Engineering Mechanics Statics - Examples Part 7 docx

Determine the x, y, z components of reaction at these supports when the member is subjected to the loading shown... The maximum allowable tensile force in the members of the truss is Tma

− 50 25

The member is supported by a square rod which fits loosely through a smooth square hole of

the attached collar at A and by a roller at B Determine the x, y, z components of reaction at

these supports when the member is subjected to the loading shown.

Given:

M = 50 lb ft ⋅

F

20 40

− 30

a + b c

The platform has mass M and center of mass located at G If it is lifted using the three cables,

determine the force in each of these cables.

Units Used:

Mg = 10 3 kg kN = 10 3 N g 9.81 m

s 2

=

The platform has a mass of M and center of mass located at G If it is lifted using the three

cables, determine the force in each of the cables Solve for each force by using a single

moment equation of equilibrium.

− 0

e

0 0

− 0

The cables exert the forces shown on the pole Assuming the pole is supported by a

ball-and-socket joint at its base, determine the components of reaction at A The forces F1 and F2

lie in a horizontal plane.

The silo has a weight W, a center of gravity at G and a radius r Determine the vertical

component of force that each of the three struts at A, B, and C exerts on the silo if it is

subjected to a resultant wind loading of F which acts in the direction shown.

Initial Guesses: A z = 1 lb B z = 2 lb C z = 31 lb

Given

ΣMy = 0; B z r cos ( ) θ 1 − C z r cos ( ) θ 1 − F sin ( ) θ 3 c = 0 [1]

ΣMx = 0; − rsin B z ( ) θ 1 − C z r sin ( ) θ 1 + A z r − F cos ( ) θ 3 c = 0 [2]

The shaft assembly is supported by two

smooth journal bearings A and B and a

short link DC If a couple moment is

applied to the shaft as shown, determine

the components of force reaction at the

bearings and the force in the link The

link lies in a plane parallel to the y-z plane

and the bearings are properly aligned on

− 0 0

If neither the pin at A nor the roller at B can support a load no greater than Fmax, determine the

maximum intensity of the distributed load w, so that failure of a support does not occur.

=

Problem 5-93

If the maximum intensity of the distributed load acting on the beam is w, determine the reactions

at the pin A and roller B.

Problem 5-94

Determine the normal reaction at the roller A and horizontal and vertical components at pin B for

equilibrium of the member.

The symmetrical shelf is subjected to uniform pressure P Support is provided by a bolt (or pin)

located at each end A and A' and by the symmetrical brace arms, which bear against the smooth

wall on both sides at B and B' Determine the force resisted by each bolt at the wall and the

normal force at B for equilibrium.

A uniform beam having a weight W

supports a vertical load F If the ground

pressure varies linearly as shown,

determine the load intensities w1 and w2

measured in lb/ft, necessary for

Problem 5-97

The uniform ladder rests along the wall of a building at A and on the roof at B If the ladder has

a weight W and the surfaces at A and B are assumed smooth, determine the angle θ for

Determine the x, y, z components of reaction at the ball supports B and C and the ball-and-socket

A (not shown) for the uniformly loaded plate.

A vertical force F acts on the crankshaft Determine the horizontal equilibrium force P that must

be applied to the handle and the x, y, z components of force at the smooth journal bearing A and

the thrust bearing B The bearings are properly aligned and exert the force reactions on the

The horizontal beam is supported by springs at its ends If the stiffness of the spring at A is kA ,

determine the required stiffness of the spring at B so that if the beam is loaded with the force F, it

remains in the horizontal position both before and after loading.

− 4.95 14.85

− 10.5

=

− 7.07 18.38

− 13

=

The truss, used to support a balcony, is subjected to the loading shown Approximate each joint

as a pin and determine the force in each member State whether the members are in tension or

Positive means Tension, Negative means Compression

− 600 400

− 1414 1600

The truss, used to support a balcony, is subjected to the loading shown Approximate each joint

as a pin and determine the force in each member State whether the members are in tension or

Joint D: ( FDC FAD − ) cos ( ) θ + FDE = 0

− 800 0 1131 1600

− 3.13 9.37

− 9.37

− 6.25 18.75

− 18.75

Positive means tension, Negative means compression.

− 4.167

− 13.125

− 1.458

− 3.125

− 0

Determine the force in each member of the truss in terms of the external loading and state if the

members are in tension or compression.

The maximum allowable tensile force in the members of the truss is Tmax, and the maximum

allowable compressive force is Cmax Determine the maximum magnitude P of the two loads

that can be applied to the truss.

− 1.374 1.374 1.667

− 471

− 667 667 0 943

− 471

Negative means compression.

− 1179

− 1167 1167 500 1650

− 471

Negative means compression.

Problem 6-12

Determine the force in each member of

the truss and state if the members are in

− sin ( ) β − FCDsin ( ) α − FEC = 0

Joint E − FFE + FED = 0

FEC P2 − = 0

Joint D − FCD cos ( ) α − FED = 0

FCDsin ( ) α = 0

Negative means Compression

− sin ( ) β − FCDsin ( ) α − FEC = 0

Joint E − FFE + FED = 0

Negative means Compression

− 233.3 47.1

− 112.7 112.7 300.0 377.1

Negative means Compression

Joint B FBC FAB cos − ( ) φ = 0

− 266.7 188.6 56.4 56.4 0.0 188.6

Negative means Compression

Problem 6-16

Determine the force in each member of the truss in terms of the load P and state if the members

are in tension or compression.

