Íà ãëàâíóþ

Êóðñîâàÿ ðàáîòà: Ñîïðîìàò


Êóðñîâàÿ ðàáîòà: Ñîïðîìàò

Çàäà÷à ¹ 1

Òåìà: Ðàñ÷åò íà ïðî÷íîñòü ñòàòè÷åñêè îïðåäåëèìûõ ñèñòåì ïðè ðàñòÿæåíèè è ñæàòèè

Òðåáóåòñÿ:

1. Ïîñòðîèòü ýïþðó ïðîäîëüíîãî óñèëèÿ Ni

2. Ïî óñëîâèþ ïðî÷íîñòè ïîäîáðàòü ðàçìåð ïîïåðå÷íîãî ñå÷åíèå «à», åñëè =160 ÌÏà

3. Äëÿ ðàññ÷èòàííîãî ðàçìåðà ïîïåðå÷íîãî ñå÷åíèÿ ïîñòðîèòü ýïþðó íîðìàëüíûõ íàïðÿæåíèé  

4. Ïîñòðîèòü ýïþðó îñåâûõ ïåðåìåùåíèé W è íàéòè íàèáîëüøóþ âåëè÷èíó îòíîñèòåëüíûõ äåôîðìàöèé , åñëè

5. Îïðåäåëèòü ïîòåíöèàëüíóþ ýíåðãèþ óïðóãèõ äåôîðìàöèé U


Äàíî:                                                            7

Ð1 = 50 êÍ;   l1 = 3 ì ;        Øa                                                                                     2a

Ð2 =65 êÍ;   l2 = 2 ì ;                                                Ø2a                    a                              2a

Ð3 =40 êÍ;   l3 = 3 ì ;                                                                             a                                         

Ð4 =10 êÍ;   l4 = 1ì ;                                       D                             C                          B                         A 

Ôîðìû ñå÷åíèÿ:                   Ra                                            P4                           P3                               P2                           P1

À1 ¹ 11    À3 ¹ 4

À2 ¹  9    À4 ¹ 7                                  IV                               III                                        II           I

                                                          l 1                        l2                                     l3                         l4

Ni = ? ;  = ? ;  = ?;                                                                                                    N1     P1

 = ? ; “a” = ? ;                                        45                           55                    

                                                                                                         15        

                                            +                                                                                    Ýï.N (kH)

                                            -

                                                      16                                                                               50

                                                                         3,69                  2

                                           +                                                                                     Ýï.σ(ÌÏà)

                                           -                                                                                                                       

                                                                                                                                                        

                                                                                                                         13

                                                                            1,99                    2,986                 3,534                     6,9

                                                             0                                                                                         

Ýï.∆l(ìì)                                 +

Ðåøåíèå:

Îïðåäåëÿåòñÿ ñèëà ðåàêöèè îïîð RÀ èç óðàâíåíèÿ ñòàòèêè:


Äåëèì íà 4 ó÷àñòêà, îáîçíà÷àÿ èõ ðèìñêèìè öèôðàìè (I, II, III, IV), à òàêæå õàðàêòåðíûå ñå÷åíèÿ ÷åðåç çàãëàâíûå áóêâû (À, Â, Ñ, D, Å).

Îïðåäåëÿåòñÿ ïðîäîëüíàÿ ñèëà íà êàæäîì ó÷àñòêå ìåòîäîì ñå÷åíèÿ:

Ñòðîèòñÿ ýïþðà ïðîäîëüíûõ ñèë Ni

Îïðåäåëÿåòñÿ ïëîùàäü ïîïåðå÷íûõ ñå÷åíèé íà êàæäîì ó÷àñòêå

À1=à*à=à2

À2=2à*à=2à2

À3=2à*2à=4à2

Îïðåäåëÿåòñÿ íîðìàëüíîå íàïðÿæåíèå íà êàæäîì ó÷àñòêå ÷åðåç 1/à2

Îïðåäåëÿåòñÿ ìàêñèìàëüíîå çíà÷åíèå íîðìàëüíîãî íàïðÿæåíèÿ, íå ïðåâûøàþùåå äîïóñêàåìîãî íàïðÿæåíèÿ, ðàâíîå 160 ÌÏà:

Ìàêñèìàëüíîå çíà÷åíèå íàïðÿæåíèÿ íà òðåòüåì ó÷àñòêå

Íàõîäèòñÿ çíà÷åíèå «à»:

Ïðèíèìàåòñÿ à = 19,4ìì

Îïðåäåëÿþòñÿ äåéñòâèòåëüíûå çíà÷åíèÿ ïëîùàäåé ïîïåðå÷íûõ ñå÷åíèé:

