1. Introduction to Simple Stress

INTRODUCTION TO SIMPLE STRESSES (Lecture 1) Mechanics of Deformable Bodies (MEC32) Engr. Derwin Daniel C. Bautista Instructor, School of CEGE Mapua Institute of Technology

MECHANICS OF MATERIALS • Also known as "Mechanics of Deformable Bodies." • Deals with the internal effects and deformations that are

caused by the applied loads. • Its main objective is to provide the future engineer with the means of analyzing and designing various machines and load bearing structures.

MECHANICS OF MATERIALS • A safe and successful design must address the following

three mechanical concerns: • Strength: Is the object strong enough to withstand the loads that

will be applied to it? Will it break or fracture? Will it continue to perform properly under repeated loadings? • Stiffness: Will the object deflect or deform so much that it cannot

perform its intended function? • Stability: Will the object suddenly bend or buckle out of shape at

some elevated load so that it can no longer continue to perform its function?

STRESS • Refers to the "unit strength" of a

body. • Intensity of the internal force • Basically the force per unit area. Stress 

R A

• Separated into two main types: (1)

due to the Resultant Force and (2) due to the Resultant Couple.

Stress 

R A

STRESS • Stresses due to the resultant force: • Normal (Axial Stress) • Force is perpendicular to the cross-

sectional area. • Either tensile or compressive. • Shearing Stress • Force is parallel to the cross-sectional

area. • Stress that causes sliding on the object.

INTERNAL AND EXTERNAL FORCES

(a)

(b)

(c)

Review of Engineering Mechanics to solve internal forces:  Fx  0

F  0 M  0 y

C

(d)

EFFECTS OF INTERNAL FORCES

PROBLEMS • PROBLEM 1

• Two solid cylindrical rods (1) and (2) are joined together

at flange B and loaded, as shown in the figure. The diameter of rod (1) is d1 = 24 mm and the diameter of rod (2) is d2 = 42 mm. Determine the normal stresses in rods (1) and (2).

PROBLEMS • PROBLEM 2

•A

simple pin-connected truss is loaded and supported as shown in the figure. All members of the truss are aluminum pipes that have an outside diameter of 42 mm and a wall thickness of 3.5 mm. Determine the normal stress in each truss member.

PROBLEMS • PROBLEM 3

• Bar (1) in the figure has a cross-sectional area of 0.75 in2.

If the stress in bar (1) must be limited to 30 ksi, determine the maximum load P that may be supported by the structure.

PROBLEMS • PROBLEM 4

• An axial load P is applied to the rectangular bar shown in

the figure. The cross-sectional area of the bar is 400 mm2. Determine the normal stress perpendicular to plane AB and the shear stress parallel to plane AB if the bar is subjected to an axial load of P = 70 kN.

PROBLEMS • PROBLEM 5 • In the figure shown, member (1) is

a steel bar with a cross-sectional area of 1.35 in2 and a yield strength of 50 ksi. Member (2) is a pair of 6061-T6 aluminum bars having a combined cross-sectional area of 3.50 in2 and a yield strength of 40 ksi. A factor of safety of 1.6 with respect to yield is required for both members. Determine the maximum allowable load P that may be applied to the structure. Report the factors of safety for both members at the allowable load.

REFERENCES • Pytel, A., & Kiusalaas, J. (2012). Mechanics of Materials

(2nd ed.). Cengage Learning. • Hibbeler, R. (2011). Mechanics of Materials (8th ed.). Prentice Hall. • Pytel, A., & Singer, F. (1987). Strength of Materials (4th ed.). Harper and Row.