Solution:

Support reactions:

ΣME = 0; Ax 3 2 d − P d = 0 Ax = 2P 3

The maximum allowable tensile force in the members of the truss is Tmax and the maximum

allowable compressive force is Cmax Determine the maximum magnitude of the load P that can

be applied to the truss.

− 0.373

− 0.333 0.373

− 1.202 0

Determine the force in each member of the truss and state if the members are in tension or

compression Hint: The horizontal force component at A must be zero Why?

Engineering Mechanics - Statics Chapter 6

− 692.82

Determine the force in each member of the truss and state if the members are in tension or

compression Hint: The resultant force at the pin E acts along member ED Why?

Units Used:

kN = 10 3 N

Units Used:

− 3 3

− 2.704 6.31

Negative means Compression

Problem 6-20

Each member of the truss is uniform and has a mass density ρ Determine the approximate force

in each member due to the weight of the truss State if the members are in tension or

compression Solve the problem by assuming the weight of each member can be represented as

a vertical force, half of which is applied at each end of the member.

− 389 314

− 736 1204

Negative means Compression

Problem 6-21

Determine the force in each member of the truss in terms of the external loading and state if the

members are in tension or compression.

Solution:

Joint B:

+ ↑ Σ Fy = 0 ; FBA sin 2 ( ) θ − P = 0

FBA = P csc 2 ( ) θ ( ) C +

→ Σ Fx = 0; FBAcos 2 ( ) θ − FBC = 0

FBC = Pcot 2 ( ) θ ( ) C

Joint C:

+

→ Σ Fx = 0; P cot 2 ( ) θ + P + FCDcos 2 ( ) θ − FCA cos ( ) θ = 0

+↑Σ F = 0; FCDsin 2 ( ) θ − FCA sin ( ) θ = 0

→ Σ Fx = 0; FDA − ⎡⎣ cot 2 ( ) θ + 1 ⎤⎦ ⎡⎣ cos 2 ( ) θ ⎤⎦ P = 0

FDA = ⎡⎣ cot 2 ( ) θ + 1 ⎤⎦ ⎡⎣ cos 2 ( ) θ ⎤⎦ P ( ) C

Problem 6-22

The maximum allowable tensile force in the members of the truss is Tmax, and the maximum

allowable compressive force is Cmax Determine the maximum magnitude P of the two loads that

can be applied to the truss

Initial guesses (assume all bars are in tension) Use a unit load

for P and then scale the answer later.

FBA = 1 kN FBC = 1 kN FCA = 1 kN

FCD = 1 kN FDA = 1 kN P = 1 kN

− 2.732 1.577

− 0.789

Engineering Mechanics - Statics Chapter 6

The Fink truss supports the loads shown Determine the force in each member and state if the

members are in tension or compression Approximate each joint as a pin.

Problem 6-24

Determine the force in each member of the double scissors truss in terms of the load P and state

if the members are in tension or compression.

Determine the force in each member of the truss and state if the members are in tension or

compression Hint: The vertical component of force at C must equal zero Why?

Units Used:

kN = 10 3 N

Given:

F1 = 6 kN

− 8 18.5 19.799

− 4.5

Negative means Compresson.

Problem 6-26

Each member of the truss is uniform and has a mass density ρ Remove the external loads F1

and F2 and determine the approximate force in each member due to the weight of the truss.

State if the members are in tension or compression Solve the problem by assuming the weight

of each member can be represented as a vertical force, half of which is applied at each end of

Guesses FAB = 1 N FAE = 1 N FBE = 1 N

FBC = 1 N FBD = 1 N FDE = 1 N Given

Joint E FDE FAE − = 0

FBE WAE WBE

− 857 1045

− 216 118

Determine the force in each member of the truss and state if the members are in tension or

Positvive means Tension, Negative means Compression

− 0 0

− 0 0

− 6.69 3.46

− 6.69 3.46

Joint I F2 + ( FGI FCI + − FAI ) cos ( ) θ = 0

FHI FBI − +(FGI FAI − − FCI)sin ( ) θ = 0

− 0

− 2.15

− 8.08

The Howe bridge truss is subjected to the loading shown Determine the force in members DE,

EH, and HG, and state if the members are in tension or compression.

Units Used:

kN = 10 3 N

The Pratt bridge truss is subjected to the loading shown Determine the force in members LD,

LK, CD, and KD, and state if the members are in tension or compression.

Units Used:

kN = 10 3 N

− 112.5 50

Problem 6-32

The Pratt bridge truss is subjected to the loading shown Determine the force in members JI,

JE, and DE, and state if the members are in tension or compression.

− 75

The roof truss supports the vertical loading shown Determine the force in members BC, CK,

and KJ and state if these members are in tension or compression.

Determine the force in members CD, CJ, KJ, and DJ of the truss which serves to support the

deck of a bridge State if these members are in tension or compression.