TAILIEUCHUNG - Ebook Strength of materials: Part 2

(BQ) Strength of materials by Stephen Timoshenko book was expanded by the addition of two new chapters, namely Chapter VIII which deals with bending of beams in a plane which is not a plane of symmetry and Chapter XII on the bending of curved bars. In Chapter VIII the notion of shear center which is of great practical importance in the case of thin walled structures is introduced. In Chapter XII is presented the material on curved bars which previously appeared in the second volume of this book. | 174 STRENGTH OF MATERIALS the condition of continuity of deformation however there can be no abrupt change from a plane middle section to warped adjacent sections. There must be a continuous increase in warping as we proceed along the beam in either direction from the middle and only at some distance from the load can the warping be such as a shearing force Pịi produces under conditions of freedom in warping. From this discussion it must be concluded that in the neighborhood of the middle cross section the stress distribution will not be that predicted by the elementary theory of bending see p. 113 . Warping will be partially prevented and the additional deflection due to shearing forces will be somewhat less than that found above see eq. g . A more detailed investigation 10 shows that in the case of a concentrated load at the middle the deflection at the middle is PF r . A2 h Y 1 i- E7L 2 8i O-84 J We have an analogous condition also in the case of a cantilever beam. If the built-in cross section can warp freely as shown in Fig. 152 the conditions will be as assumed in the derivation of eq. A . The deflection of a cantilever of rectangular cross section will be obtained by substituting for ỈỊi and p for P 2 in this equation giving Ỗ V When the built-in cross section is completely prevented from warping Fig. 152 A the conditions will be the same as assumed in the derivation of eq. A and the deflection will be A2 1 -7I p - o-10 PF r Ỗ TF71 3 L 7 w which is less than the deflection given by . 10 See L. N. G. Filon Phil. Trans. Roy. Soc. A Vol. 201 p. 63 1903 and s. Timoshenko Phil. Mag. Vol. 47 p. 1095 1924. See also Th. V. Kármán Scripta Universitatis atque Bibliothecae Hierosolmi-tanarum 1923 and writer s Theory of Elasticity p. 95 1934. CHAPTER VI STATICALLY INDETERMINATE PROBLEMS IN BENDING 40. Redundant Constraints. In our previous discussion three types of beams have been considered d a cantilever beam Z a beam supported at the ends and r a beam with overhangs.

• Cơ khí - Chế tạo máy
• Strength of materials
• Energy of strain
• Combines bending
• Helical spring
• Close coiled
• Critical load
• Finite element modelling
• Rectangular concrete filled steel tube stub columns incorporating high strength
• Ultra high strength materials
• Concentric axial compression
• Axial compression
• Theory and problems of strength of materials
• Statically indeterminate force systems tension
• Direct shear stresses
• Bending moment
• Moments of inertia
• Lecture Strength of materials
• Modulus of elasticity
• Statically indeterminate systems
• Statically indeterminate
• Stress transformation
• Plane stress state
• Transformation of plane stress
• Failure theories
• Permanently distorted
• Ductile material deforms
• Properties of cross sections
• Center of gravity – centroid
• Moment of Inertia of an area
• Radius of gyration
• Beam deflection
• Beam under transverse loading
• Statically indeterminate beams
• Torsional loads on circular shafts
• Torsion of noncircular members
• Helical spring under axial load
• Combined loading
• Eccentric axial loadings
• General combined loadings
• The secant formula
• Stability of structures
• Eccentric loadings
• Cementitious materials
• high strength concrete
• Strength required
• Placing procedures
• Splitting tensile strength
• Concentrically loaded columns
• Selected topics on strength
• The strength of materials
• Basic hypothesis
• Internal forces
• Three dimensional state
• Dimensional state
• Deflection of beams
• Sức bền vật liệu
• Bài giảng Sức bền vật liệu
• Bending stress
• Shearing stress
• Strength condition
• Torsional loads
• Circular shafts
• Engineering materials
• Their properties
• Price and availability
• The elastic moduli
• Yield strength
• Tensile strength
• Fast fracture
• Toughness and fatigue
• Mechanical engineering principles
• Forces acting at a point
• Forces in structures
• Analysis of stress
• The elastic limit
• Deflection of transversally leaded beams
• Statically indeterminate problems
• Applied strength of materials
• Engineering stress
• Thermal expansion
• Properties of areas
• Torsion in round shafts
• Beam reactions
• Shear diagrams
• Moment diagrams
• Stresses in beams
• Combined stresses
• Visualizing stress
• Elastic deflection
• Double integration method
• Plastic deformations
• Mechanics and strength of materials
• The stress tensor
• The strain tensor
• Constitutive law
• Fundamental concepts
• Shear force
• Bending deflections
• Structural stability
• Energy theorems
• The total potential energy