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【正文】 of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 ?sinPxM ? where x is the distance from the free end to section mn. Thus, through the use of a freebody diagram and equations of static equilibrium, we are able to calculate the stress resultants without difficulty. The stresses in the beam due to the axial force N acting alone have been discussed in the text of 。 Now we will see how to obtain the stresses associated with bending moment M and the shear force 裝控 091 專業(yè)英語翻譯 unit 1Static Analysis of BeamsA bar that is ubjected to for ces acting tr asverse to it s axis is cal ed a beam. I n t his section we Wil l consider only a f ew of the simplest ypes of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇 礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 The stress resultants N, V and M will be assumed to be positive when they act in the directions shown in (b). This sign convention is only useful, however, when we are discussing the equilibrium of the lefthand part of the beam. If the righthand part of the beam is considered, we will find that the stress resultants have the same magnitudes, but opposite directions[see (c)]. Therefore, we must recognize that the algebraic sign of a stress resultant does not depend upon its direction in space, such as to the left or to the right, but rather it depends upon its direction with respect to the material against which it acts. To illustrate this fact, the sign conventions for N, V and M are repeated in , where the stress resultants are shown acting on an element of the 裝控 091 專業(yè)英語翻譯 uni t 1Static Analysis of BeamsA bar that i s ubj ect ed to f orces act ing trasverse to its axis i s caled a beam. In this section we Wil consi der only a f ew of the simpl est types of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 We see that a positive axial force is directed away from the surface upon which it acts (tension), a positive shear force acts clockwise about the surface upon which it acts, and a positive bending moment is one that presses the upper part of the 裝控 091 專業(yè)英語翻譯 unit 1St atic Anal ysi s of BeamsA bar t hat issubjected to for ces acting tr asver se t o i ts axis iscal led a beam. In t his section we Wi l consider only a few of the simplest ypes of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 Example 過程裝備與控制工程課后材料專業(yè)英語翻譯 裝控 091 專業(yè)英語翻譯 uni t 1Staic Analysis of BeamsA bar that i s ubjected t o f orces act ing trasverse to its axis i s caled a beam. In this ect ion we Wil consi der only a few of the simpl est types of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 A simple beam AB carries two loads, a concentrated force P and a couple Mo,acting as shown in (a). Find the shear force and bending moment in the beam at cross sections located as follows: (a) a small distance to the left of the middle of the beam and (b) a small distance to the right of the middle of the 英語翻譯 裝控 091 專業(yè)英語翻譯 unit 1Staic Analysis of BeamsA bar that is subjected t o f orces acti ng trasverse to its axis i s caled a beam. In this ect ion we Wil consi der only a few of t he simpl est types of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬 阻便兌扔雜減綻醚蛆馱虛掃 Solution 過程裝備與控制工程課后材料專業(yè)英語翻譯 裝控 091 專業(yè)英語翻譯 uni t 1Static Analysis of BeamsA bar that is ubj ect ed to f orces act ing trasverse to its axis is cal ed a beam. I n this section we Wil l consider only a f ew of the simplest types of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇 嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 The first step in the analysis of this beam is to find the reactions RAand RB. Taking moments about ends A and B gives two equations of equilibrium, from which we find 過程裝備與控制工程課后材料專業(yè)英語翻譯 裝控 091 專業(yè)英語翻譯 unit 1Static Analysis of BeamsA bar that is ubjected to for ces acting tr asverse to it s axis is cal ed a beam. I n t his section we Wil l consider only a f ew of the simplest ypes of beam s, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡 泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 LMoPR A ?? 43 LMoPRB ?? 4 Next, the beam is cut at a cross section just to the left of the middle, and a freebody diagram is drawn of either half of the beam. In this example we choose the lefthand half of the beam, and the corresponding diagram is shown in (b). The force P and the reaction RA appear in this diagram, as also do the unknown shear force V and bending moment M, both of which are shown in their positive directions. The couple Mo does not appear in the figure because the beam is cut to the left of the point where Mo is applied. A summation of forces in the vertical direction gives 過程裝備與控制工程課后材料專業(yè)英語翻譯 裝控 091 專業(yè)英語翻譯 unit 1Stai c Analysis of BeamsA bar that isubjected to for ces acting tr asverse t o it s axis iscal ed a beam. I n t his section we Wi l consider only a few of the simplest ypes of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 LMoPPV R A ????? 4 which shows that the shear force is negative。 hence, it acts in the opposite direction to that assumed in (b). Taking moments about an axis through the cross section where the beam is cut [(b)] gives 過程裝備與控制工程課后材料專業(yè)英語翻譯 裝控 091 專業(yè)英語翻譯 unit 1St atic Anal ysi s of BeamsA bar t hat issubjected to forces acting t rasver se to i ts axis iscal led a beam. In this secti on we Wil consider onl y a few of the simplest ypes of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃 2842 MoPLPLLR AM ???? Depending upon the relative magnitudes of the terms in this equation, we see that the bending moment M may be either positive or 裝控 091 專業(yè)英語翻譯 uni t 1Static Analysis of BeamsA bar that i s ubj ect ed to f orces act ing trasverse to its axis i s caled a beam. In this ection we Wil consi der only a f ew of the simpl est types of beams, 遮名型苗臥淑繁鎢詐敞步剩岸馳封肇嬌甥邵尖顆歡泌重塌淀仇奮炙肇礦痞掃莉彭摯嚇訴叭牌合斬偏夢怠妝算佳卸惹琺彬阻便兌扔雜減綻醚蛆馱虛掃