Download presentation

Presentation is loading. Please wait.

Published byXiomara Kimbro Modified over 2 years ago

1
**Forces and Moments MET 2214 Ok. Lets get started.**

My name is Dr Simin Nasseri, a faculty member here at MET and I am going to teach this course MET ????, Course name. Statics (MET 2214) Prof. S. Nasseri

2
Moments and Forces Part 2 Statics (MET 2214) Prof. S. Nasseri

3
**Calculating the moment using rectangular components**

The moment of a force F about the axis passing through point O and perpendicular to the plane containing O and F can be expressed using the cross product: Mo = r x F The magnitude of the moment is the area shown below: Statics (MET 2214) Prof. S. Nasseri

4
**Calculating the moment using rectangular components**

Mo = | r x F | = r F sinθ r = x i + y j + z k F = Fx i + Fy j + Fz k Statics (MET 2214) Prof. S. Nasseri

5
Resultant Moment Statics (MET 2214) Prof. S. Nasseri

6
Moments and Forces Part 3 Statics (MET 2214) Prof. S. Nasseri

7
Moment about an axis Sometimes the moment about a point is known and you are supposed to calculate its component about an axis. To find the moment, consider the dot product of Mo and unit vector along axis a: O: any point on a-a Statics (MET 2214) Prof. S. Nasseri

8
Moment about an axis You can also find the tangent force Fθ and then r x Fθ is the moment about aa: Statics (MET 2214) Prof. S. Nasseri

9
Example 1 Force F causes a moment MO about point O. What is the component of MO along axis oy (My)? Statics (MET 2214) Prof. S. Nasseri

10
**Scalar Analysis There are 2 methods to find My Scalar Analysis**

Vector Analysis (1) Scalar Analysis (first way): MO = (20)(0.5) = 10 N.m Imagine that we have found the direction of this moment (shown in figure) MO tends to turn the pipe around axis ob. The component of MO along the y-axis, My, tends to unscrew the pipe from the flange at O. Thus it is important to know its value. My = (3/5)(10) = 6 N.m Statics (MET 2214) Prof. S. Nasseri

11
**Scalar Analysis Scalar Analysis (second way):**

To find My directly (not form MO) it is necessary to determine the moment-arm, knowing that the distance from F to the y-axis is 0.3m: My = (20)(0.3) = 6 N.m In general, If the line of action of a force F is perpendicular to any specific axis aa thus: Ma = F .da Statics (MET 2214) Prof. S. Nasseri

12
Vector Analysis First, use the cross product formula to calculate the moment about O: MO = rA × F MO = (0.3i + 0.4j) × (-20k) MO = {-8i + 6j} N.m Then use the dot product of MO and the unit vector along y-axis to get My: My = MO . ua My = (-8i + 6j). (j) My = 6 N.m Statics (MET 2214) Prof. S. Nasseri

13
Vector Analysis We can always combine the two previous equations that you saw into one: MO = rA × F yielding a scalar My = MO . Ua My = (rA × F) . ua Or My = ua . (rA × F) Which is called triple scalar product Statics (MET 2214) Prof. S. Nasseri

14
**Remember the triple scalar product from Math section?!!**

Magnitude of moment M about axis aa’ Vector of moment M about axis aa’ Statics (MET 2214) Prof. S. Nasseri

15
Example 2 Statics (MET 2214) Prof. S. Nasseri

16
Example 2 Statics (MET 2214) Prof. S. Nasseri

17
Example 2 Statics (MET 2214) Prof. S. Nasseri

Similar presentations

OK

VECTORS AND THE GEOMETRY OF SPACE 12. VECTORS AND THE GEOMETRY OF SPACE So far, we have added two vectors and multiplied a vector by a scalar.

VECTORS AND THE GEOMETRY OF SPACE 12. VECTORS AND THE GEOMETRY OF SPACE So far, we have added two vectors and multiplied a vector by a scalar.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on weapons of mass destruction definition Ppt on bank lending policies Download ppt on android operating system Ppt on animal kingdom classification class 9 Ppt on financial inclusion in india Ppt on two point perspective city Ppt on trans-siberian railway Ppt on arc welding process Ppt on semi solid casting Ppt on national parks and sanctuaries in india