Îïðåäåëÿþòñÿ èñòèííûå çíà÷åíèÿ íîðìàëüíîãî íàïðÿæåíèÿ íà êàæäîì ó÷àñòêå:

10. Ñòðîèòñÿ ýïþðà íîðìàëüíîãî íàïðÿæåíèÿ  

11. Îïðåäåëÿåòñÿ îòíîñèòåëüíàÿ ïðîäîëüíàÿ äåôîðìàöèÿ íà êàæäîì ó÷àñòêå:

, ãäå Å = 2 105ÌÏà

12. Îïðåäåëÿåòñÿ îòíîñèòåëüíàÿ ïðîäîëüíàÿ äåôîðìàöèÿ  ïî ñå÷åíèÿì:

13. Îïðåäåëÿåòñÿ îòíîñèòåëüíîå óäëèíåíèå  è ñòðîèòñÿ ýïþðà ýòèõ çíà÷åíèé (Ðèñ 1ä):

Îïðåäåëÿåòñÿ ìàêñèìàëüíîå çíà÷åíèå îòíîñèòåëüíîãî óäëèíåíèÿ:

14. Îïðåäåëÿåòñÿ óäåëüíàÿ ïîòåíöèàëüíàÿ ýíåðãèÿ

15. Îïðåäåëÿåòñÿ ïîëíàÿ óäåëüíàÿ ïîòåíöèàëüíàÿ ýíåðãèÿ

16. Îïðåäåëÿåòñÿ îòíîñèòåëüíàÿ ïîãðåøíîñòü íîðìàëüíîãî íàïðÿæåíèÿ:

Çàäà÷à ¹2

Òåìà: Ðàñ÷åò íà ïðî÷íîñòü ñòàòè÷åñêè íåîïðåäåëèìûõ ñèñòåì ïðè ñæàòèè è ðàñòÿæåíèè

Äàíî:

Ñõåìà áðóñà

Ðàçìåðû è íàãðóçêè

Ìàòåðèàë áðóñüåâ – ñòàëü 3

Äîïóñêàåìîå íàïðÿæåíèå

Ìîäóëü ïðîäîëüíîé óïðóãîñòè


Òðåáóåòñÿ:

Îïðåäåëèòü äîïóñêàåìóþ íàãðóçêó äëÿ ñòóïåí÷àòîãî áðóñà

Äàíî:

l = 30 ñì = 0,3 ì = 300 ìì

À = 10 ñì2 =

Ê = 0,15

[Ð] = ?

                                                                                         Ýï. N (kH)            Ýï. σ (kH)                           Ýï. l (ìì)   

                              Ra

                                                                                             +   -                       + -                                    + -

         

                      A                                                                                                                                          A

1.5l                                                 3A      I               255                            53

                                                                                                                                                                   0,02

                                                                                                                                                                       

        B                          2A           II                                      133                                              Â

    l                                                                                                                                                          0,047

                                                                                                                                                                 C

               C                                                          425                                                                       Ñ

1.5l                                   4P           4A   III                                              66,4                                       0,066

                                                                                                                                                           D

                 D

     l                                          A             IV                                      255                               159

                             E                                                                                                                             0,035

                                                                                                                                                            E

    ∆                                    Re

Ðåøåíèå:

Ñîñòàâëÿåòñÿ óðàâíåíèå ñòàòèêè

Ñîñòàâëÿåòñÿ óðàâíåíèå ñîâìåñòíîñòè äåôîðìàöèè ÓÑÄ:

 - îò çàäàííûõ ñèë

 - ÓÑÄ (1)

Îïðåäåëÿþòñÿ ïðîäîëüíûå ñèëû íà êàæäîì ó÷àñòêå:

 =? êîãäà íåò RE

Íàõîäèì îòíîñèòåëüíîå óäëèíåíèå íà êàæäîì ó÷àñòêå

Îïðåäåëÿåòñÿ  - îòíîñèòåëüíîå óäëèíåíèå ñèëû ðåàêöèè îïîð, êîãäà íåò ñèë Ð è 2Ð:

Ïîäñòàâëÿåì çíà÷åíèÿ  è  â óðàâíåíèå (1)

Ïîäñòàâëÿåì çíà÷åíèå ñèëû  â óðàâíåíèå ñòàòèêè

Îïðåäåëÿåì çíà÷åíèÿ ïðîäîëüíûõ ñèë, ïîäñòàâëÿÿ çíà÷åíèÿ

Îïðåäåëÿåòñÿ çíà÷åíèå íîðìàëüíîãî íàïðÿæåíèÿ íà êàæäîì ó÷àñòêå

Íàõîäèì ìàêñèìàëüíîå çíà÷åíèå íîðìàëüíî íàïðÿæåíèÿ

Ïðèíèìàåì Ð = 170 êÍ

Îïðåäåëÿþòñÿ äåéñòâèòåëüíûå çíà÷åíèÿ ïðîäîëüíûõ ñèë:

