Engineering Mechanics - Statics Episode 2 Part 8 pdf

Determine the internal normal force, shear force, and moment in the beam as a function of x.. Hint:The moment loading is to be determined from a point along the centerline of the beam x

Support Reactions: From FBD (b),

The beam has depth a and is subjected to a uniform distributed loading w which acts at an

angle θ from the vertical as shown Determine the internal normal force, shear force, and

moment in the beam as a function of x Hint:The moment loading is to be determined from a

point along the centerline of the beam (x axis).

=

Problem 7-56

Draw the shear and moment

diagrams for the beam.

ΣFy = 0; − V 1

2 x w x L

The beam will fail when the maximum shear force is Vmax or the maximum moment is Mmax.

Determine the largest intensity w of the distributed loading it will support.

Solution:

The beam will fail when the maximum internal moment is Mmax Determine the position x of the

concentrated force P and its smallest magnitude that will cause failure.

Draw the shear and moment diagrams

for the beam.

A y w a

6

M C a

=

A y

2 w x a

0 2 4 6 8 10 12200

1000100

Problem 7-60

The cantilevered beam is made of material having a specific weight γ Determine the shear and

moment in the beam as a function of x.

Draw the shear and moment

diagrams for the beam.

=

0 2 4 6 8 10 12500

0500

Draw the shear and moment

diagrams for the beam.

0 10 20 30 40 50 60400

2000200

− 2250.00

Determine the normal

force, shear force, and

moment in the curved rod

The quarter circular rod lies in the horizontal

plane and supports a vertical force P at its

end Determine the magnitudes of the

components of the internal shear force,

moment, and torque acting in the rod as a

function of the angle θ

Draw the shear and moment

diagrams for the beam.

200010000

Problem 7-66

Draw the shear and moment diagrams

for the beam.

Problem 7-68

Draw the shear and moment

diagrams for the beam.

0 1 2 3 4 5 6 7 85

051015

Draw the shear and moment

diagrams for the beam.

0 0.5 1 1.5 2 2.5 3 3.5 44

202

Draw the shear and moment diagrams

for the beam.

−

=

0 2 4 6 8 10 12200

1000100

Problem 7-71

Draw the shear and moment

diagrams for the beam.

=

0 2 4 6 8 10 12500

0500

Draw the shear and moment diagrams for

the shaft The support at A is a journal

bearing and at B it is a thrust bearing.

Given:

F 1 = 400 lb F 2 = 800 lb

w 100 lb

2000020004000

Problem 7-73

Draw the shear and moment

diagrams for the beam.

0 1 2 3 4 5 6 7 815

1050510

Draw the shear and moment

diagrams for the shaft The support

at A is a journal bearing and at B it

is a thrust bearing.

0 1 2 3 4 5 6300

2001000

Problem 7-76

Draw the shear and moment diagrams for

the shaft The support at A is a thrust

bearing and at B it is a journal bearing.

Problem 7-77

Draw the shear and moment

diagrams for the beam.

0 10 20 30 400

100020003000

Problem 7-78

The beam will fail when the maximum moment

is Mmax or the maximum shear is Vmax.

Determine the largest distributed load w the

beam will support.

Units used: kip = 103lb

Given: M max = 30 kip ft ⋅ V max = 8 kip a = 6 ft b = 6 ft

Solution: Set w 1 kip

Moment limit - check critical points at A and betwen A and B

The beam consists of two segments

pin connected at B Draw the shear

and moment diagrams for the beam.

0 2 4 6 8 10 12 14 16 18 201000

500050010001500

1.104

500005000

Problem 7-80

The beam consists of three segments

pin connected at B and E Draw the

shear and moment diagrams for the

Guesses A y = 1 N B y = 1 N C y = 1 N

D y = 1 N E y = 1 N F y = 1 N Given

− 15.20 1.40 6.00

− 6.00

0 2 4 6 8 10 12 1430

20100102030

Problem 7-82

Draw the shear and moment diagrams

for the beam.

⎛⎜

⎝ ⎞⎟ ⎠ +

100102030

Problem 7-83

Draw the shear and moment

diagrams for the beam.

⎛⎜

⎝ ⎞⎟ ⎠ +

V1( ) x1

V2( ) x2

0 1 2 3 4 5 65

0510

Draw the shear and moment

diagrams for the beam.