isolating Member AB

A

B

Isolating Member AC

Av

RB

A

B

Isolating Member AC

A

C

Note that RB is perpendicular to AC

Av

C


Points to ponder for mech 400 prelims

  • NORMAL REACTIONS are normal to the surface of THE MEMBER whose side or surface is acted upon by the tip or end of the other member in contact


Distinguishing frames from trusses
Distinguishing Frames from Trusses

  • Problems about FRAMES are usually those involving members with THREE FORCES

  • Remember that three-force members (as in the case of frames) can only be solved using the Method of Members

  • In the Method of Members, we always solve the reactions by ISOLATING each members and drawing the FREE BODY DIAGRAMS (FBDs) of each isolated member

  • Know when to distinguish external from internal reactions (stated in previous slides)

  • ONLY EXTERNAL REACTIONS are exposed when considering the WHOLE SYSTEM

  • Internal forces (with respect to certain members and joints) only come out when the member being considered has been ISOLATED


Trusses
Trusses

  • Always start the solution by taking moments at the SUPPORTS

  • The forces on the trusses are found ONLY AT THE JOINTS

  • NEVER FORGET to include all the members connected to the JOINT considered when using the Method of Joints


Trusses1
Trusses

When using the Method of Sections, always include ALL the external forces and reactions AND the CUT MEMBER forces of the considered side of the cutting line

Isolating Joint C

15KN

C

FBC

FCD

RE

FCF

FCG


When to eliminate reactions
When To Eliminate Reactions

  • TRUSS SYSTEMS: When ALL LOADS are vertical AND the truss is SIMPLY SUPPORTED, the horizontal reaction can be eliminated.

  • A SIMPLY SUPPORTED system means the system has ONE ROLLER AND ONE HINGE/PINfor the supports

  • IF BOTH ROLLER AND HINGE/PIN are lying on the HORIZONTAL SURFACE, there are TWO VERTICAL REACTIONS and ONE HORIZONTAL REACTION. Therefore, the horizontal reaction can be equated to ZERO.


Simple reactions
Simple Reactions

10 k

5 k

10 k

This truss system that is SIMPLY SUPPORTED has a hinge at A and a roller at G and both supports are lying on the horizontal surface.

Because all loads are vertical, the horizontal reaction at A is equal to ZERO.


Simple reactions1

F

A

80 mm

B

320 mm

Simple Reactions

For this example, even if the system is simply supported, the HORIZONTAL REACTIONS cannot just be cancelled or equated to zero!

Note that the supports are stuck along the vertical.

In this case, there are TWO HORIZONTAL REACTIONS. Hence, you cannot just cancel the horizontal reactions or equate them to ZERO even if there is NO HORIZONTAL LOAD on the system.


Other cases
Other Cases

Example: The horizontal member AB has been isolated. Assuming both A and B are pin connected, how do you solve for the reactions?

The member is carrying a vertical load W.

W

Horizontal Member

A

B

Ah and Bh can both be cancelled BECAUSE the horizontal reactions pass through a horizontal member!


Other cases1
Other Cases

What happens if the isolated member AB is diagonal?

B

Diagonal Member

W

A

Ah and Bhare NOT EQUAL TO ZERO because they don’t pass through a horizontal member.


Other cases2
Other Cases

What happens if the isolated diagonal member AB is carrying a horizontal loading?

B

W

A

Don’t forget to include the load W when solving for the reactions by taking the moment at any of the supports (or joints for this case)!

Av and Bvare NOT EQUAL TO ZERO even if there is no vertical load and even if the weight has been neglected because they don’t pass through a vertical member.

Note that if you take the moment at either A or B, the vertical reactions will have perpendicular distances respectively!


Other cases3
Other Cases

A and D are both supported by hinges.

Similarly for trusses that have horizontal loads only, and there are vertical reactions at the supports, the vertical reactions CANNOT JUST BE CANCELLED!

C

B

W

D

E

A

F

Take note that there are TWO Vertical Reactions here and they don’t pass through just one vertical member.

Taking moments at any of the supports, Av and Dv would each have its perpendicular distance.


Other cases4
Other Cases

A and D are both supported by hinges.

For this case, there are no horizontal loads BUT the horizontal reactions of A and D are also NOT EQUAL TO ZERO.

C

W

B

D

E

A

F

Take note that there are TWO Horizontal Reactions here and they don’t support and pass through just one horizontal member.

Taking moments at any of the supports, Ah and Dh would each have its perpendicular distance.


Points to ponder for mech 400 prelims


God bless and best of luck on your preliminary examinations
God bless and best of luck on your preliminary examinations! THE SOLUTION OF A CERTAIN PROBLEM. THAT WAY, IT WILL BE EASIER FOR YOU TO SOLVE JUST ABOUT ANY PROBLEMS THAT WILL COME OUT IN THE EXAMS. 