Mechanics of Deformable Bodies T-CEET222 The Lasallian Prayer “Let us remember that we are in the holy presence of God.” 7 March 2021 Prepared by: Engr. Jeric Sarte 2 Ang Panalanging Lasalyano “Ating alalahanin na ang Diyos ay ating kapiling.” 7 March 2021 Prepared by: Engr. Jeric Sarte 3 Gospel 7 March 2021 Prepared by: Engr. Jeric Sarte 4 The Lasallian Prayer “I will continue, O my God, to do all my actions for the love of Thee.” Saint John Baptist de La Salle, pray for us. Live Jesus in our hearts, forever. 7 March 2021 Prepared by: Engr. Jeric Sarte 5 Ang Panalanging Lasalyano “Ipagpapatuloy ko, O Diyos, ang lahat ng aking gawain upang Ikaw ay lalong pakaibigin.” San Juan Bautista de La Salle, ipanalangin mo kami. Hesus, manahan ka sa aming puso, magpakailanman. 7 March 2021 Prepared by: Engr. Jeric Sarte 6 Simple Stress 7 March 2021 Prepared by: Engr. Jeric Sarte 7 STRESSES IN THE MEMBERS OF A STRUCTURE •Normal Stress Consider the rod shown subjected to force FBC. Whether rod will break or not under this loading depends upon the value found for the internal force FBC, the cross-sectional area of the rod A, and the material of which the rod is made. Internally, the force FBC is represented by elemental forces distributed over the cross sectional area, A. The magnitude of these elemental forces is equal to the force per unit area. πΉπ΅πΆ ππ΅πΆ = π΄ This is called stress and is typically denoted by, s. 7 March 2021 Prepared by: Engr. Jeric Sarte 8 STRESSES IN THE MEMBERS OF A STRUCTURE •Normal Stress In the same manner how axial forces behave, whether tension or compression, is same with stress. Positive sign indicates tension. As shown in the figure, the section through the rod to determine the internal force in the rod and the corresponding stress is perpendicular to the axis of the rod. The corresponding stress is described as a normal stress. π= 7 March 2021 π π΄ππππππππππ’πππ Prepared by: Engr. Jeric Sarte 9 STRESSES IN THE MEMBERS OF A STRUCTURE •Normal Stress Note that this uniform distribution of stress is possible only if the line of action of the concentrated loads P and P′ passes through the centroid of the section considered. This type of loading is called centric loading. However, if a member is loaded axially, but eccentrically, as shown in the figure, doing statics suggests that a given section must be equivalent to a force P applied at the centroid of the section and a couple M of moment M = Pd. This distribution of forces—the corresponding distribution of stresses—cannot be uniform. 7 March 2021 Prepared by: Engr. Jeric Sarte 10 Stress units The SI unit for stress is pascal (Pa). π= In engineering, we may use (metric units) ππ πππππππ πππ πππ = 10 ππ = 2 π 3 π π = 2 = ππ π΄ π In English units, π πππππππ πππ πππ = 10 ππ = ππ2 ππ 1 2 ππ ππ π = 6,894.757 ππ ππ ππ πππππππ πππ πΊππ = 10 ππ = ππ2 6 ππππ 1 2 ππ ππ π = 1000 ππ π ππ 9 Other units may be used as well such as 1 atm = 101,325 Pa 1 torr = 133.322 Pa 1 mmHg = 133.322 Pa 1 bar = 100,000 Pa 7 March 2021 Prepared by: Engr. Jeric Sarte 11 Problem 1 Assume a rod made of a steel with a maximum allowable stress σall = 155 MPa. Can the rod safely support the load to which it will be subjected? The magnitude of the force FBC in the rod was 50 kN and its diameter is 20 mm. If not, redesign the rod. 7 March 2021 Prepared by: Engr. Jeric Sarte 12 Problem 1 7 March 2021 Prepared by: Engr. Jeric Sarte 13 Problem 1 7 March 2021 Prepared by: Engr. Jeric Sarte 14 STRESSES IN THE MEMBERS OF A STRUCTURE •Shear Stress A very different type of stress is obtained when transverse forces P and P′ are applied to a member AB. If we pass a plane at C cutting the member, we obtain a new plane where internal forces are exposed whose resultant is P. This resultant is called shear force. 7 March 2021 Prepared by: Engr. Jeric Sarte 15 STRESSES IN THE MEMBERS OF A STRUCTURE •Shear Stress Dividing the resultant P to the cross sectional area of member AB gives us the average shearing stress. Note: this time, the area is parallel to the force. πππ£π = 7 March 2021 π π΄ππππππππ Prepared by: Engr. Jeric Sarte 16 STRESSES IN THE MEMBERS OF A STRUCTURE •Shear Stress – single shear 7 March 2021 Prepared by: Engr. Jeric Sarte 17 STRESSES IN THE MEMBERS OF A STRUCTURE •Shear Stress – double shear 7 March 2021 Prepared by: Engr. Jeric Sarte 18 Problem 2 Two wooden planks, each 1/2 in. thick and 9 in. wide, are joined by the dry mortise joint shown. Knowing that the wood used shears off along its grain when the average shearing stress reaches 1.20 ksi, determine