Group Exercises I

7/31/2019 Group Exercises I

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Group exercise 02 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Name the units for weight and mass in the SI and U.S. Customary

systems.

Weight: N and lb Mass: kg and slug



Group exercise 03 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Graphically resolve the 250 N force vector into components in

the u and v directions.



Group exercise 04 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Sketch the unit vector in the direction of F on the diagram and

label it using appropriate notation. What is the magnitude of the

unit vector (be sure to include units)?

ˆF

u

lblb

ˆ 1 1F

u



Group exercise 05 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Sketch the position vector of point A relative to the origin and

label it using proper notation. What units does the magnitude of

the position vector have?

OAr

2 22 m 4 m 2 5 m

OAr



Group exercise 06 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Draw the free body diagram (FBD) of ring E for the problem

below. Be sure to label all know quantities as specified by the

procedure for drawing FBDs.

40 9.81 N BF

AF

BF



Group exercise 07 – EMCH 211 – Fall 2011 – Dr. Kevin McFall What are the unknown quantities for a free body diagram (FBD)

consisting of ring A? Is this single FBD and its accompanying

equations of equilibrium sufficient to solve for all the identified

unknowns?

The tensions in cables AB, AD, and AC are the unknownquantities, and the three equations of equilibrium are sufficient

to solve for all of them.



Group exercise 08 – EMCH 211 – Fall 2011 – Dr. Kevin McFall If d = 1 ft and F = 12 lb then the magnitude of the resulting

moment about pointO

is M

O

=

12

ft

lb. Write the vector MO.

12 ft lbO

M k

x

y

z



Group exercise 09 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Provide definitions for the following terms:

Couple Couple moment

Couple: two parallel forces of equal magnitude and

opposite direction Couple moment: the moment produced by a couple



Group exercise 10 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Answer true or false to the following statements:

1. For any system of forces and moments acting on a freebody, an equivalent system exists only if equilibrium is

satisfied by the original system.

2. Figure 1 represents a coplanar force system.

3. Figure 2 represents a concurrent force system.

4. It is possible to reduce the force system in Figure 1 with an

equivalent system consisting of only a force (and no

moment) about any arbitrary choice of point O.

Figure 1 Figure 2

1. False – an equivalent system always exists

2. False – this is a parallel force system

3. False – this is a coplanar force systems

4. False – only one point exists where this is true



Group exercise 11 – EMCH 211 – Fall 2011 – Dr. Kevin McFall For a beam of length L and width b experiencing a pressure p

varying only in the x direction, the coplanar distributed load w is

denoted as the product of pressure and width. Describe in words

the physical significance of the quantity w and indicate its

dimensions.

The coplanar distributed load represents the intensity of the

loaded force per unit length of the beam and has dimensions of

force over length.



Group exercise 12 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Consider connecting a bar of negligible weight to the ground

with either a fixed connection (like a weld) as in the left figure,

or with a pin connection as in the right figure. If a horizontal

force is applied as shown, will the bar move in each case? What

is the difference in the load(s) experienced between the bar and

the connection in both cases?

The fixed connection will not allow movement (neither

translation nor rotation), but the bar with the pin connection will

rotate. Both fixed and pinned connections support a force (which

may be point in any direction), but only the fixed connection

supports a moment (and thus prevents rotation).

F

F



Group exercise 13 – EMCH 211 – Fall 2011 – Dr. Kevin McFall For each of the four cases

1) The system is statically indeterminate2) The system is partially constrained

3) The system is improperly constrained

4) The system is unstable

identify which of the following statement(s) could be true.

a) The number of unknown reactive loads is zero

b) The number of unknown reactive loads is fewer than the

number of available equations of equilibrium

c) The number of unknown reactive loads is equal to the

number of available equations of equilibrium

d) The number of unknown reactive loads exceeds the number

of available equations of equilibrium

1) d2) b3) c4) a, b or c



Group exercise 14 – EMCH 211 – Fall 2011 – Dr. Kevin McFall How many equations of equilibrium are available for the 2D and

3D method of joints (two potentially different answers)?

Bonus (1 point): Consider solving for the forces in each

member of the truss illustrated below. If any useful information

is to be gained from beginning with an analysis of the free body

diagram of point A, what step must first be completed?

With a point as the free body, only sum of forces is available.

This leads to 2 or 3 available equations of equilibrium in 2D and

3D, respectively. The reactions at A and C must first be

determined using a FDB of the entire truss if point A is to be

analyzed first.



Group exercise 15 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Draw a single free body diagram (FBD) sufficient to solve for

the force in member DG. Mark each external load in the FBD as

a known or unknown quantity.

FGF

DGF

DC F

Known Unknown





Group exercise 17 – EMCH 211 – Fall 2011 – Dr. Kevin McFall Name one significant difference between truss analysis and the

analysis of frames and machines.

Frames and machines generally consist of multiforce members.

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Group Exercises I