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CHAPTER 5
DESIGN FOR DIFFERENT
TYPES OF LOADING
ͳǤߪ ൌ ܨȀܣǣܣ ൌ గሺଵሻమ
ସൌͺǤͷͶଶ
ߪ
ൌ ͷͲͲȀܣ ൌ Ǥૠۻ۾܉
ʹǤ ߪ ൌ ܨȀܣǣܣ ൌ ሺͳͲ݉݉ሻሺ͵Ͳ݉݉ሻൌ ͵ͲͲଶ
ߪ
௫ ൌሺʹͲൈͳͲଷܰሻȀ͵ͲͲଶൌǤૠۻ۾܉
͵Ǥ ߪ ൌ ܨȀܣǣܣ ൌ ሺͲǤͶͲ݅݊ሻଶൌ ͲǤͳଶ
ܨ
ൌሺͺͲെͳʹͲሻȀʹ ൌ ͵Ͳ
ߪ
ൌ ͵ͲȀܣ ൌ ܘܛܑ
Stress
122
ߪ
ൌߪ
௫ െߪ
ൌͷ͵ͷെʹ͵ͳ͵ൌܘܛܑ
ܴൌߪ
Ȁߪ௫ ൌെͷͲȀͷ͵ͷൌെǤ
ͶǤ ߪ ൌ ܨȀܣǣܣ ൌ గమ
ସൌగሺǤଷହሻమ
ସൌͲǤͳͳͲͶଶ
ߪ
௫ ൌͳͺͲͲȀͲǤͳͳͶͲଶൌૢૠܘܛܑ
ͷǤ ߪ ൌ ܨȀܣǣܣ ൌ గమ
ସൌగሺଷǤሻమ
ସൌǤͲͻଶ
ߪ
௫ ൌͺͲȀǤͲͻଶൌǤۻ۾܉
123
Ǥ ߪ ൌܯȀܵǢܵ௬ൌ ͳǤͶͺଷͶൈʹൈͳͶ
ൗ ǣȏͳͷǦͳͶȐ
ǣߪ
௫ ൌሺͳͶͶͲͲήሻȀͳǤͶͺଷൌ ૢૠܘܛܑ
ߪ
ൌଷ଼ସ
ଵǤସ଼ ൌૢܘܛܑ
ߪ
ൌሺͻ͵ͲʹͷͻͷሻȀʹൌ ܘܛܑ
Loading
M
M
(lbin)
(lb)
M
(lbin)
124
Ǥ ȏȐǣߪ ൌெ
ௌǣܵ ൌ ͵ǤͲͶଷͶൈǤ
ߪ
௫ ൌଷή
ଷǤସమൌ ૢૡૡܘܛܑ
ߪ
ൌͷͲͲͲȀ͵ǤͲͶൌܘܛܑ
ͺǤ
ுమ
M
(Nm)
Beam cross
Loading case I Loading case II
(N)
M
M
(Nm)
Time
125
ߪ
ൌሺͳͲǤͳͲǤͶሻȀʹ ൌ ૢǤۻ۾܉
ߪ
ൌߪ
௫ െߪ
ൌͳͲǤെͷͻǤͳ ൌ ૡǤۻ۾܉
ܴൌߪ
Ȁߪ௫ ൌͳͲǤͶȀͳͲǤൌǤૢૠ
ͻǤ ȂȋȌͳͶǦ͵Ǥ
ǤǤ
ǣ
ܫൌ
ሺହሻሺǤሻయ
ଵଶ ൌͲǤͻͲସ
ܵൌ
ହሺǤሻమ
ଵଶ ൌͲǤ͵Ͳଷ
ǣ
ܯ
ൌି
ଶమሺܾܮሻൌെሺଵହሻሺଶହሻ
