Lecture Strength of Materials I: Chapter 2 - PhD. Tran Minh Tu

Chapter 2 - Axial force, shear force and bending moment. The following will be discussed in this chapter: Internal stress resultants; relationships between loads, shear forces, and bending moments; graphical method for constructing shear and moment diagrams; normal, shear force and bending moment diagram of frame.
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Lecture Strength of Materials I: Chapter 2 - PhD. Tran Minh Tu STRENGTH OF MATERIALS1/10/2013 TRAN MINH TU - University of Civil Engineering, 1 Giai Phong Str. 55, Hai Ba Trung Dist. Hanoi, VietnamCHAPTER 2 Axial Force, Shear Force and Bending Moment 1/10/2013 2 Contents 2.1. Introduction 2.2. Internal Stress Resultants 2.3. Example 2.4. Relationships between loads, shear forces, and bending moments 2.5. Graphical Method for Constructing Shear and Moment Diagrams 2.6. Normal, Shear force and bending moment diagram of frame1/10/2013 32.1. Introduction- Structural members are usually classifiedaccording to the types of loads that theysupport.- Planar structures: if they lie in a singleplane and all loads act in that same plane.2.1.1. Support connections.- Structural members are joined together in various ways depending onthe intent of the designer. The three types of joint most often specifiedare the pin connection, the roller support, and the fixed joint 1/10/2013 42.1. Introduction - Types of supports- Pin support: prevents the translation at theend of a beam but does not prevent therotation. A Idealized HA 1/10/2013 V 5 A2.1. Introduction- Roller support: prevents the translation inthe vertical direction but not in the horizontaldirection, and does not prevent the rotation. A V A 1/10/2013 62.1. Introduction- Fixed (clamped) support: the bar can neither translate nor rotate. A MA HA V A 1/10/2013 72.1. Introduction1/10/2013 82.1. Introduction2.1.2. Types of beams1/10/2013 92.2. Internal Stress Resultants In general, internal stress resultants(internal forces) consist of 6 components Mx x • Nz – Normal force Mz Qx • Qx, Qy – Shear forces NZ z • Mx, My – Bending moments My Qy • Mz – Torsional moment y Planar structures: if they lie in asingle plane and all loads act in thatsame plane => Only 3 internal stress x Mxresultants exert on this plane (zoy) . • Nz – axial force (N); • Qy – shear force (Q); NZ z • Mx - bending moment (M) Qy y 1/10/2013 102.2. Internal force Resultants To determine the internal force resultants => Using the method ofsections. N N N N Q Q N1/10/2013 112.2. Internal force Resultants Sign convention: • Axial force: positive when outward N N N N of an element, negative when inward of an element• Shear force: positive when actsclockwise against an element,negative when acts counterclockwiseagainst an element• Bending moment: positive whencompresses the upper part of thebeam and negative whencompresses the lower part of thebeam 1/10/2013 122.2. Axial, Shear and Moment diagram2.1.3. Axial, Shear and Moment diagram • Because of the applied loadings, the beams develop an internal shear force and bending moment that, in general, vary from point to point along the axis of the beam. In order to properly design a beam it therefore becomes necessary to determine the maximum shear and moment in the beam. • One way to do this is expressing N, Q and M as the functions of their arbitrary position z along the beam’s axis. These axial, shear and moment functions can then be plotted and represented by graph called the axial, shear and moment diagram 1/10/2013 ...