Mechanics of Materials PDF

***1. Introduction*** Mechanics of materials\ - branch of mechanics that studies the **[internal effects of stress]** and strain in a solid body subjected to an external loading Stress\ - associated with **[strength of the material]** from which the body is made Strain\ - **[measure of deformatio...

***1. Introduction*** Mechanics of materials\ - branch of mechanics that studies the **[internal effects of stress]** and strain in a solid body subjected to an external loading Stress\ - associated with **[strength of the material]** from which the body is made Strain\ - **[measure of deformation]** Galileo\ - performed experiments, **[during 17th Century]**, to study the effects of load on rods and beams 18th Century\ - improved experimental methods for testing materials\ [Theoretical studies undertaken]\ - Saint-Venant\ - Poisson\ - Lame\ - Navier **EQUILIBRIUM OF A DEFORMABLE BODY** External Loads\ - A body **[subjected to only 2 types]** of external loads, namely surface forces or body forces Surface forces\ - caused by **[direct contact]** of one body with the surface of another Body Forces\ - developed when one body exerts a force on another body **[without physical contact]** **SUPPORT REACTIONS**\ Reactions\ - surface forces that **[develop at the supports or points of contact]** between bodies  Types of Connection\ - Cable, roller, smooth support, pin, fixed support **EQUATIONS OF EQUILIBRIUM** \- This equation **[balances the forces]** to prevent the body from translating motion, and balances the moments and prevents the body from rotating. Equilibrium\ - requires both a **[balance of forces and a balance of moments]** Internal Resultant Loadings\ Statics\ - primarily used to determine the resultant loadings that act within the body **4 Types of Resultant Loadings**\ - Normal Force (N)\ - Shear Force (V)\ - Torque (T)\ - Bending Moment (M) Normal Force (N)\ - perpendicular to the area\ - whenever external loads tend to **[push or pull]** on 2 segments of the body Shear Force (V) \- lies in the plane of the area \- developed when external loads cause 2 segments to **[slide over]** one another. Torque (T)\ - developed when external loads **[twist]** Bending Moment (M)\ - caused by external loads that tend to **[bend]** ***2. STRESSES*** Stress\ - describes the intensity of the internal force acting on a specific plane passing through a point. **[- formerly expressed as psi, now in N/mm\^2 or MPA]** **[- ksi/psi used in the English System]** Normal Stress\ - occur to members that are **[axially loaded]** Axial force\ - can be tension or compression & applied at the centroid of cross-section. 2 Types of Normal Stress \- Compressive stress \- Tensile stress Shear Stress\ - forces **[parallel to the area resisting force]** \- also known as tangential stress Bearing Stress\ - **[contact pressure between separate bodies]**\ - **[internal stress]** caused by compressive forces Thin-Walled Vessel = tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces which resist bursting, developed across longitudinal and transverse sections. 3 Types of Stress in Thin Walled Vessel \- Tangential Stress (Circumferential Stress) \- Longitudinal Stress\ - Spherical Stress Tangential Stress ( Circumferential Stress) Longitudinal Stress  3\. STRAIN Simple Strain\ - known as unit deformation Strain\ - ratio of change in length caused by the applied force Stress-strain Diagram (i don't fucking understand this, nilapag ko na lang) Metallic engineering materials get either as ductile or brittle\ Ductile Material\ - large tensile strains up to point of rupture Brittle Material\ - small strain up to the point of rupture Proportional Limit (Hooke's Law) What is Hooke's Law\ - Stress and strain take different forms in different situations\ - for **small deformations**, [the stress and strain are proportional] \- States the **[strain of material is proportional to the applied stress within the elastic limit]** of that material F = -kx Elastic Limit \- limit beyond wherein the material will no longer go back to its original shape when load is removed Elastic Range \- Region in stress from O to E Plastic Range \- Region in stress from E to R Yield Point\ - point in which the material will have an **[appreciable elongation or yielding without any increase in load]**. Ultimate Strength \- **[Maximum ordinate]** in the stress - strain diagram Rapture strength\ - strength of material at rupture\ - also known breaking strength Modulus of Resilience \- work done on a unit volume of material, gradually increased from O to P The **[resilience of the material]** is its ability to **[absorb energy w/o creating permanent distortion]** Modulus of Toughness \- work done on a unit volume of material, gradually increased from O to R \- The **[toughness of a material]** is its ability to **[absorb energy w/o causing it to break]** Hooke's Law Disadvantages\ - ceases to apply past the elastic limit\ - accurate only for solid bodies\ - isn't a universal principle Hooke's Law FAQs\ - applies to any elastic object of arbitrary complexity \- is linear, states that restoring force is proportional to displacement \- applies to perfectly elastic material but not beyond the elastic limit of material \- the negative sign on the spring's force means that the force exerted by the spring opposes the displacement \- essential because it helps us understand \- due to repeated stress and strain, the materials used in the bridge loses elastic strength and ultimately may collapse\ - When substance is subjected to repeated strain, the elastic properties of material get greatly impaired Various Types of Strain\ - Longitudinal Strain\ - Volumetric Strain\ - Shear Strain AXIAL DEFORMATION \- Stress is proportional to strain\ - given by  Stiffness\ - ratio of the **[steady force acting on an elastic body]** to the resulting displacement\ - unit of N/mm Shearing Deformation\ - Shearing forces cause shearing deformation\ - An element subject to shear does not change in length but in shape. Poisson's Ratio\ - measure of the amount of **[lateral strain caused due to the longitudinal strain]** of material\ - essential property and finds application primarily in engineering and design \