ଶሺସሻమሺʹͷͶͲሻൌ െǤͳܲ
V
M
126
ߪ
ൌሺͶͷʹͻሻȀʹൌૡۻ۾܉
ͳͲǤ ݏ
ᇱǢͳͲͶͲǢݏ௨ൌ ͺͲǢݏൌ͵ͳሺሻ
ܦ ൌͲǤͷǢܥ௦ൌ ͲǤͻͲሾͷെͳʹሿ
ͳͳǤ ݏԢǣͷͳͲͳ͵ͲͲǢݏ௨ൌ ͻͷǢݏൌ ͵ͲͲሾͷെͳͳሿ
ͳʹǤ ݏ
ᇱǣͶͳ͵Ͳͳ͵ͲͲǢݏ௨ൌ Ǣݏൌ ʹͲሾͷെͳͳሿ
ͷǦʹͷǣܦൌ ͲǤͺͲͺξ݄ܾ ൌͲǤͺͲͺඥሺͲሻሺʹͲሻൌʹͺǤͲ
ͳ͵Ǥ ݏ
ᇱǣ͵ͲͳǡΦǢݏ௨ൌ ͳͷͲǢݏൌ ͷʹǣሾͷെͳͳሿ
127
ͳͶǤ ݏԢǣʹͶʹǢݏ௨ൌ ͲǢݏൌ ʹǤͲǡ ሾͷെͳͳሿ
ȏȋͷǦʹͷȌȐǢܦൌ ͲǤͺͲͺξ݄ܾ ൌͲǤͺͲͺඥሺ͵ǤͷሻሺͲǤ͵ͷሻൌͲǤͻʹǢܥ௦ൌ ͲǤͺͺ͵
ͳͷȂͳͺǦǤ
GeneralDesignProcedureͷǦͳͳǤ
ͷǦͳͲ
Ǥ
ͷǦͻǤǡͷǦʹͳ
ͷǦǤ
ͳͷǤ ǤͷǦͳͲǤ
ͳͻǤ ͷǦͺǤͺǤȂǣ
ଵ
ேൌఙ
௦ೠఙೌ
௦
ᇲሾሺͷെʹͺሻሿǢߪൌ ͷͻǤͳǢߪൌ ͶͺǤ
ܰǤͳͲʹͲǢݏ௬ൌ ʹͲǢݏ௨ൌ ͵ͻǢݏൌͳͶͲȏͷǦͳͳ
Ȑ
ʹͲǤ Ȃ
ǣͲǤ
ʹͳǤ ͶൈǤሺܣ்ൌ ʹǤʹଶሻ
ǤǤͷǦʹͺͷǦʹͻȂǤ
ଵ
ᇲൌǣ͵Ǣݏ௬ൌ͵Ǣݏ௨ൌ ͷͺ
129
ʹʹǤ ͻǤȂǤ
ߪ
ൌ͵ͺǢߪൌ ͺͻǤ͵ǣͶͳͶͲͶͲͲ
ݏ
௨εͳͲΨǤ
ݏ
௨ൌʹͲͲͲǢݏ௬ൌ ͳ͵ͲǢݏൌͶͷͲሺܨ݅݃ݑݎ݁ͷെͳͳሻ
ʹ͵Ǥ ǤȂ
Bǣߪൌ ͺͶ͵ʹǢߪൌ ʹͷͻͷ
Cǣߪൌ ͳʹǢߪൌ ͵ͷͺ
ͷͲͲǣݏ௨ൌ ͷͺǢݏ௬ൌ Ͷ
ݏ
ൌʹͲǢܴ ൌͲǤͻͻ՜ܥோൌ ͲǤͺͳǢܥ௦ͶൈͶൈͳͶ
ൗǣ
ଶ
ʹͶǤ ǤͷǦʹͶǤൌͲǤͲǢ ൌ ɎଶȀͶ ൌ ͲǤʹͺ͵ଶ
Ǥܨ௫ ൌ ͳͷͲͲǢܨ ൌ െͶͲͲǢ
ܨൌሺͳͷͲͲെͶͲͲሻȀʹ ൌ ͷͷͲǢܨൌͳͷͲͲെͷͷͲൌͻͷͲ
ݏ
131
ʹͷǤ Ȃǣܰ ൌݏ௨Ȁߪ௫
ߪ
௫ ൌி
ൌሺଵǤଽଽሻሺହሻ
గሺସǤሻమȀସ ൌ ͳͳͺ
ʹǤ Ȃǣܰ ൌݏ௨௧Ȁߪ௫
ʹǤ ȂȂͷǦͶ
ǤȏͷǦͺͷǦͻȐ
ߪ
