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            Influence lines£¨Ó°ÏìÏߣ©have important application for£¨Ó¦Óã©the design of structures that resist large live loads£¨»îºÉÔØ£©. An influence line represents£¨´ú±í£©the variation of either the reaction, shear, moment, or deflection at a specific £¨Ìض¨µÄ£©point in a member as concentrated force moves over the member. Once this line is constructed£¨×÷ͼ£©, one can tell at a glance£¨Ò»ÑÛ±ãÖª£©where a live load should be placed on the structure so that it creates£¨ÒýÆð£©the greatest influence at the specified point. Furthermore, the magnitude£¨´óС£©of the associated £¨Ïà¹ØµÄ£©reaction, shear, moment, or deflection at the point can then be calculated from the ordinates£¨×Ý×ø±ê£©of the influence-line diagram.
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    For these reasons£¨Òò´Ë£©, influence lines play an important part in the design of bridges, industrial crane rails£¨µõ³µ¹ìµÀ£©, conveyors, and other structures where loads move across their span£¨È«³¤£©. Although the procedure£¨²½Ö裩for constructing an influence line is rather basic£¨»ù±¾µÄ£©, one should clearly be aware of the difference between constructing an influence line and constructing a shear or moment diagram. Influence lines represent the effect of a moving load only at a specified point on a member, whereas shear and moment diagrams represent the effect of fixed loads at all points along the axis of the member.
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             Deflections of structures can occur from various sources£¨Ô­Òò£©, such as loads, temperature, fabrication errors, or settlement. In design, deflections must be limited in order to prevent cracking of attached£¨¸½ÊôµÄ£© brittle materials such as concrete or plaster (ʯ¸à) . Furthermore, a structure must not vibrate or deflect£¨±ä룩severely in order to “appear” safe for its occupants£¨¾ÓסÕߣ©. More important, though£¨È»¶ø£©, deflections at specified points in a structure must be computed if one is to analyze statically indeterminate structures. We often determine the elastic deflections of a structure using both geometrical and energy methods. Also, the methods of double integration£¨Ë«ÖØ»ý·Ö£©are used. The geometrical methods include the moment-area theorems£¨Íä¾ØͼÃæ»ý¶¨Àí£©and the conjugate-beam method£¨¹²éîÁº·¨£©, and the energy methods to be considered are based on virtual work£¨Ð鹦£©and Castigliano’s theorem£¨¿¨ÊÏ×îС¹¦¶¨Àí£©. Each of these methods has particular advantages or disadvantages.
           ½á¹¹µÄÄӶȿÉÒÔÒò²»Í¬µÄÔ­Òò¶ø·¢Éú£¬ÈçºÉÔØ¡¢Î¶È¡¢ÖÆÔì´íÎó»ò³Á½µ¡£Éè¼ÆÖУ¬ÄӶȱØÐë¼ÓÒÔÏÞÖÆÒÔ×èÖ¹¸½ÊôµÄ´àÐÔ²ÄÁÏÈç»ìÄýÍÁ»òʯ¸àµÄ¿ªÁÑ¡£¶øÇÒ£¬ÎªÁËÏò¾ÓסÕßÏÔʾ°²È«ÐÔ£¬½á¹¹²»ÄÜÑÏÖصØÕñ¶¯»ò±äλ¡£¶ø¸üÖØÒªµÄÊÇÈç¹ûÓÐÈËÒª·ÖÎö³¬¾²¶¨½á¹¹£¬±ØÐë¼ÆËã³ö½á¹¹Öй涨µãµÄÄӶȡ£ÎÒÃÇͨ³£²ÉÓü¸ºÎ·¨ºÍÄÜÁ¿·¨À´È·¶¨½á¹¹µÄµ¯ÐÔÄӶȡ£Ò²²ÉÓÃË«ÖØ»ý·Ö·¨¡£¼¸ºÎ·¨°üÀ¨Íä¾ØͼÃæ»ý¶¨ÀíºÍ¹²éîÁº·¨£¬¶ø¿¼ÂǵÄÄÜÁ¿·¨ÊÇ»ùÓÚÐ鹦¶¨ÀíºÍ¿¨Ê½×îС¹¦¶¨Àí¡£Ã¿Ò»ÖÖ·½·¨¶¼ÓÐÆäÌرðµÄÓÅȱµã¡£
          We can determine the equation of the elastic curve by integration of equation d2v / dx2 = M / EI. Solution of this equation requires two successive£¨Á¬ÐøµÄ£©integrations to obtain the deflection v of the elastic curve. For each integration, it is necessary to introduce£¨ÒýÈ룩a “constant of integration”£¨»ý·Ö³£Êý£©, and then solve for the constants to obtain a unique solution£¨Î¨Ò»½â£©for a particular£¨Ìض¨µÄ£©problem. It should be realized that the method of double integration is suitable only for elastic deflections£¨±ä룩such that the beam’s slope is very small. Furthermore, the method considers only deflections due to bending.