3 stress transformations
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This document discusses stress transformations, which are calculations of stresses in multiple planes within rigid bodies. It provides learning objectives about calculating stresses in different planes, defines stresses within rigid bodies and stress elements. It then recalls the definition of stresses in 3D and discusses summing forces on an inclined stress element. Finally, it presents equations to calculate the transformed stresses σxx', σyy' and τxy' in a new coordinate system defined by the angle θ.
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This document discusses diarthrodial joints and joint motion. It identifies important connective tissue structures in diarthrodial joints like synovial fluid, articular cartilage, meniscus, ligaments, tendons, and muscles. These structures provide lubrication, load distribution, joint stability, and transmission of forces. Joints allow six degrees of freedom consisting of three translations and three rotations. Applying statics to joint biomechanics problems requires assumptions like known axes of rotation and muscle attachments, negligible friction, and consideration of only two-dimensional forces. Anthropometric data provides average human body measures used in the analysis.
10 hard and soft tissue biomechanics
This document discusses the viscoelastic properties of biological materials like bone and ligament, noting that the elastic modulus and strength of bone increases as the strain rate increases from slow walking to fast running. It also explains that bone is composed of mineralized collagen fibrils, giving it viscoplastic behavior where it will continue to deform under constant stress over time without fracturing. Graphs are presented showing the relationship between bone strain over time and increases in modulus and strength with higher loading rates.
8 beam deflection
This document discusses beam deflection. It begins by defining beam deflection and the factors that affect it, including bending moment, material properties, and shape properties. It then presents the general formula for calculating beam deflection using double integration of the bending moment equation. Examples are given of using boundary conditions to solve for deflection in simply supported beams, cantilever beams, and beams under various loading types. Common deflection formulas are also presented.
6 internal forces and moment
This document discusses internal forces and moments in bending structures. It defines shear forces and bending moments, and explains that when a structure is loaded, internal forces and moments keep it from being pulled apart. It outlines how to determine these internal forces and moments by drawing a free body diagram of the structure, then making imaginary cuts along the structure and analyzing the forces and moments at each cut section. Resources for learning about free body diagrams, support reactions, and shear forces and bending moments are also provided.
Biomechanical testing of clavicle fx devices
The document describes a study that tested various clavicle fracture fixation devices under torsion and bending loads. The objectives were to compare the mechanical strength, stiffness, and failure modes of different plate designs. Devices from Synthes and DePuy were tested, including dynamic compression plates, locking plates, and a pin. Results showed differences in torsional strength and stiffness between devices, as well as differences in failure mechanisms. Calculated torque values based on plate geometry and material properties were generally consistent with experimental torque measurements at yield, though assumptions introduce some error.
5 torsion
This document discusses torsion and stresses in structures subjected to twisting forces. It begins by describing the torsion formula which relates shear stress to radius and polar moment of inertia. Maximum shear stress occurs at the outer radius. Torque is dependent on position along the length. Principal stresses in torsion occur at 45 degrees to the centerline and are equal in magnitude but opposite in direction (tensile and compressive). The magnitude of the principal stresses equals the maximum shear stress.
4 Principal Stresses
This document discusses principal stresses, maximum shear stress, and how to calculate and visualize them. It describes principal stresses as the minimum and maximum normal stresses in a material, which occur when shear stress is zero. It presents equations to calculate principal stresses and maximum shear stress from the normal and shear stresses, and how to find the angles at which they act. The document also discusses sketching and visualizing these stresses on a stress element.
3 strain transformations
Strain transformation equations and explanation; function, design and biomedical applications of strain gauges
2 mechanical properties of bone
This document discusses the mechanical properties of bone. It begins by outlining the learning objectives, which are to conduct stress analysis on bone samples, identify how bone's anisotropic material properties arise, and analyze how changes in bone composition affect stress and strain. It then explains that mechanical testing of materials involves applying and measuring forces and deformations. The document discusses how bone is a composite material made of collagen and hydroxyapatite mineral, giving it anisotropic properties, and strongest in compression. It attributes bone's anisotropic properties to its cortical and cancellous bone structures. Finally, it notes bone is a dynamic material that repairs itself and changes with aging and weight-bearing levels.
2 stress and strain intro for slideshare
This document defines key concepts related to stress and strain in engineering. It introduces terminology like stress, strain, Young's modulus, and Poisson's ratio. It explains that internal forces develop in objects under load to prevent separation. Stress is defined as the internal force per unit area, and can be normal or shear. Strain is the deformation from loading, and can be normal changes in length or shear changes in angle. Constitutive equations relate stress and strain through material properties like Young's modulus and Poisson's ratio.
2 stress and strain intro
This document defines key concepts in stress and strain analysis:
1) It defines normal stress, shear stress, normal strain, shear strain, and material properties like Young's modulus and Poisson's ratio.
2) It explains that internal forces develop in materials under loading to prevent separation, and that stress is calculated as the limit of force over area as the area approaches zero.
3) It notes that stress is a tensor with directional components, while strain describes changes in size and shape from loading.
1 Bone Structure and Composition
Bone is a composite material made up of cells and an extracellular matrix. At the micro level, bone contains osteoblasts that build bone tissue, osteoclasts that resorb bone, and osteocytes embedded in the matrix. The matrix is made of collagen fibers mineralized with hydroxyapatite crystals. Bones can be classified by their macro structure as long, short, flat, or irregular. Long bones have a diaphysis and epiphyses. Bone structure is adapted to its mechanical functions according to Wolff's law.
