chapter 1 mechanic of material fundamentalin theoretical mechanic, bodie are aumed to be perfectly rigid.the deformation of bodie are important, however, a far a the reitance of the tructure and machine to failure i concerned.therefore, the bodie in mechanic of material will no longer be aumed to be perfectly rigid a conidered in theoretical mechanic.mechanic of material tudie the ability of tructure and machine to reit failure, and mainly involve the following tak: ① trength, i.e., the ability of member to upport a pecified load without experiencing exceive tree; ② rigidity, i.e., the ability of member to upport a pecified load without undergoing unacceptable deformation; ③ tability, i.e., the ability of member to upport a pecified aal preive load without cauing a udden lateral deflection.any material dealt with in mechanic of material i aumed to be: ① continuou, i.e., the material conit of a continuou ditribution of matter without void; ② homogeneou, i.e., the material ee the ame mechanical propertie at all point in the matter; ③ iotropic, i.e., the material ha the ame mechanical propertie in all direction at any one point of the matter.the trength and rigidity of a material depend on it abilitie to upport a pecified load without experiencing both exceive tree and unacceptable deformation.thee abilitie are inherent in the material itelf and mut be determined by experimental method.one of the mot important tet to determine the mechanical propertie of a material i the tenile or preive tet.thi tet i often ued to determine the tretrain relation of the material ued.1.1 external forceany external force applied to a body can be claified a either a urface force or a body force.1.urface forcean external force that i applied to the urface of a body i called a urface force.if the urface force i ditributed over a finite area of the body, it i aid to be a ditributed load on a urface, fig.1.1(a).if the urface force i applied along a narrow area, thi force i defined a a ditributed load along a line, fig.1.1(b).if the area ubjected to a urface force i very mall, pared with the urface area of the body, then thi urface force can be regarded a a concentrated load, fig.1.1(c).fig.1.12.body forcean external force that i applied to every point within a body i called a body force.a gravitational force i an excellent example of the body force ince it act upon each of the particle forming the body.1.2 internal forcewhen variou external load are applied to a member, the correpon ditributed internal force will be developed at any point within the member.the ditributed internal force on any ection within the member can be determined by uing the method of ection.we imagine to ue a ne , fig.1.2(a), to ection the member where the ditributed internal force need to be determined.for determination of the ditributed internal force on the cut ne, the portion of the member to the right of the cut ne i removed, and it i reced by the ditributed internal force acting on the left portion, fig.1.2(b).fig.1.2for equilibrium of the remaining portion of the member, the ditributed internal force can be determined by uing the equation of tatic equilibrium.although the exact ditribution of internal force may be unknown, we can ue the equation of tatic equilibrium to relate the applied external load to the reultant force r and reultant couple mo about point o on the cut ne, which are caued by the ditributed internal force, fig.1.3(a).fig.1.3generally peaking, the reultant force r and reultant couple mo have arbitrary direction,neither perpendicular nor parallel to the cut ne.however,we can reolve the reultant force and couple into ix ponent, repectively along the x, y, and z axe, fig.1.3(b).(1) aal force.the normal ponent, along the x direction, of the reultant force i called the aal force (normal force), n.it i developed when the external load tend to pull or puh the two egment of the member.(2) hearing force.the tangential ponent, repectively along the y and z direction, of the reultant force are regarded a the hearing force, denoted by vy and vz, which are developed when the external load tend to caue the two egment of the member to lide over one another.(3) torional moment.the normal ponent, rotating about the x a, of the reultant couple i called the torional moment (twiting moment, or torque), t, and developed when the external load tend to twit one egment of the member with repect to the other.(4) ben moment.the tangential ponent of the reultant couple tend to bend the member about the y and z axe, repectively.thee t