10. Îïðåäåëÿþòñÿ èñòèííûå çíà÷åíèÿ íîðìàëüíîãî íàïðÿæåíèÿ íà êàæäîì ó÷àñòêå :

Íàõîäèì îòíîñèòåëüíîå óäëèíåíèå

Íàõîäèì îòíîñèòåëüíîå óäëèíåíèå ïî ñå÷åíèÿì

Îïðåäåëÿåì îòíîñèòåëüíîå óäëèíåíèå

Ïî çàäàííîé ôîðìóëå âû÷èñëÿåì çíà÷åíèå çàçîðà , îíî äîëæíî ñîîòâåòñòâîâàòü çíà÷åíèþ

Ïðîâåðêà

Çàäà÷à ¹ 3

Òåìà: Ðàñ÷åò íà ïðî÷íîñòü ñòàòè÷åñêè íåîïðåäåëèìûõ ñèñòåì ïðè ðàñòÿæåíèè è ñæàòèè.

Òðåáóåòñÿ:

Íàéòè óñèëåíèå è íàïðÿæåíèå â ñòåðæíÿõ, âûðàçèâ ÷åðåç ñèëó Ð1

Îïðåäåëèòü äîïóñêàåìóþ íàãðóçêó [Ð], åñëè [σ] = 160 ÌÏà

Íàéòè ïðåäåëüíóþ íàãðóçêó Ðïð, åñëè [σ1] = 240 ÌÏà è h1 = 1,5

Ñðàâíèòü âåëè÷èíû äîïóñêàåìûõ íàãðóçîê Ðïð è Ð, äëÿ ÷åãî íàéòè èõ îòíîøåíèÿ.

Äàíî:

À=14ñì2 = 14·10 - 4ì

à=2,3ì

â=2,7ñì

ñ=1,7ñì

[σ] =160 ÌÏà

hÒ = 1,5


Íàéòè: Ð=?, ÐÒ =?, [ÐÒ] =?

Ðåøåíèå.

1. Ñîñòàâëÿåòñÿ óðàâíåíèå ñòàòèêè äëÿ ñòåðæíåâîé ñèñòåìû

1. Σ Ìi = 0; Ν1·a-P(a+c) +N2cos 45·b =0

2. Σ Zi =0; Z0 +Ν2· cos45 = 0

3. Σ Yi =0; Y0 + Ν1– P - N2·cos 45 = 0

 òðè óðàâíåíèÿ ðàâíîâåñèÿ âõîäÿò ÷åòûðå íåèçâåñòíûå ñèëû, è, ñëåäîâàòåëüíî, çàäà÷à ÿâëÿåòñÿ ñòàòè÷åñêè íåîïðåäåëèìîé. Äëÿ ñîñòàâëåíèÿ óðàâíåíèÿ ðàññìîòðèì äåôîðìàöèþ êîíñòðóêöèè.

2. Ðàññìîòðèì ïîäîáèå äâóõ òðåóãîëüíèêîâ ;


Ðàññìîòðèì   äëÿ íàõîæäåíèÿ äåôîðìàöèè ñèñòåìû.

             OB=b       OA=a

                                                                             y0                                                          N1
                                                                                                                    

                                 N2                                                           Ð                   P


            B1                                                                ∆l1

          B2                  O                                     A

             B                                                                A1            ∆l2

     

3. Ïîäñòàâëÿåì  â óðàâíåíèå ìîìåíòîâ è âûðàæàåì èõ ÷åðåç Ð

 

4. Íàõîäèì çíà÷åíèÿ íîðìàëüíûõ íàïðÿæåíèé σ1, σ2

σ1 =  

σ1 =  

Ïðèíèìàåì

5. Íàõîäèì äåéñòâèòåëüíûå çíà÷åíèÿ Ni

6. Íàõîäèì äåéñòâèòåëüíûå çíà÷åíèÿ σi

σ1 = =678,57=160ÌÏà

σ2 = =339,29=79,7ÌÏà

7. Îïðåäåëÿåì ïðåäåëüíóþ íàãðóçêó Pïð, èñõîäÿ èç óñëîâèÿ ðàâíîâåñèÿ

Σ Ìi = 0; Ν1·à– з(a+c) + N2cos 45·b =0, ãäå N1 = σò · À, è N2 = σò · 2À; σò=240ÌÏà

8. Íàõîäèì ïðåäåëüíî äîïóñêàåìóþ íàãðóçêó

Çàäà÷à ¹ 4

Òåìà: Ðàñ÷åò ñòàòè÷åñêè îïðåäåëèìûõ áðóñüåâ íà ïðî÷íîñòü è æåñòêîñòü ïðè êðó÷åíèè.