the magnitude P of the axial load that will cause the joint to fail. 7 March 2021 Prepared by: Engr. Jeric Sarte 19 Problem 2 7 March 2021 Prepared by: Engr. Jeric Sarte 20 Problem 2 7 March 2021 Prepared by: Engr. Jeric Sarte 21 STRESSES IN THE MEMBERS OF A STRUCTURE •Bearing Stress This is the stress that is generated in contact between two different components/body (e.g. bolt against plate as shown, footing against earth-ground, etc). Take for example the previous illustration in the discussion of shear stress. The bolt exerts on plate A a force P equal and opposite to the force F exerted by the plate on the bolt. 7 March 2021 Prepared by: Engr. Jeric Sarte 22 STRESSES IN THE MEMBERS OF A STRUCTURE •Bearing Stress Take for example the previous illustration in the discussion of shear stress. The bolt exerts on plate A a force P equal and opposite to the force F exerted by the plate on the bolt. The force P represents the resultant of elementary forces distributed on the inside surface of a half-cylinder of diameter d and of length t equal to the thickness of the plate. The average of this equal to P divided by the rectangular projection of the half-cylinder is called bearing stress. π π ππ = = π΄ ππ‘ 7 March 2021 Prepared by: Engr. Jeric Sarte 23 Problem 3 A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing, (b) (b) the size of the footing for which the average bearing stress in the soil is 145 kPa. 7 March 2021 Prepared by: Engr. Jeric Sarte 24 Problem 3 7 March 2021 Prepared by: Engr. Jeric Sarte 25 Problem 3 7 March 2021 Prepared by: Engr. Jeric Sarte 26 DESIGN CONSIDERATIONS •Ultimate Strength of a Material Ultimate strength is the largest stress a material is subjected to where it breaks or begins to carry less load. Ultimate normal stress is determined by ππ ππ = π΄ 7 March 2021 Prepared by: Engr. Jeric Sarte Several test procedures may be done to determine the ultimate shearing stress. This may involved twisting of a circular tube, etc. It is represented by the equation ππ ππ = π΄ 27 DESIGN CONSIDERATIONS •Allowable Load and Allowable Stress The maximum load that a structural member or a machine component will be allowed to carry under normal conditions is considerably smaller than the ultimate load. This smaller load is the allowable load (sometimes called the working or design load). The remaining portion of the load-carrying capacity of the member is kept in reserve to assure its safe performance. 7 March 2021 Prepared by: Engr. Jeric Sarte The ratio of the ultimate load to the allowable load is the factor of safety: πΉπππ‘ππ ππ πππππ‘π¦ = πΉ. π. = Similarly, πΉπππ‘ππ ππ πππππ‘π¦ = πΉ. π. = π’ππ‘ππππ‘π ππππ πππππ€ππππ ππππ π’ππ‘ππππ‘π π π‘πππ π πππππ€ππππ π π‘πππ π 28 Problem 4 Find the stresses in members BC, BD, and CF for the truss shown in the figure. Indicate the tension or compression. The cross section nal area of each member 1600 mm2. 7 March 2021 Prepared by: Engr. Jeric Sarte 29 Problem 4 7 March 2021 Prepared by: Engr. Jeric Sarte 30 Problem 4 7 March 2021 Prepared by: Engr. Jeric Sarte 31 Problem 5 A load P is supported as shown by a steel pin that has been inserted in a short wooden member hanging from the ceiling. The ultimate strength of the wood used is 60 MPa in tension and 7.5 MPa in shear, while the ultimate strength of the steel is 145 MPa in shear. Knowing that b = 40 mm, c = 55 mm, and d = 12 mm, determine the load P if an overall factor of safety of 3.2 is desired. 7 March 2021 Prepared by: Engr. Jeric Sarte 32 Problem 5 7 March 2021 Prepared by: Engr. Jeric Sarte 33 Problem 5 7 March 2021 Prepared by: Engr. Jeric Sarte 34 Problem 6 Two wooden members of uniform cross section are joined by the simple scarf splice shown. Knowing that the maximum allowable tensile stress in the glued splice is 75 psi, determine (a) the largest load P that can be safely supported, (b) (b) the corresponding shearing stress in the splice. 7 March 2021 Prepared by: Engr. Jeric Sarte 35 Problem 6 7 March 2021 Prepared by: Engr. Jeric Sarte 36 Problem 6 7 March 2021 Prepared by: Engr. Jeric Sarte 37 END OF PRESENTATION ONE HEART. ONE COMMITMENT. ONE LIFE. 1719 – 2019 #300LaSalle Prepared 7 Marchby: 2021 Engr. Joshua Hernandez 38 The Lasallian Prayer “Let us remember that we are in the holy presence of God.” 7 March 2021 Prepared by: Engr. Jeric Sarte 39 The Lasallian Prayer “I will continue, O my God, to do all my actions for the love of Thee.” Saint John Baptist de La Salle, pray for us. Live Jesus in our hearts, forever. 7 March 2021 Prepared by: Engr. Jeric Sarte 40
