ARC5554 Fall 2024 Lecture 11 Stress and Strain PDF

NO. TYPE DESCRIPTION CLASS 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 10: STRESS AND STRAIN OUTLINE: 1. Mechanics of Materials 2. Stress Types 3. Stress vs. Strain 1  NO. TYPE DESCRI...

NO. TYPE DESCRIPTION CLASS 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 10: STRESS AND STRAIN OUTLINE: 1. Mechanics of Materials 2. Stress Types 3. Stress vs. Strain 1  NO. TYPE DESCRIPTION CLASS 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS Structural elements must resist deformation and displacement in order to transmit loads. The subject treating the relationship between applied forces and induced deformations such as the deflection of a beam under transverse loads, elongation of a steel rod under tension, shortening of a truss member in compression or the twist of a shaft under torque is called mechanics of materials. Mechanics of materials deals with material properties such as strength, ductility and stiffness. Understanding this subject is a critical step in designing safe structures and structural components. 2  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS TENSION FORCES: When an external load pulls on a structural member, the particles composing the material move apart and undergo tension. Tension forces stretch and elongate the material. The amount of elongation depends on the stiffness of the material, cross section area and the magnitude of the load. 3  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS COMPRESSION FORCES: A compression force produces the opposite effect of a tension force. When an external load pushes on a structural member, the particles of the material compacts together. Compression forces result in the shortening of the material. 4  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS SHEAR FORCES: A shear force is an effect that is developed from the action of opposing forces. Shear forces produce simultaneous shifting of horizonal and vertical parallel planes of a material and cause deformation. 5  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS FLEXURE FORCES: Flexure is the bending of a material under load application. A structural member will deform and bend when subjected to transverse loads. When flexure or bending occurs, compression, tension and shear are all present in the material. 6  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN MECHANICS OF MATERIALS TORSION FORCES: Torsion is the twisting and distortion of a material’s fibers in response to an applied load. In most cases, torsion in a structural member is the result of eccentric loading. In building structures, torsion is an undesirable condition and should be avoided. Lateral forces like wind and earthquakes can produce significant torsion in various members of a structure. 7  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS TYPES STRESS TYPES: Stress describes the intensity of a force. In simple words, stress is the quantity or the amount of force which acts on a unit area. Stresses can be classified according to the type of internal reactions they produce. 1. Normal or Axial Stress 2. Shear Stress 3. Bearing Stress 4. Strain 8  NO. TYPE DESCRIPTION CLASS DATE ARC5554 11 LECTURE STRESS AND STRAIN LECTURE 11: STRESS AND STRAIN STRESS TYPES NORMAL/AXIAL STRESS: This type of stress is produced by the effect of a tension (pull) or a compression (push) force on an area. Normal or axial stresses are exerted at right angles to the surface area. 𝑇 𝑃 𝑓! = 𝐴 stress "# 𝑓! = axial stress in 𝑝𝑠𝑖 $%! 𝑃 = tension or compression force in 𝑙𝑏𝑠, 𝑘 𝑜𝑟 𝑁 𝐴 = cross section area in 𝑖𝑛& 𝑇 9  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS TYPES SHEAR STRESS: Shear stress is produced when a force is applied at right angles to the axis of member(s). Shear stress acts in a plane which is parallel to the cross-sectional area. bolt 𝑉 𝑓" = 𝑉 𝑉 𝐴# "# 𝑓' = shear stress in 𝑝𝑠𝑖 $% ! 𝑉 = shear force in 𝑙𝑏𝑠, 𝑘 𝑜𝑟 𝑁 𝐴( = area subjected to shear force in 𝑖𝑛& 10  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS TYPES BEARING STRESS: Bearing stress is pressure or intensity of a force that is produced at the contact point of a body and its support. 𝑃 𝑓$ = 𝐴$ "# 𝑓# = bearing stress in 𝑝𝑠𝑖 $% ! 𝑃 = force in 𝑙𝑏𝑠, 𝑘 𝑜𝑟 𝑁 𝐴# = bearing area in 𝑖𝑛& 11  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS TYPES STRAIN: Strain is a deformation of the physical dimension of a body under stress. Normal or axial stresses result in elongation or shortening of the member. For example, a straight bar will become longer under tension and shorter under compression. The following expression describes normal or axial strain: 𝜀 = strain or elongation per unit weight Δ𝐿 Δ𝐿 = elongation in unit length or the change (D) in length 𝜀= 𝐿 = length of the member 𝐿 12  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN In 1678, an English scientist named Robert Hooke noted that most engineered structures were composed of elastic materials. Elasticity is a property that enables the material to deform under stress and return to its original dimensions after the load has been removed. Hooke’s investigation was based on mathematical relationships and a series of experiments that required applying weights to spring-like materials and measuring and recording the resulted deformation. Through his extensive experiments, Hooke also discovered that the stress-strain relationship in elastic materials was linear and proportion under moderate loading. This relationship is referred to as Hooke’s Law. 13  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN Yield Stress Elastic Yield Range Stress Failure 𝑓! = Ultimate Strength 𝑓 STRESS 𝑓 STRESS 𝑝𝑠𝑖 𝑜𝑟 𝑘𝑠𝑖 𝑝𝑠𝑖 𝑜𝑟 𝑘𝑠𝑖 Plastic Range Strain Hardening 𝜀 STRAIN 𝜀 STRAIN 𝑖𝑛/𝑖𝑛 𝑖𝑛/𝑖𝑛 14 Stress/Strain Curve For Steel Stress/Strain Curve For Concrete  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN ELASTIC RANGE: Material acts like a spring and deformation is removed once the loading is removed. PLASTIC RANGE: Material will have permanent deformation after the loading is removed. YIELD STRESS: Stress beyond which permanent deformation will occur. STIFFNESS: Measure of how much that material strains for a given amount of stress. 15  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN STIFFNESS VALUE: The stiffness is the slope of the stress-strain curve (the magnitude of this slope is called the modulus of elasticity or Young’s modulus) and is designated by the symbol E. The unit of measure for the modulus of elasticity is in psi or ksi. The E value or stiffness of concrete is about 1/10 that of steel, while structural wood is about ½ as stiff as concrete. 16  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN CREEP: When loaded over an extended time, some materials undergo additional deformation called creep. Creep is usually more of a concern in high temperatures and with materials such as concrete and wood. Creep of long span structures composed of concrete and wood should be considered and accounted for at the early stage of structural design. 17  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN THERMAL STRESS AND STRAIN: Changes in temperature result in the expansion and contraction of materials and produce thermal stress if restrained from movement. The volume and dimension of a material will change when it is heated or cooled. The change in the material dimension is directly proportional to temperature changes and is known as thermal strain. In some cases, thermal strain may exceed acceptable limits and produce damage. There are various ways to accommodate thermal stress and strains and minimize their impact on a structure. 18  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN STRESS CONCENTRATION: When defining actual stresses, there is an assumption that stresses are uniformly distributed across the entire cross section of a structural element. However, in many cases structural members have abrupt geometrical changes that produce high stress levels in very small regions. This condition is called stress concentration and occurs in discontinuous geometries such as holes, grooves and notches. 19  NO. TYPE DESCRIPTION CLASS DATE 11 LECTURE STRESS AND STRAIN ARC5554 LECTURE 11: STRESS AND STRAIN STRESS VS. STRAIN STRESS CONCENTRATION: Under static loads, stress concentration in steel is not critical and can be reduced or eliminated by design measures that redistribute the stresses. However, sharp discontinuities in concrete are critical. Under dynamic loads, the areas of high-localized stresses are significant and can become the initial location of structural failure. 20