# me16a: chapter one

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ME16A: INTRODUCTION TO STRENGTH OF MATERIALSCOURSE INTRODUCTION

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Details of LecturerCourse Lecturer: Dr. E.I. Ekwue Room Number: 216 Main Block, Faculty of Engineering Email: ekwue@eng.uwi.tt , Tel. No. : 662 2002 Extension 3171 Office Hours: 9 a.m. to 12 Noon. (Tue, Wed and Friday)

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COURSE GOALS        This course has two specific goals: (i)  To introduce students to concepts of stresses and strain; shearing force and bending; as well as torsion and deflection of different structural elements. (ii) To develop theoretical and analytical skills relevant to the areas mentioned in (i) above.

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COURSE OUTLINE

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Course Objectives  Upon successful completion of this course, students should be able to: (i)  Understand and solve simple problems involving stresses and strain in two and three dimensions. (ii) Understand the difference between statically determinate and indeterminate problems. (iii) Understand and carry out simple experiments illustrating properties of materials in tension, compression as well as hardness and impact tests.

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COURSE OBJECTIVES CONTD. (iv) Analyze stresses in two dimensions and understand the concepts of principal stresses and the use of Mohr circles to solve two-dimensional stress problems. (v) Draw shear force and bending moment diagrams of simple beams and understand the relationships between loading intensity, shearing force and bending moment.   (vi) Compute the bending stresses in beams with one or two materials.

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OBJECTIVES CONCLUDED (vii) Calculate the deflection of beams using the direct integration and moment-area method.   (viii)  Apply sound analytical techniques and logical procedures in the solution of engineering problems.

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Teaching StrategiesThe course will be taught via Lectures. Lectures will also involve the solution of tutorial questions. Tutorial questions are designed to complement and enhance both the lectures and the students appreciation of the subject. Course work assignments will be reviewed with the students.

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Lecture TimesWednesday: 2.00 to 2.50 p.m. Thursday: 11.10 a.m. to 12.00 noon Friday: 1.00 to 1.50 p.m. Lab Sessions: Two Labs per student on Mondays (Details to be Announced Later) Attendance at the Lectures and Labs is Compulsory.

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Time-Table For Labs

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More Course DetailsBOOK – Hearn, E.J. (1997), Mechanics of Materials 1, Third Edition, Butterworth, Heinemann  COURSE WORK 1. One Mid-Semester Test (20%); 2. Practical report (15%) and 3. End of Semester 1 Examination (65%).

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ME16A: CHAPTER ONESTRESS AND STRAIN RELATIONS

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1.1 DIRECT OR NORMAL STRESSWhen a force is transmitted through a body, the body tends to change its shape or deform. The body is said to be strained. Direct Stress = Applied Force (F) Cross Sectional Area (A) Units: Usually N/m2 (Pa), N/mm2, MN/m2, GN/m2 or N/cm2 Note: 1 N/mm2 = 1 MN/m2 = 1 MPa

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Direct Stress Contd.Direct stress may be tensile, t or compressive, c and result from forces acting perpendicular to the plane of the cross-section TensionCompression

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1.2 Direct or Normal Strain When loads are applied to a body, some deformation will occur resulting to a change in dimension. Consider a bar, subjected to axial tensile loading force, F. If the bar extension is dl and its original length (before loading) is L, then tensile strain is:

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Direct or Normal Strain Contd.Direct Strain ( ) = Change in Length Original Length i.e. = dl/LdlFFL

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Direct or Normal Strain Contd.As strain is a ratio of lengths, it is dimensionless. Similarly, for compression by amount, dl: Compressive strain = - dl/L Note: Strain is positive for an increase in dimension and negative for a reduction in dimension.

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1.3 Shear Stress and Shear StrainShear stresses are produced by equal and opposite parallel forces not in line. The forces tend to make one part of the material slide over the other part. Shear stress is tangential to the area over which it acts.

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Shear Stress and Shear Strain Contd.PQSRFDD’ABCC’LxShear strain is the distortion produced by shear stress on an element or rectangular block as above. The shear strain, (gamma) is given as: = x/L = tan

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Shear Stress and Shear Strain ConcludedFor small , Shear strain then becomes the change in the right angle. It is dimensionless and is measured in radians.

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1.3 Complementary Shear StressaPQSRConsider a small element, PQRS of the material in the last diagram. Let the shear stress created on faces PQ and RS be

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Complimentary Shear Stress Contd.The element is therefore subjected to a couple and for equilibrium, a balancing couple must be brought into action. This will only arise from the shear stress on faces QR and PS. Let the shear stresses on these faces be .

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Complimentary Shear Stress Contd.Let t be the thickness of the material at right angles to the paper and lengths of sides of element be a and b as shown. For equilibrium, clockwise couple = anticlockwise couple i.e. Force on PQ (or RS) x a = Force on QR (or PS) x b

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Complimentary Shear Stress ConcludedThus: Whenever a shear stress occurs on a plane within a material, it is automatically accompanied by an equal shear stress on the perpendicular plane. The direction of the complementary shear stress is such that their couple opposes that of the original shear stresses.

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1.4 Volumetric Strain Hydrostatic stress refers to tensile or compressive stress in all dimensions within or external to a body. Hydrostatic stress results in change in volume of the material. Consider a cube with sides x, y, z. Let dx, dy, and dz represent increase in length in all directions. i.e. new volume = (x + dx) (y + dy) (z + dz)

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Volumetric Strain Contd.Neglecting products of small quantities: New volume = x y z + z y dx + x z dy + x y dz Original volume = x y z = z y dx + x z dy + x y dz Volumetric strain, = z y dx + x z dy + x y dz x y z = dx/x + dy/y + dz/z

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Last Updated: 8th March 2018