Formulas.docx

𝛿𝑦 = 14 𝑚𝑚 = 14𝑥10−3 𝑚 𝛿𝑥 = 0.85 𝑚𝑚 = −0.85𝑥10−3 𝑚 𝐸 =?

𝐺 =?

𝑣 =?

Considerando que: Ley de Hook : 𝜎𝑦 = 𝐸. 𝜖𝑦 También

: 𝜖𝑦 =

𝛿𝑦 𝐿𝑜

𝑃 𝛿𝑦 𝑃 𝐴 𝐸= = = 𝐿𝑜 ∈𝑦 𝐴 ∈𝑦 6𝑥103 𝑁 𝐸= 𝜋 14𝑥10−3 𝑚 −3 2 4 (20𝑥10 𝑚) . 150𝑥10−3 𝑚 6𝑥103 𝑁. 150𝑥10−3 𝑚

𝐸=𝜋 −3 2 −3 4 (20𝑥10 𝑚) . 14𝑥10 𝑚 𝐸 = 204.627𝑥106 𝑃𝑎 = 204.627 𝑀𝑃𝑎

𝐸 𝐸 =1+𝑣 →𝐺 = 2𝐺 2(1 + 𝑣) 𝐷𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝑢𝑛𝑖𝑡𝑎𝑟𝑖𝑎 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑣= 𝐷𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝑢𝑛𝑖𝑡𝑎𝑟𝑖𝑎 𝑎𝑥𝑖𝑎𝑙

𝜖𝑦 =

𝛿𝑦 𝐿𝑜

𝛿

14 𝑚𝑚

= 150 𝑚𝑚 = 0.093

𝜖𝑥 = 𝐿 𝑥 = 𝑜

𝑣=−

𝐺=

0.85 𝑚𝑚 20 𝑚𝑚

−0.042 0.093

= −0.0425

= 0.456

204.627𝑥106 𝑁/𝑚2 2(1+0.456)

= 70.27 𝑀𝑃𝑎

2.65 𝐸 = 200𝑥109 𝑁/𝑚2 ∆𝑑 = 13𝜇𝑚 = 13𝑥10−6 𝑚 𝑣 = 0.29 𝑃𝑖𝑛𝑡 = ? 𝛿𝑑 = 13𝑥10−6 𝑚 Sabiendo que: 𝜎=

𝑃

→ 𝑃 = 𝜎. 𝐴 𝐴

2.827𝑥10−3 𝑚2

𝜋

𝐴 = 4 (0.06𝑚)2 =

Ley de Hooke

𝜎 = 𝐸. 𝜖 𝛿𝑦 13𝑥10−6 𝑚 𝜖𝑦 = = = − 216.667𝑥10−6 𝑚 −3 𝐿 60𝑥10 𝑚 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑣=− → 0.29 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝑎𝑥𝑖𝑎𝑙 (−216.667𝑥10−6 ) =− 𝜖𝑥 𝜖𝑥 = 747.127𝑥10−6 𝜎𝑥 = 𝐸. 𝜖𝑥

𝜎𝑥 = 200𝑥109

𝑁 𝑥 747.127𝑥10−6 2 𝑚

𝜎𝑥 = 149.425𝑥106 𝑃𝑎 = 149.425 𝑀𝑃𝑎 𝑃 = 𝜎. 𝐴 𝑁

𝑃 = 149.425𝑥106 𝑚2 𝑥 2.827𝑥10−3 𝑚2 𝑃 = 422.425𝑥103 𝑁 = 422.425 𝐾𝑁

2.64 𝐸 = 29𝑥106 𝑙𝑏/𝑖𝑛2 𝐿 = 72𝑖𝑛 𝑑𝑒 = 12 𝑖𝑛 𝑑𝑖 = 11 𝑖𝑛 𝑡 = 0.5 𝑖𝑛 𝑣 = 0.3 𝑃 = 300𝑥103 𝑙𝑏f 𝛿𝐿 = ? 𝛿𝑑 = ? 𝛿𝑡 = ? Sabiendo que: 𝛿 = 𝜖. 𝐿

𝐴= 𝐴=

Ley de Hooke

𝜎𝑦 𝜖𝑦 = 𝐸 𝑃𝑦 𝜖𝑦 = 𝐴 𝐸 1

𝜋

𝜋 4

(𝑑𝑒 2 − 𝑑𝑖 2 )

((12𝑖𝑛)2 − (11𝑖𝑛)2 ) → 𝐴 = 18.064𝑖𝑛2 4

𝜖𝑦 =

300𝑥103 𝑙𝑏 18.064 𝑖𝑛2 𝑥 29𝑥106

𝑙𝑏 𝑖𝑛2

𝜖𝑦 = −572.676𝑥10−6 𝛿𝐿 = −572.676𝑥10−6 𝑥 72 𝑖𝑛 𝛿𝐿 = −41.232𝑥10−3 𝑖𝑛 RECORDANDO QUE:

𝑣=−

𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑐𝑖𝑜𝑛 𝑎𝑥𝑖𝑎𝑙

𝜖

→ 𝑣 = − 𝜖𝑥 → 𝜖𝑥 = 𝑣. 𝜖𝑦

𝜖𝑥 = 0.3 𝑥 (527.676𝑥10−6 ) 𝜖𝑥 = 171.802𝑥10−6 𝛿𝑑 = 𝜖𝑥 . 𝑑 = 171.802𝑥10−6 𝑥 12𝑖𝑛 𝛿𝑑 = 2.061𝑥10−3 𝑖𝑛

𝛿𝑡 = 𝜖𝑥 ∗ 𝑡 𝛿𝑡 = 171.802𝑥10−6 ∗ 0.5 𝑖𝑛 𝛿𝑡 = 85.901𝑥10−6 𝑖𝑛

𝑦