Äàíî:

Ñõåìà áðóñà.

Ðàçìåðû íàãðóçêè.

Òðåáóåòñÿ:

Ðàññ÷èòàòü áðóñ íà ïðî÷íîñòü è æåñòêîñòü

Ïîñòðîèòü ýïþðû êðóòÿùèõ ìîìåíòîâ, êàñàòåëüíûõ íàïðÿæåíèé è óãëîâ ïîâîðîòà.


Äàíî:

m1 = 400 Í∙ì

m2 = 1200 Í∙ì

m3 = 2400 Í∙ì

m4 = 400 Í∙ì

m5 = m5 Í∙ì

[τ] = 40 ÌÏà

[θ] = 0,5

d = 0,5

d1 = 1.5b

d2 = 2b

d3 = 2.5b

a = 0.3 ì

Íàéòè: Ò, τ, θ - ?

Ðåøåíèå.

Ñîñòàâèì óðàâíåíèå ñòàòèêè:

Σ Ìi = 0

m1 – m2 – m3 + m4 + m5 = 0

m5 = - m1 + m2 + m3 – m4 = - 400 + 1200 + 2400 – 400 = 2800 H·ì

T1 = + m1 = 400 H·ì

T2 = m1 – m2 = 400 – 1200 = - 800 H·ì

T3 = m1 – m2 – m3 = - 800 – 2400 = - 3200 H·ì

T4 = m1 – m2 – m3 = - 800 – 2400 = - 3200 H·ì

T5 = m1 – m2 – m3 + m4 = – 2800 H·ì

T6 = m1 – m2 – m3 + m4 + m5 = 0 H·ì

Îïðåäåëÿåì ïîëÿðíûé ìîìåíò ñîïðîòèâëåíèÿ íà êàæäîì ó÷àñòêå Wpi:

Îïðåäåëÿåòñÿ êàñàòåëüíîå íàïðÿæåíèå íà êàæäîì ó÷àñòêå ïî ôîðìóëå , âûðàæàÿ êàæäîå çíà÷åíèå ÷åðåç 1/b3

Îïðåäåëÿåì ìàêñèìàëüíîå çíà÷åíèå êàñàòåëüíîãî íàïðÿæåíèÿ èç ïÿòè çíà÷åíèé:

τmax = max {τ1, τ2, τ3, τ4, τ5} ≤ [τ] ;

τ3 ≤ [τ]

Îïðåäåëÿåòñÿ ïîëÿðíûé ìîìåíò èíåðöèè ïî äàííîé ôîðìóëå  íà êàæäîì ó÷àñòêå:

5. Îïðåäåëÿåì îòíîñèòåëüíûé óãîë çàêðó÷èâàíèÿ ïî ôîðìóëå

Îïðåäåëÿåì ìàêñèìàëüíîå çíà÷åíèå:

Ïðèìåì ìàêñèìàëüíîå çíà÷åíèå èç ïîëó÷åííûõ çíà÷åíèé b:

b≥ = b1 = 54,3 ìì = 54,3·10 - 3 ì = 55ìì

6. Îïðåäåëÿåì äåéñòâèòåëüíûå çíà÷åíèÿ êàñàòåëüíîãî íàïðÿæåíèÿ τi:

Îïðåäåëÿåì äåéñòâèòåëüíûå çíà÷åíèÿ îòíîñèòåëüíîãî óãëà çàêðó÷èâàíèÿ θi:

Îïðåäåëÿåì ïî ôîðìóëå çíà÷åíèå ïåðåìåùåíèÿ

Íàõîäèì ÷èñëîâûå çíà÷åíèÿ ïåðåìåùåíèÿ Δφi ïî ñå÷åíèÿì:

φÀ = 0

φ = φÀ + φ1 = 0 + 0,000176053 = 0,000176053 ðàä;

φÑ = φ + φ2 = 0,000176053 + 0,000149169 = 0,000325222 ðàä;

φD = φÑ + φ3 = 0,000325222 + 0,000168185 = 0,000493407 ðàä;

φÅ = φD + φ4 = 0,000493407 + 0,000168185 = 0,000661592 ðàä;

φF = φÅ + φ5 = 0,000661592 + 0,003477358 = 0,00413895 ðàä;

φG = φF + φ6 = 0,00413895 + 0= 0,00413895 ðàä.


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