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Compute Tension T1 & T2
Static is a computational analysis study to determine that a rigid body under analysis will remain in equilibrium state or static. In order for a rigid body to remain in static or equilibrium state, the summation of all known acting forces on a rigid body must be equal to zero. There are many known acting forces on a rigid body that you will encounter in your study of engineering such as tensional force, compression force, torsional force, axial force, radial force and so on.
What will happen if the system of forces are not in equilibrium state or static? You will see cables are snapping, chain are breaking, bridge failing, building structures failing and so on. Because of computer technology and the guidance from many experts that reviewed and analyzed previous failures it is now easy to predict ahead of time if the rigid body structure will remain stable for 50 years or more .
Engineering schools and many engineering professional society are leading the way for transferring the knowledge on how to do computational analysis. With internet and cloud technology, now we have additional ways for knowledge transfer.
In mathematical formula :
∑Fx=0 , This symbol means adding all the forces along x-axis, it must be zero for equilibrium.
∑Fy=0 , This symbol means adding all the forces along y-axis, it must be zero for equilibrium.
Read below the manual calculation. Automated Intelligence is another meaning of AI. This becomes possible because of internet, cloud technology, 5G communication, and fast microprocessor.
Tensile strength vs Working load of a rope ? Explain the difference. How is this related to calculating the tension in order for the system of forces to remain in static equilibrium that you are trying to learn? Remember when the ropes or cables breaks while lifting load it means the system of forces is no longer in static equilibrium.
Assuming the rope used in above figure is 1/2 inch diameter with a tensile strength of 9,600 lbf (pound force) . Will the rope break when used to lift the engine weighing 3,500 N ?
Now assume again that you don't have any tensile strength data for 5/16 inch diameter rope. But you know by experience the tensile strength of 1/2 diameter of rope is about 9,600 lbf. Will the 5/16 inch rope break when used to lift the 3,150 N load? To answer this safety question, we go back to manufacturer design and specification and review engineering analysis.
These are the types of questions technician, supervisor, engineer, manager or any qualified and trained person with responsibility to make safety decision in relation to equipment or employee are facing from time to time.
And since most of us forget our formula and how to use our scientific calculator to calculate the tension (related to tensile strength - breaking of rope or cable ) because we seldom use it. Would it be nice to have a smartphone apps to help us find the formula and calculator to help us make safe decision at the moment we needed it? That is the reason why, INVBAT.COM was created to help any qualified and trained person who has the responsibility to make safe decision.
reference material :
Tensile strength is the average pound force where the new rope tested according to ASTM method D - 6268 standard is expected to break.
While working load is the rope's manufacturer recommended tensile strength with comfortable safety margin and longer usage of the rope. Usually the working load is between 15% and 25% of the published tensile strength of the rope.
HOW TO USE: Enter new number on white input boxes. Answer is automatic. To prove it, what is the tension of T-1 and T-2 if the weight = 6000 N.
With the same angles.
Answer T-1 = 6286 N and T-2 = 1108 N.
Given angle in degree ∠ T2 , 80 °
Given angle in degree ∠ T1 , 10 °
Given weight, 3150 in N, Newton
ANSWER: T-1 =
N,
ANSWER: T-1 = lbf, pound force
ANSWER: T-2 = N,
ANSWER: T-2 = lbf, pound force
∑Fx=0 , This symbol means adding all the forces along x-axis, it must be zero for equilibrium.
∑ Fx = 0
T-2x +
T-1x = 0
T-2 + T-1 = Equation 1
Derivation of equation 1 and equation 2 are explain below.
100% of Tension 2 (T-2) is also the same as 100% of hypotenuse as shown by the free body diagram of forces. 100% written in decimal form is (1)T-2 , which is the hypotenuse from the free body diagram of forces.
Memory recall lesson learned about vector addition, the hypotenuse, is also called the resultant vector. It is the result of adding the horizontal vector force of T-2 and the vertical vector force of T-2.
We are only interested in finding what is the value of horizontal vector force of T-2.
To do that we recall our lesson learned in Trigonometry about definition of Cosine and Sine. For example sine 80° = opposite side of angle 80° (T-2x) / hypotenuse (T-2) = 0.9848
You do the same analysis for sine 10° = 0.1736 ; cosine 80° = 0.1737 and finally for cosine 10° = 0.9848.
|
Given data ∠ T2
Sine ° |
= |
T-2 , opposite side
T-2 , hypotenuse
|
|
Given data ∠ T1
Sine ° |
= |
T-1, opposite side
T-1 , hypotenuse
|
∑Fy=0 , This symbol means adding all the forces along y-axis, it must be zero for equilibrium.
T-1y + T-2y + W = 0
∑Fy=0; T-1 + T-2 = W Equation 2
Then using your acquired knowledge of solving two simultaneous linear equations to find the value of T-1 (Tension 1 Force) and T-2 (Tension 2 Force). You will get T-1 = 3,300.13 N and T-2 = 581.74 N if your calculations are close to those numbers they are correct due to the round off error.
|
Given data ∠ T2
Cosine ° |
= |
T-2 , adjacent side
T-2 , hypotenuse
|
|
Given data ∠ T1
Cosine ° = |
= |
T-1 , adjacent side
T-1 , hypotenuse side
|
ANSWER:
T-1 = N
T-2 = N
Formula Recall:
Sine of angle = opposite side of angle divided by hypotenuse.
Cosine of angle = adjacent side of angle divided by hypotenuse
Reposted by Kiran Vedante, Senior Transformer Design Engineer - Neeltran Inc.
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