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Least Common Multiple and Greatest Common Factor

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algebraic language (Algebra)

algebraic language is simply to translate what we usually talk to particular expressions with symbols and numbers. When we speak of a situation where we need to find an answer, on all sides we hear phrases like: "it is best to write an equation."

The idea behind this is to manipulate unknown quantities with symbols easy to write. A simple example is the following statement:

What I spent on sweets in the shop was the price of each candy by the number of candy I bought.
Written

Algebraic Language may be as follows:

G = P · N

Here G means "what I spent," P means "sweet price" and N means "the amount of candy."

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With Pride ... We are winning. Thank you very much. Task 14

have received from Professor Luis Parada an appreciation for the work of this blog.

On behalf of myself and my readers thank you very much, these surveys we serve as encouragement to all those our blog visitors have a better guide to mathematics, and that messages that are placed here for reflection and motivation to serve in this magical world of letters and numbers.



These awards are not economic, however, serve to enhance the brotherhood between bloggers and thus strengthen the bonds of friendship between all of us.



I say, I should reward bloggers other friends, I decided to return the favor to my friend Luis and reward if Blog:

123xyz_Matemáticas and more

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beams Task topic homogeneous subjected to pure bending:

Exercises 4.4 & 4.5

The steel beam shown is made of steel s _And = 250 MPa and s U = 400 MPa . Using a safety factor of 2.50, a) determine the maximum torque that can be applied to the beam when flexed to the axis z .

b) Now suppose that the beam is bent about the center and , determine the maximum torque that can be applied to beam.

Exercise 4.6 & 4.7

A beam that has the section shown is made of an aluminum alloy, s _And = 45 ksi and s U = 70 ksi . Using a safety factor of 3.00, a) find the maximum torque that can be applied to the beam when flexed to the axis z .

Now suppose that the beam is bent with respect to the axis and b) determine the maximum torque that can be applied to the beam.

Exercise 4.8

two vertical forces are applied to the beam cross section shown. Find the maximum forces of tension and compression in the BC portion beam.

Exercise 4.9

two vertical forces are applied to the beam cross section shown. Halle voltage maximum efforts and compression in the BC portion beam.

Exercise 4.10

two vertical forces are applied to the beam cross section shown. Find the maximum forces of tension and compression in the BC portion beam.

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Solid Mechanics Solid Mechanics Task 13 Task 12

Task topic shaft angle of twist non-circular section:

Exercises 3,112, 3,113, 3,114 & 3,115

Each of the three steel bars, shown in the figure below, is subject a torque of magnitude T = 275 Nm . Knowing that the allowable shear stress is 50 MPa , find: a) the size b required in each bar.

Each of the three bars, shown below, is subject to a torque of 5 kips ¨ and . If the allowable shear is 8 ksi , find: b) dimension b required of each bar.

Each of the three bars of aluminum, shown in the figure below, should be subjected to torsion angle of 1.25 °. Knowing that b = 1.5 in. , adm t = 7.5 ksi and G = 3.7 ' ⁶ 10 psi , find: c) the minimum allowable size of each bar.

Each of the three aluminum bars, which are shown below, should be subjected to torsion angle of 2 º. Knowing that b = 30 mm , adm t = 50 MPa and G = 26 GPa , Find: d) the minimum allowable size of each bar.

Exercises 3,116, 3,117, 3,118 & 3,119

axes A and B are the same material and have the same cross-sectional area, but A a circular section and B square section. Determine the ratio of maximum shear stresses occurring in A and B, respectively, when the two axes are subjected to the same torque (T _A B T = ). Assume that both deformations are elastic.

axes A and B are the same material and have equal length and equal cross-sectional area, but A is circular section and section B square. Determine the ratio of maximum torque _A T and T B can be safely applied to A and B, respectively.

axes A and B are the same material and have equal length and equal cross-sectional area, but A have circular cross section and B has section square. Find the relationship between the maximum angle of twist f _A and B f they can safely undergo axes.

axes A and B are the same material and have equal length and equal cross-sectional area, but A a circular section and B square section. Determine the ratio of the torsion angles f _A and B f when subjected to both axles at the same torque (T _A = T _B ). Assume that both deformations are elastic.

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Solid Mechanics

Task topic Power Transmission Shafts:

Exercises 3.62 & 3.63

When a hollow shaft rotates at 180 rpm , a strobe indicates that the torsion angle is 3 °. Knowing that G = 77 GPa , determine: a) the transmitted power, b) the maximum shear stress in the shaft. The shaft dimensions are shown in the figure below.

The hollow shaft, shown in the figure above ( G = 77 GPa , t Adm = 50 MPa ) rotates at 240 rpm . Determine c) the maximum power that can be transmitted, d) the corresponding torsion angle of the shaft.

Exercise 3.64

A hollow steel shaft (G = 11.2 x 10 ⁶ psi) has 8 feet in length and inner and outer diameters are 2.50 and 2.25 inches , respectively. Knowing that the shaft 200 transmits hp at 1500 rpm , determine: a) the maximum shear stress, b) the torsion angle of the shaft.

Exercise 3.65

Knowing that G = 11.2 x ⁶ 10 psi and adm t = 6000 psi for steel to be used, determine: a) the capacity of a smaller diameter solid shaft to be transmitted 18 hp at 2400 rpm , b) the corresponding angle of twist in a length of 6 feet on the shaft.

Exercises 3.66 & 3.67

Two solid shafts and two gears (shown in the figure below) are used to transmit 12 kW engine A , spinning at 20 Hz to a machine tool D . Knowing that each axis has 25 mm in diameter, find the maximum shear stress: a) on the axis AB , b) on the shaft CD.

The two solid axles and gears shown in the figure above are used to transmit 12 kW motor A , spinning at 20 Hz , a machine tool D . Knowing that the maximum permissible shear stress is 60 MPa for each axis, find the diameter: c) AB axis , d) axis CD.

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Task 11 Solid Mechanics 9 & 10 Task

Task Torsion Axles issue Statically Indeterminate:

Exercises 3.45 & 3.46

Two solid steel shaft (G = 11.2 x ^{10 6 psi} ) are connected to a coupling disk B fixed media and A and C . For the load shown in the figure below, determine: a) the reaction at each support, b) the maximum shear stress AB, c) the maximum shear stress in BC.

Now suppose that the axis AB is replaced by a hole in the same outside diameter and 1 inch inner diameter, determine: d) the reaction at each support, e) the maximum shear stress AB , f) the maximum shear stress BC .

Exercises 3.47 & 3.48

cylinders AB and BC are united in B, and A and C to fixed supports. Knowing that AB is Aluminum ( G = 26 GPa ) and BC Brass ( G = 39 GPa ), find for the load shown in the figure below: a) reaction at each support, b) the maximum shear stress AB, c) the maximum shear stress in BC.

Now suppose that AB is steel (G = 77 GPa) instead of aluminum, finds to the load shown in the figure below: d) The reaction at each support, e) the maximum shear stress in AB , f) the maximum effort shear BC.

Exercises 3.49 & 3.50

solid shaft AB and CD sleeve are both attached to short cylinder E . The steel shaft AB has a G _s ^{= 11.2 x10 6 psi} and (t adm) _s = 12 ksi while shirt Brass CD has a G _b = 5.6 x 10 6 psi and (t adm) _b = 7 ksi . Find the maximum torque that can be applied to the cylinder E shown in the figure below.

If you apply a torque T of 20 kips ¨ and the cylinder E the figure below, determine: a) the maximum shear stress on the shaft AB, b) the maximum shear shirt CD .

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