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Design of Beams ÁºµÄÉè¼Æ

         Up to this point£¨ÖÁ´Ë£©we have looked at£¨¿¼ÂÇ£©the beam problem as a problem in analysis; that is£¨¼´£©, for a given set of loads, span, and cross section we have been calculating the stress. The more commonly encountered problem is to select a standard section, or design a member, for a given span and loads without exceeding a certain allowable stress. Under some conditions the allowable stress may be dependent upon the dimensions and shape of the cross section, in which case the selection of the member becomes more difficult. For the present£¨ÔÝʱ£©we will take the allowable stress as though£¨Ëƺõ£©it depends only on the strength of the material and the safety factor.
            ÖÁ´Ë£¬ÎÒÃÇÒѾ­¿¼ÂÇÁËÁºµÄÎÊÌâ¶ø½øÐÐÁË£¨ÎÊÌ⣩·ÖÎö£¬¼´¶Ô¸ø¶¨µÄÒ»×éºÉÔØ¡¢¿ç¶ÈºÍºá½ØÃ棬ÎÒÃÇÒѾ­¼ÆËãÁËÓ¦Á¦¡£¸ü³£Óöµ½µÄÎÊÌâÊÇÔÚ²»³¬¹ýij¸öÐíÓÃÓ¦Á¦Ï¶ÔÒ»¸ö¸ø¶¨µÄ¿ç¶ÈºÍºÉÔØÑ¡ÔñÒ»¸ö£¨¹¹¼þµÄ£©±ê×¼½ØÃ棬»òÉè¼ÆÒ»¸ö¹¹¼þ¡£ÔÚijЩÌõ¼þÏ£¬ÐíÓÃÓ¦Á¦¿ÉÄÜÒÀÀµÓÚºá½ØÃæµÄ³ß´çºÍÐÎ×´£¬ÕâÖÖÇé¿öÏµĹ¹¼þÑ¡Ôñ»á±äµÃ±È½ÏÀ§ÄÑ¡£ÔÝʱÎÒÃǽ«²ÉÓÃÐíÓÃÓ¦Á¦·¨£¬ËƺõËüֻȡ¾öÓÚ²ÄÁϵÄÇ¿¶ÈºÍ°²È«ÏµÊý¡£
    In the usual design process the maximum bending moment is taken from£¨È¡×ÔÓÚ£©the bending moment diagram£¨Íä¾Øͼ£© and the allowable stress is determined (quite frequently in accordance with£¨¸ù¾Ý£©the rules of some legally constituted code) from standard strength tests in combination with£¨Óë..½áºÏ£©a safety factor. The right-hand side of (4-6) is then known, and it remains£¨ÈÔÈ»ÊÇ£© to select or design a member that will satisfy the inequality. When a standard section is to be used, the tables£¨±í¸ñ£©could be searched until a member is found such that the combination of I and c satisfies (4-6). This takes more time than is really necessary, since the tables also provide the value of I/c for each member under the heading£¨±êÌ⣩S, the section modulus£¨½ØÃæÄ£Á¿£©.
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To select a member, the S column£¨ÁУ© is consulted£¨²éÔÄ£© and any member that satisfies (4-8) could be used. The members with very high values of S will obviously be understressed£¨Ó¦Á¦²»×ãµÄ£©and wasteful of material. The best design, if there are no other constraints, will be that which satisfies (4-8) with the minimum amount of material.
        The smallest acceptable S does not necessarily coincide with£¨·ûºÏ£©the most economical member. To select the lightest and most economical standard section, the listed values of mass should be examined to find the lightest member with an acceptable S. The problem becomes much more complex if built-up£¨×éºÏ£©member is being designed because its cost will depend upon the combined costs of web plate, angles and cover plates as well as fabrication£¨×°Å䣩costs so that the lightest member is not necessarily the most economical.