Introduction to Active Learning
This document discusses active learning techniques that can be used in undergraduate engineering courses. It defines active learning as engaging students through activities that promote higher-order thinking skills. Examples of active learning include collaborative problem solving, brainstorming, and case studies. Research shows benefits of active learning include improved attendance, deeper questioning, greater interest, and higher grades. The document provides tips for incorporating active learning, such as starting with simple tasks and activities. It also addresses managing student resistance to active learning.
Engineering Knowledge, Skills, and Abilities
This document discusses key knowledge, skills, and abilities (KSAs) that engineering students need to develop for successful careers. It defines three ways of knowing - "knowing that" which involves declarative knowledge, "knowing how" which involves procedural knowledge, and "knowing why" which involves curiosity and continuous learning. The document proposes assessing students' problem-solving processes and provides examples of activities that develop different ways of knowing in engineering courses. It assigns reflection essays for students to discuss experiences with "knowing that, how, why" and how to develop important KSAs in future teaching.
Syllabus and Course Design
This document provides guidance on designing a course syllabus. It compares key elements of course design to those of a research project. Some of the main steps outlined include determining student backgrounds and interests, formulating learning objectives based on these as well as the instructor's expertise, and choosing an appropriate scope and content. The document also discusses developing learning experiences and assessments to achieve the objectives and preparing the syllabus. Key components that should be included in the syllabus are identified, such as course information, policies, and required materials. The purpose of writing learning objectives and designing the syllabus from a learner-centered perspective are also addressed.
Learning Objectives
This document discusses learning objectives and how to write effective ones. It begins by defining learning objectives as statements of what students should be able to do after instruction. Objectives must be specific and measurable. The document then reviews Bloom's Taxonomy and its cognitive processes as a framework for writing objectives at different levels. It provides guidelines for constructing objectives and reasons for using them in course and lesson design. It also discusses potential issues with overusing objectives and how to align them with criteria like ABET outcomes. Finally, it instructs students to write objectives for their own lesson to use in a microteaching assignment.
Frameworks and External Requirements for Eng and Sci Education
This document discusses various educational frameworks and accreditation criteria that engineering instructors must consider when designing learning activities. It outlines ABET criteria for engineering programs, including abilities in math/science, experiment design, engineering problem-solving, communication, and professional responsibilities. General education requirements at universities are also examined, showing similarities to traditional liberal arts of grammar, logic, rhetoric, arithmetic, music, geometry and astronomy. The effect of general education requirements on engineering education is discussed, considering how they may support or conflict with developing engineering skills based on ABET criteria.
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3 stress transformations
- 1. Stress Transformations “It is a narrow mind which cannot look at a subject from various points of view.” ― George Eliot BIOE 3200 - Fall 2015
- 2. Learning Objectives Calculate stresses in multiple planes (stress transformations) in rigid bodies BIOE 3200 - Fall 2015
- 3. Stresses within a rigid body BIOE 3200 - Fall 2015
- 4. Stress elements BIOE 3200 - Fall 2015
- 5. Recall stresses defined in 3D: BIOE 3200 - Fall 2015
- 6. Summing forces on an inclined stress element BIOE 3200 - Fall 2015
- 7. Stress Transformations 𝜎𝑥𝑥 ′ = 𝜎 𝑥𝑥+𝜎 𝑦𝑦 2 + 𝜎 𝑥𝑥−𝜎 𝑦𝑦 2 𝑐𝑜𝑠2𝜃 + 𝜏 𝑥𝑦 𝑠𝑖𝑛2𝜃 𝜎 𝑦𝑦 ′ = 𝜎 𝑥𝑥+𝜎 𝑦𝑦 2 + 𝜎 𝑦𝑦−𝜎 𝑥𝑥 2 𝑐𝑜𝑠2𝜃 − 𝜏 𝑥𝑦 𝑠𝑖𝑛2𝜃 𝜏 𝑥𝑦 ′ = 𝜎 𝑦𝑦−𝜎 𝑥𝑥 2 𝑠𝑖𝑛2𝜃 + 𝜏 𝑥𝑦 𝑐𝑜𝑠2𝜃 BIOE 3200 - Fall 2015
Editor's Notes
- To obtain a complete picture of the stresses in a bar, we must consider stresses acting on an “inclined” (as opposed to a “normal”) section through the bar. Stresses on both normal and inclined sections are uniformly distributed.
- When working with stress elements, only one intrinsic state of stress exists at a point in a stressed body, regardless of the orientation of the element used to portray the state of stress. We can rotate axes to represent stresses in a new coordinate system, oriented at any angle to the original x-y system. (Draw x’ – y’ axes at angle theta to x-y axes)
- Normal stresses σxx, σyy, σzz (tension is positive) Shear stresses τxy = τyx, τxz = τzx, τyz = τzy Shear stress sign convention: for τij: Subscript “i” refers to direction normal to the plane on which it acts – the “face” of the stress element Subscript “j” refers to the direction the shear stress is applied. Now consider plane stress in the xy plane: only x and y faces are subjected to stresses (σz = 0 and τzx = τxz = τzy = τyz = 0). Such a stress element could be located on the free surface of a body (no stresses acting normal to the free surface).
- Stress transformation equations derived from summing forces on 2D stress element, and using shear stress equalities and trig identities Full explanation of math behind stress transformation equations is in text and as annotated pdf (posted on Blackboard).
- Point out stress components on plane stress element and transformation of stress components (primes) For stresses on the y’ face, substitute 𝜃+90 for 𝜃 in the x’ equation Summing the expressions for σ’x and σ’y can be used to find σ’x or σ’y instead of full transformation equation