INTRODUCTION TO MECHANICS OF MATERIALS - UPRM

1 INTRODUCTION TO MECHANICS OF MATERIALS (INGE 4019)Pablo G. Caceres-Valencia ( , , )AssessmentThe course will be assessed in the following manner: 1stExam 25% 2ndExam 30% Quizzes*30% Others**15% (*)(*) Date due WebCT or Moodle Quizzes and Pop Quizzes (max 6). Missed quizzes will be graded with zero. Lack of access to WebCT or Moodle is not an excuse for not submitting your answers. (**) Class participation and Attendance. After the third missed class, one point will be deducted in the final grade for each missed class (up to 15 points). GENERAL INFORMATIONC ourse Number INGE 4019 Course TitleIntroduction to MECHANICS of MaterialsCredit Hours4 InstructorDr.

2 Pablo G. Caceres-ValenciaOfficeLucchetti L-212, Extension 2358 Office HoursM-W from 9-12am and Grade RangeFinal Letter Grade100 90A89 80B79 70C69 60D59 0 FAttendanceAttendance and participation in the lecture are compulsoryand will be considered in the grading. Students should bring calculators, rulers, pen and pencils to be used during the lectures. Students are expected to keep up with the assigned reading and be prepared toanswer questions on these readings during lecture and for the pop quizzes. Please refer to the Bulletin of Information for Undergraduate Studies for the Department and Campus Indetermined09/14 Torsion09/28 Shear and Bending10/12 Holiday10/26 Hooke s Law11/09 Combined Loadings11/23 Combined Loadings08/19 Linear Elasticity08/24 Axial Loads08/26 Axial Loads09/02 Thermal EffectsTuesday 09/07 Stresses on Inclined Planes09/09 Stress Concentration09/16 Thin Walled Tubes09/211st Exam09/23 Holiday09/30 Shear and Bending10/05 Principal Stresses10/07 Mohr s Circle10/14 Triaxial Stresses10/19 Plane Stresses10/21 Plane Stresses10/28 Plane Strain11/02 Plane Strain11/04 Elasticity11/11 Holiday11/16 Combined Loadings11/182ndExam11/25 Deflection of Beams11/30 Deflection of Beams12/02

3 Deflection of BeamsTentative DatesOutcomesUpon the completion of the course the student should be able to: Calculate the principal stresses and strains in a loaded component Solve problems using stress transformation and Mohr s circle Apply Hooke s law for plane stress and plane strain Calculate stresses in thin walled spherical or cylindrical pressure vessels Calculate the stresses produced by combined axial, bending and torsional loads TexbooksJames M. Gere and Barry J. Goodno, MECHANICS of MATERIALS , 7thEdition, lecture notes are available in the web syllabus of the course for recommended exams will be conducted during lecture periods on the specified dates. There will be no final exam. Neatness and order will be taking into consideration in the grading of the exams.

4 Up to ten points can be deducted for the lack of neatness and order. You must bring calculators, class notes and blank pages to the of StaticsMechanics of MATERIALS is a branch of MECHANICS that develops relationships between the external loads applied to a deformable body and the intensity of internal forces acting within the body as well as the deformations of the of equilibrium ( , statics) are mathematical expressions of vector relationships showing that for a body not to translate or move along a path then F = 0. For a body not to rotate, M = has two components, one acting perpendicular to the plane of the area and the other acting parallel to the area. Mathematically, the former component is expressed as a normal stress which is the intensity of the internal force acting normal to an incremental area such that:where + = tensile stress = "pulling" stress and - = compressive stress = "pushing latter component is expressed as a shear stress which is the intensity of the internal force acting tangent to an incremental area such that:COMPRESSION(*squeezing)TENSION(*str etching)Prismatic bar in tension.

5 (a) free-body diagram of a segment of the bar, (b) segment of the bar before loading, (c) segment of the bar after loading, and (d) normal stresses in the bar = Section does not change in the length of the bar-ve+vestrain- normalstress====LAP LAPAP ===22 LLAP ===22 Normal Stress and Normal StrainUniform Normal Stress 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under stress distribution in a prismatic bar: (a) axial forces P, and (b) cross section of the are constant over the cross sectional have uniform stresses (tension or compression) over the cross-section area (A), the axial force must act along the centroid. AAyyAAxx == Does the material resist the applied force?

6 What is the relationship between the stress applied and the deformation?Tensile Testing The sample is pulled slowly The sample deforms and then fails The load and the deformation are measuredForceExtension or change in lengthDetermine the deformation of the steel rod shown under the in. = dDE22121in 12====AALL233in 16==AL Apply free-body analysis to each component to determine internal forces,lb1030lb1015lb1060333231 = = =PPP Evaluate total deflection,()()() = + + = ++= =ALPALPALPEEALP iiiii = Find the stresses and strains:(a) Change in length of the pipe(b) Lateral strain(c) Increase in outer and inner diameters(d) Increase in wall thickness(*tearing)Normal stress ( ) :the subscript identifies the face on which the stress acts.

7 Tension is positive and compression is stress ( ) :it has two subscripts. The first subscript denotes the face on which the stress acts. The second subscript denotes the direction on that shear stress is positive if it acts on a positive face and positive direction or if it acts in a negative face and negative direction. x xx xy From equilibrium principles: xy = yx, xz = zx , zy= yz3 DTORSION(*twisting)BENDING(*flexure)IMcM = MFor 2-D: yyxxmaFmaF= = zzzIM = Where zis the angular accelerationMoment of a Force about an axisFree body DiagramChange the steel for steel strut S serving as a brace for a boat hoist transmits a compressive force P to the deck of a pad in shear. Elastomer with Modulus of Rigidity GeThe connection shown in the figure consists of five steel plates, each thick, to be joined by a single bolt.

8 Determine the required diameter of the bolt if the allowable bearing stress, b, is and the allowable shear stress, allow, is the allowable load P based on the following four truss ABC supporting a sign of weight W. Determine the required cross-sectional area of bar AB and the required diameter of the pin at support C