Engineering Mechanics - Statics Episode 2 Part 9 ppsx

Engineering Mechanics - Statics Chapter 7024 Determine the force P needed to hold the cable in the position shown, i.e., so segment BC remains horizontal.. Engineering Mechanics - Static

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Engineering Mechanics - Statics Chapter 7

1050

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Draw the shear and moment diagrams for the beam.

Solution:

Problem 7-85

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Problem 7-86

Draw the shear and moment diagrams

for the beam.

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0 1 2 3 4 5 620

100

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0 5 10 15 2060

4020020

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024

Determine the force P needed to hold the cable in the position shown, i.e., so segment BC

remains horizontal Also, compute the sag yB and the maximum tension in the cable.

Units Used:

kN = 103N

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T max = max T ( AB , T BC , T CD , T DE ) y B = 3.53 m

P = 800.00 N

T max = 8.17 kN

Problem 7-90

Cable ABCD supports the lamp of mass M1 and the lamp of mass M2 Determine the maximum

tension in the cable and the sag of point B.

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⎛⎜

⎝ ⎞⎟ ⎠ ft

=

Problem 7-92

The cable supports the three loads shown Determine the magnitude of P1 and find the sag yD for

the given data.

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Problem 7-95

Determine the forces P1 and P2

needed to hold the cable in the

position shown, i.e., so segment CD

remains horizontal Also, compute the

maximum tension in the cable.

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⎝ ⎞⎟ ⎠ kN

=

T max = max F ( AB , F BC , F CD , F DE ) T max = 12.50 kN

F max = max F( AB , F BC , F CD , F DE) F max = 12.50 kN

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The cable supports the loading shown Determine the distance xB from the wall to point B.

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d d

The minimum tension occurs at θ = 0 deg

Problem 7-99

The cable is subjected to the triangular loading If the slope of the cable at A is zero, determine

the equation of the curve y = f(x) which defines the cable shape AB, and the maximum

tension developed in the cable.

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Apply boundary conditions y = x = and 0

x y

d d

γ x

F H

=

Guesses x 1 = 1 ft F H = 1 lb

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The cable is subjected to the triangular

loading If the slope of the cable at

point O is zero, determine the equation

of the curve y = f(x) which defines the

cable shape OB, and the maximum

tension developed in the cable.

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y 1

w x a

d d

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d d

The cable will break when the maximum tension reaches Tmax Determine the minimum sag h if

it supports the uniform distributed load w.

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A fiber optic cable is suspended over the poles so that the angle at the supports is θ

Determine the minimum tension in the cable and the sag The cable has a mass density ρ and

the supports are at the same elevation.

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A cable has a weight density γ and is supported at points that are a distance d apart and at the

same elevation If it has a length L, determine the sag.

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first two terms are retained (The answer indicates that the catenary may be replaced by a

parabola in the analysis of problems in which the sag is small In this case, the cable weight is

assumed to be uniformly distributed along the horizontal.)

Solution:

cosh x ( ) 1 x2

2 ! + +

A uniform cord is suspended between two points having the same elevation Determine the

sag-to-span ratio so that the maximum tension in the cord equals the cord's total weight.

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A cable has a weight denisty γ If it can span a distance L and has a sag h determine the length of

the cable The ends of the cable are supported from the same elevation.

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Problem 7-109

The transmission cable having a weight density γ is strung across the river as shown Determine the

required force that must be applied to the cable at its points of attachment to the towers at B and C.

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A chain of length L has a total mass M and is suspended between two points a distance d apart.

Determine the maximum tension and the sag in the chain.

d d

The cable has a mass density ρ and has length L Determine the vertical and horizontal components

of force it exerts on the top of the tower.

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Applying boundary conditions at x = 0; s = 0 to Eq.[1] and using the result

C 1 = F H tan ( ) θ yields C 2 = − asinh tan ( ( ) θ ) Hence

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Problem 7-113

A cable of length L is suspended between two points a distance d apart and at the same elevation.

If the minimum tension in the cable is Tmin, determine the total weight of the cable and the

maximum tension developed in the cable.

Units Used: kip = 103lb

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Problem 7-114

The chain of length L is fixed at its ends and

hoisted at its midpoint B using a crane If the

chain has a weight density w, determine the

minimum height h of the hook in order to lift

the chain completely off the ground What is

the horizontal force at pin A or C when the

chain is in this position? Hint: When h is a

minimum, the slope at A and C is zero.

A steel tape used for measurement in surveying has a length L and a total weight W How

much horizontal tension must be applied to the tape so that the distance marked on the ground

is a? In practice the calculation should also include the effects of elastic stretching and

temperature changes on the tape’s length.

Given:

L = 100 ft

W = 2 lb

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A cable of weight W is attached between two points that are a distance d apart, having equal

elevations If the maximum tension developed in the cable is Tmax determine the length L of the cable and the sag h.

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The beam is supported by a pin at C and a rod AB Determine the internal normal force, shear

force, and moment at point D.

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⎝ ⎞⎟ ⎠ kN

Problem 7-122

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