MODULE-1-PRINCIPLE-OF-STATICS-RESULTANT-OF-FORCE-SYSTEM

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Pangasinan State University**We aren't endorsed by this school

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BS ARCHITE 12

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Mechanical Engineering

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Jan 15, 2025

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STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System PRINCIPLES OF STATICS, RESULTANT OF FORCE SYSTEM Prepared by: Engr. Edsel A. Balberan STATICS OF RIGID BODIES

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System TOPIC OUTLINE Lesson 1: Force System Lesson 2: Axioms of Mechanics Lesson 3: Introduction to Free-Body Diagram Lesson 4: Forces and Components Lesson 5: Resultant of Three or More Concurrent Forces Lesson 6: Moment of a Force Lesson 7: Varignon’s TheoremLesson 8: Resultant of Non-Concurrent Force System LEARNING OBJECTIVES At the end of this module, you as BS Architecture students should be able to: a. Illustrate the principles of statics b. Show or draw free-body diagram; c. Solve problems relating to resultant force d. Categorize force and moment e. Analyze and solve problems relating to moments. ACTIVITING PRIOR KNOWLEDGEEngineering Mechanics–science which considers the effect of forces on rigid bodies. Types: Statics–considered the effects and distribution of forces on rigid bodies Dynamics–considered are the motion of rigid bodies cause by forces acting upon them. Force –that which changes or trends to change the state of motion of a body. This definition applies to the external effects of a force. The internal effects of a force is to produce stress and deformation in the body on which the force acts. Characteristics of a Force: 1. Its magnitude 2. The position of its line of action 3. The direction or sense in which the force acts along its line or action 1.1 FORCE SYSTEM Force System–any arrangement where two or more forces acts on a body or any group of related bodies.

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System Coplanar Force System–lines of action of all the forces lie in one plane. Non Coplanar Force System–lines of action of two or all the forces do not lie in one plane. 1.2 AXIOMS OF MECHANICS 1. The parallelogram law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces. 2. Two forces are equilibrium only when equal in magnitude, opposite in direction, and collinear in action. 3. A set of forces in equilibrium may be added to any system of forces without changing the effect of the original system. 4. Action and reaction forces are equal but oppositely directed. 1.3 INTRODUCTION TO FREE-BODY DIAGRAM A sketch of the isolated body which shows only the forces acting upon the body is defined as a free-body diagram. The forces acting on the free body are the action forces, also called the applied forces. The reaction forces are those exerted by the free body upon other bodies. 1.4 FORCES AND COMPONENTS RESULTANT OF FORCE SYSTEM Components for Force Fx = F Cosɵx Fy= F SInɵxIf values of Fx and Fy are known, F = √(𝑭?)𝟐+ (𝑭?)𝟐, tan ɵx= 𝐅?𝐅?

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System Sign convention: Fx = (+) if direction to the right Fx = (-) if direction to the left Fy = (+) if direction is upward Fy = (-) if direction is downward (Examples 1; 204/18) Determine the x and y components of each of the forces shown in figure below. Solution: (Example 2; 206/19)The triangle block shown below is subjected to the loads P = 1600lb and F = 600lb. If AB = 8in and BC = 6in, resolve each load into components normal and tangential to AC. Solution:

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System 1.5 RESULTANT OF THREE OR MORE CONCURRENT FORCES (Example 3; 221/24) The resultant of the concurrent forces shown below is 300lb pointing up along the y-axis. Compute the values of F and ɵrequired to give this resultant. Solution: ΣFx = Rx = Fx + Px + Qx ΣFy = Ry = Fy +Py - Qy R = √(𝑹?)𝟐+ (𝑹?)𝟐ɵx= Arctan𝐑?𝐑?

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System 1.6 MOMENT OF A FORCE The moment of a force about an axis or line is the measure of its ability to produce turning or twisting about the axis. The magnitude of the moment of a force about an axis which is perpendicular to a plane containing the line of action of the force is defined as the product of the force and the perpendicular distance from the axis to the line of action of the force. M = Fd unit will be N-m,lb-in, kips-ft 1.7 VARIGNON’STHEOREM THE PRINCIPLE OF MOMENTS. VARIGNON’S THEOREMThe moment of the force is equivalent to the sum of the moments of its components Mo = F(d) = Fx(y) –Fy(x) (Example 4; 226/30) From the figure on right side, assuming clockwise moments as positive, compute the moment of Force F = 450lb and Force P = 361lb about points A, B, C and D.Solution:

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System 1.8 RESULTANT OF NON- CONCURRENT FORCE SYSTEM Rx = ΣFx , Ry = ΣFy ,

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System R = √(𝑹?)𝟐+ (𝑹?)𝟐, M = Rd (Example 5; 265/45) Compute the resultant of the 3 forces shown below. Locate its intersection with the X and Y axes. Solution:

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System LEARNING ACTIVITY Let us test what you have learned for today. Problem 1: Find the components of parallel to x and y of the forces acting as shown Problem 2: Find the resultant of concurrent forces shown in the figure below. Problem 3: Compute the perpendicular distance from E and G to the line BD.

STATICS OF RIGID BODIES MODULE 1: Principles of Statics, Resultant of Force System MODULE 1: Principles of Statics, Resultant of Force System Problem 4: Determine the resultant of the 3 forces acting on the dam shown and locate its intersection with the base AB. Problem 5: The block shown below is acted upon by its weight W = 200lb, a horizontal force Q = 600lb, and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint: Take one axis parallel to the incline \ SU SUMMARY In In Engineering mechanics, the subjects divides naturally into two parts: statics and dynamics In the force system, the X component of Resultant is the summation of X components of all forces acting on a body. While the Y component of Resultant is the summation of Y components of all forces acting on a body. The sign convention of moments are positive (+) if the moment direction is clockwise and negative (-) if the moment direction is counter clockwise. SU REFERENCES Engineering Mechanics 2ndEdition by Ferdinand L. Singer