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【文章內(nèi)容簡(jiǎn)介】 ess. A necessary condition for Eq.() to be valid is that the stressб must be uniform over the cross section of the bat . This condition will be realized if the axial force p acts through the centroid of the cross section , as can be demonstrated by statics. When the load P doses not act at thus centroid , bending of the bar will result, and a more plicated analysis is necessary . Throughout this book , however , it is assumed that all axial forces are applied at the centroid of the cross section unless specifically stated to the contrary ④. Also, unless stated otherwise, it is generally assumed that the weight of the object itself is neglected, as was done when discussing this bar in .3. Strain The total elongation of a bar carrying force will be denoted by the Greek letterб[see Fig .(a)], and the elongation per unit length , or strain , is then determined by the equation ε=δ/L ()Where L is the total length of the bar . Now that the strain ε is a nondimensional quantity . It can be obtained accurately form Eq.() as long as the strain is uniform throughout the length of the bar . If the bar is in tension , the strain is a tensile strain , representing an elongation or a stretching of the material。 if the bar is in pression , the strain is a pressive strain , which means that adjacent cross section of the bar move closer to one another. ( Selected from Stephen and James M. Gere, Mechanics of Materials,Van NostrandReinhold Company Ltd.,1978.)Shear Force and Bending Moment in Beams Let us now consider, as an example , a cantilever beam acted upon by an inclined load P at its free end [(a)]. If we cut through the beam at a cross section mn and isolate the lefthand part of the beam as free body [(b)], we see that the action of the removed part of the beam (that is , the righthand part)upon the lefthand part must as to hold the lefthand in equilibrium. The distribution of stresses over the cross section mn is not known at this stage in our study , but wee do know that the resultant of these stresses must be such as to equilibrate the load P. It is convenient to resolve to
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