Medieval Muslim engineers employed gears in mills and water-raising machines, and used dams as a source of water power to provide additional power to watermills and water-raising machines. Such advances made it possible for many industrial tasks that were previously driven by manual labour to be mechanized and driven by machinery to some extent in the medieval Islamic world.
Concrete has been in use as a primary building material since Roman times. As it is
strong in compression but weak in tension, it was used in arches, vaults and walls
where it is stressed principally in compression.
In the mid-nineteenth century, it was discovered that iron and later steel bars could
be embedded in the concrete, effectively giving it tensile strength. This allowed it to be
used in beams and slabs, where it worked in bending. Buildings, bridges, retaining walls
and many other structures were made in this reinforced concrete.
Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor, Michigan Charles R. Mischke, Ph.D., RE. Professor Emeritus of Mechanical Engineering Iowa State University Ames, Iowa
50.1 50.2 50.3 50.4 50.5
STIFFNESS OR SPRING RATE / 50.2 DEFLECTION DUE TO BENDING / 50.3 PROPERTIES OF BEAMS / 50.3 COMPUTER ANALYSIS / 50.3 ANALYSIS OF FRAMES /50.
C H A P T E R
A Textbook of Machine Design
Torsional and Bending Stresses in Machine Parts
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Introduction. Torsional Shear Stress. Shafts in Series and Parallel. Bending Stress in Straight Beams. Bending Stress in Cur ved Beams. Pr incipal Stresses and Principal Planes. Determination of Principal Stresses for a Member Subjected to Biaxial Stress. Application of Principal Stresses in Designing Machine Members. Theories of Failure under Static Load.
The elements of a force system acting at a section of a member are axial force, shear force and bending moment and the formulae for these force systems were derived based on the assumption that only a single force element is acting at the section. Figure-22.214.171.124 shows a simply supported beam while figure-126.96.36.199 shows the forces and the moment acting at any cross-section X-X of the beam. The force system can be given as: Axial force
The Beneﬁts of Tensegrity • Deﬁnitions and Examples • The Analyzed Structures • Main Results on Tensegrity Stiffness • Mass vs. Strength
Planar Tensegrity Structures Efﬁcient in Bending
Bending Rigidity of a Single Tensegrity Unit • Mass Efﬁciency of the C2T4 Class 1 Tensegrity in Bending • Global Bending of a Beam Made from C2T4 Units • A Class 1 C2T4 Planar Tensegrity in Compression • Summary
Understand the behaviour of beams
with openings under bending and
!Design the opening using Mechanism
Approach, Plasticity Truss Method or
!Detail the reinforcement to satisfy
serviceability and ultimate limit states
CURVED BEAMS AND RINGS
Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor, Michigan
16.1 BENDING IN THE PLANE OF CURVATURE / 16.2 16.2 CASTIGLIANO'S THEOREM / 16.2 16.3 RING SEGMENTS WITH ONE SUPPORT / 16.3 16.4 RINGS WITH SIMPLE SUPPORTS /16.10 16.5 RING SEGMENTS WITH FIXED ENDS / 16.15 REFERENCES/16.22
NOTATION A B C E e F G / K M P Q R r r T U V W w X Area, or a constant Constant Constant Modulus of elasticity Eccentricity Force Modulus of rigidity Second moment of area (Table 48.1) Shape constant (Table 49.1), or second polar...
Tài liệu tham khảo giáo trình nhôm trong thiết kế xây dựng bằng tiếng anh - Chương 8
8.1 GENERAL APPROACH This chapter covers the performance of aluminium beams under static loading, for which the main requirement is strength (limit state of static strength). In order to check this there are, as in steel, four basic failure modes to consider: 1. 2. 3. 4. bending-moment failure; shear-force failure; web crushing; lateral-torsional (LT) buckling.
Torsional Shear Stress. Shafts in Series and Parallel. Bending Stress in Straight Beams. Bending Stress in Cur ved Beams. Pr incipal Stresses and Principal Planes. Determination of Principal Stresses for a Member Subjected to Biaxial Stress. Application of Principal Stresses in Designing Machine Members. Theories of Failure under Static Load. Maximum Principal or Nor mal Stress Theor y (Rankine’s Theory). Maximum Shear Stress Theory (Guest’s or Tresca’s Theory). Maximum Principal Strain Theor y (Saint Venant’s Theory). Maximum Strain Energy Theory (Haigh’s Theory).