ଵߪଶǤ
ǣܴ ൌξʹ͵ͷͷଶͷͻ͵ͻଶൌ͵ͺͻ
ߪ
ଵൌߪ
ܴ ൌ െͷͻ͵ͻ͵ͺͻ ൌͶͷͲ
132
(kNmm) 0
M = 2.7x
ʹͺǤ ȂǣȏͷǦʹͺȐ
ͳͳ͵Ǣݏ௬ൌ ͷͷ
ܵൌߨܦ
ଷȀ͵ʹǣܦ ൌ ඥ͵ʹܵȀߨ
యൌʹǤ͵
ߪ αǦͷͻ͵ͻ
͵ͲǤ ͷǦʹͺʹͺʹͻǤܭ௧ൌ ʹǤͲ
ǣ
ଵ
ேൌሺఛೌሻೌೣ
௦ᇱೞ ሺఛሻೌೣ
௦ᇱೞೠ
135
͵ͳǤ ݏ௬ൌ͵ͲǢ߬ௗൌͲǤͷݏ
௬Ȁܰ ൌͲǤͷሺ͵ͲሻȀ͵ൌͷൌͷͲͲͲ
ȂǡǤ
Ǥ߬Ȃ
ǤȂͶǡͶǦʹʹ
ͶǦʹ͵Ǥ
͵ʹǤ ǣǤ
ଵ
ேൌఛ
௦ᇱೞೠ ఛೌ
௦ᇱೞ
ܦ
ൌඥͳܼȀߨ
యൌඥͳሺͲͺሻ݉݉ଷȀߨ
యൌͳͷǤ͵
Ta = 17.5
65.0
137
͵͵Ǥ ǣǢͷǦʹͺ
ଵ
ேൌఙ
௦ೠఙೌ
௦
ᇲͷെͳͳ
ܵൌܾ
ଷȀǢܣ ൌ ܾଶ
ଵ
ேൌభఱబబ
್మାమఴఴబబ
್య
ହ మఴఴబబ
್య
ଶସ ൌǤଶ
మǤଷ଼ସ
యଵǤସଵଶ
యൌǤଶ
మଵǤଽ
య
ܾଶǣ
యൌ ͳǤͷ՜ ܾ ൌ ͳǤͺͲെ
ݏ
b
b
M
(lbin)
138
ǣ
ଵ
ேൌభఱబబ
್మାమఴఴబబ
್య
ହ మఴఴబబ
್య
ଵଽହ ൌǤଶ
మǤଷ଼ସ
యଵǤହଵଶ
యൌǤଶ
మଵǤ଼ଽ
య
ଵ
ேൌǤଶ
ሺଵǤ଼ሻమଵǤ଼ଽ
ሺଵǤ଼ሻయൌ ͲǤ͵͵ͳǢࡺ ൌ Ǥെ۽ܓ܁ܘ܍܋ܑܡ࢈ ൌ Ǥૡܑܖ
͵ͶǤ ǣ
ଵ
ேൌሺఛሻೌೣ
௦ೞೠ ൌሺఛೌሻೌೣ
௦ೞ
ᇲ
ɒǣȋ͵ǦͳͲȌ
ǣ߬ൌߪ
Ȁʹ
ሺ߬ሻ௫ ൌଵ
ଶଶ଼଼
యൌଵସସ
య
ǣଵ
್య
್య
Mohr’s circle – Mean
stress
Genera
l
(Wm)max =
R
5401
2700
139
ǣ
͵Ǥ ߪ ൌ ܨȀܣ ൌ ሺͷͲͲͲܰሻȀሺͳʹ݉݉ሻଶൌ ͵ͶǤǣܰ ൌݏ௬Ȁߪ
Ȍ ͳͲʹͲǣܰ ൌʹͲȀ͵ͶǤൌǤૢ
Ȍ ͺͷͲǦͳͲͲͲǢܰ ൌͳͲͲȀ͵ͶǤൌǤૡ
͵Ǥ ߪ ൌி
ൌଵଶ
ሺሺଶǤଶହሻమିሺଶǤሻమሻమൌ ͳͳͺͷͻǣܰ ൌ ݏ௬Ȁߪ ൌ ͶͲͲͲͲȀͳͳͺͷͻൌ Ǥૠ