ΪѡÔñ¹¹¼þ¶ø²éÔÄSÕâÒ»ÁУ¬ÔòÈκÎÂú×ãʽ£¨4-8£©µÄ¹¹¼þ¶¼¿É²ÉÓá£ÏÔ¶øÒ×¼û£¬¶ÔSÖµºÜ¸ßµÄ¹¹¼þ£¬ÆäÓ¦Á¦ÊDz»×ãµÄ£¬²¢ÀË·ÑÁ˲ÄÁÏ¡£Èç¹ûûÓÐÆäËûµÄÏÞÖÆ£¬×îºÃµÄÉè¼Æ½«ÊÇÒÔ×îÉٵIJÄÁÏÂú×ãʽ£¨4-8£©¡£ÄܽÓÊܵÄ×îСµÄSÖµ²»±ØÊÇ×î¾­¼ÃµÄ¹¹¼þ¡£ÎªÁËÑ¡Ôñ×îÇáºÍ×î¾­¼ÃµÄ±ê×¼½ØÃ棬Ӧ¼ì²éÁгöµÄÖÊÁ¿Öµ£¬ÒÔÕÒµ½ÄܽÓÊܵÄSֵϵÄ×îÇá¹¹¼þ¡£Èç¹ûÔÚÉè¼ÆÒ»¸ö×éºÏ¹¹¼þʱ£¬ÔòÎÊÌâ±äµÃ¸´Ôӵö࣬ÒòΪËüµÄ·ÑÓý«ÒÀÀµÓÚ¸¹°å¡¢½Ç¸ÖºÍ¸Ç°åµÄ·ÑÓÃÒÔ¼°×°ÅäµÄ·ÑÓã¬Òò´Ë£¬×îÇáµÄ¹¹¼þδ±ØÊÇ×î¾­¼ÃµÄ¹¹¼þ¡£
           The main purpose of this chapter£¨±¾½Ú£© was to develop£¨Ìá³ö£©the flexure£¨ÇüÇú£©formulas, and to provide some experience in applying them. Statically indeterminate£¨³¬¾²¶¨£©cases were encountered and some insight£¨ÈÏʶ£© gained as to£¨¾Í..£©the difficulty and importance of this category of problem.
            ±¾½ÚµÄÖ÷ҪĿµÄÊÇÌá³öÇüÇú¹«Ê½£¬²¢ÔÚÔËÓù«Ê½Ê±ÌṩһЩ¾­Ñé¡£µ±Óöµ½³¬¾²¶¨µÄÇé¿öʱ£¬¾Í´ËÀàÎÊÌâµÄÄѵãºÍÖصã»ñµÃһЩÈÏʶ¡£
             Superposition£¨µþ¼Ó·¨£©was presented£¨Ìá³ö£© as the preferred£¨ÓÅÏȵģ©method for solving certain problems. However, becoming familiar with£¨ÊìϤ£©superposition was more important than finding solutions to the problems£¨ÎÊÌâµÄ´ð°¸£© because superposition has application in many areas of stress analysis and will be used frequently in our future studies.
            Ϊ½â¾öijЩÎÊÌ⣬µþ¼Ó·¨×÷ΪÓÅÏȵķ½·¨±»Ìá³ö¡£µ«ÊÇ£¬ÊìϤµþ¼Ó·¨Ô¶±ÈÕÒµ½ÎÊÌâµÄ´ð°¸ÖØÒª£¬ÒòΪµþ¼Ó·¨ÒѾ­ÓÃÓÚÓ¦Á¦·ÖÎöµÄºÜ¶àÁìÓò£¬¶øÇÒ£¬ÔÚÎÒÃǽñºóµÄÑо¿Öл¹»á¾­³£Ê¹Óá£
            Moment-area£¨Íä¾àͼÃæ»ý·¨£©was found to be a convenient method for solving various problems. It is a method that becomes quite complicated and requires further development£¨Õ¹¿ª£© when more advanced structures are encountered. At the present stage it is sufficient for you to be acquainted with£¨Á˽⣩the fundamentals£¨»ù±¾Ô­Àí£©of the method. Deflection of long-radius£¨³¤°ë¾¶£© curved beams was introduced£¨ÒýÈ룩to illustrate the power of the principles underlying£¨¹¹³É..µÄ»ù´¡£©the moment-area method and so that you would appreciate£¨ÖªµÀ£©the differences between straight and curved beams.