2 1 4 3

F

Q1

Q2

F = 6[kN]

Q1 = 4[kN/m]

Q2 =10[kN/m]

2 3 7 10

F

Q1

Q2

VA VB F1 F2

0 5 17/3

F1 = 16[kN]

F2 =12[kN/m]

−퐹 + 푉 − 퐹 − 퐹 + 푉 = 0 ⇒ 푉 + 푉 = 34

2 ∙ 퐹 − 3 ∙ 퐹 −113∙ 퐹 + 8 ∙ 푉 = 0 ⇒ 푉 = 10[푘푁] ⇒ 푉 = 24[푘푁]

0 - 2

−퐹 − 푉 = 0 ⇒ 푉 = −6[푘푁]

퐹 ∙ 푥 + 푀 = 0 ⇒ 푀 = −6 ∙ 푥

푉⃗

푀⃗ 푥

퐹⃗

0

푀 = 0[푘푁 ∙ 푚]

푀 = −12[푘푁 ∙ 푚]

2 - 3

2

F VA

0

푉⃗

푀⃗ 푥

−퐹 + 푉 − 푉 = 0 ⇒ 푉 = 18[푘푁]

퐹 ∙ 푥 − 푉 ∙ (푥 − 2) + 푀 = 0

⇒ 푀 = 18 ∙ 푥 − 48

푀 = −12[푘푁 ∙ 푚]

푀 = 6[푘푁 ∙ 푚]

푥 =83

= 2. 6[푚]

2 3

F Q1 VA

0

푦

푉⃗

푀⃗ 푥

3 - 7

Q1

Q2

푦

3 7 푥

푄 − 푄7− 3

=푦 − 푄푥 − 3

푦 =32∙ 푥 −

12

푦 =12∙ (3 ∙ 푥 − 1)

−퐹 + 푉 − 푄 ∙ (푥 − 3) −(푦 − 푄 ) ∙ (푥 − 3)

2− 푉 = 0 ⇒ 푉 =

−34∙ 푥 +

12∙ 푥 +

934

푉 = 18[푘푁] ; 푉 = −10[푘푁] ; 푥 =−1 ± 2√70

3≈ 5.244[푚] ; 푥 =

13

= 0. 3[푚] ∌ [3 − 7][푚]

퐹 ∙ 푥 − 푉 ∙ (푥 − 2) + 푄 ∙ (푥 − 3) ∙

(푥 − 3)2

+(푦 − 푄 ) ∙ (푥 − 3)

2∙

(푥 − 3)3

+ 푀 = 0

⇒ 푀 =−14∙ 푥 +

14∙ 푥 +

934∙ 푥 −

2374

푀 = 6[푘푁 ∙ 푚] ; 푀 = 30[푘푁 ∙ 푚] ; 푥 = (−10.284, 2.678, 8.606)[푚] ∌ [3 − 7][푚]

7 - 10

푉⃗

푀⃗ 푥

2 3 7

F VA

F1 F2

0 5 17/3

−퐹 + 푉 − 퐹 − 퐹 − 푉 = 0 ⇒ 푉 = −10[푘푁]

퐹 ∙ 푥 − 푉 ∙ (푥 − 2) + 퐹 ∙ (푥 − 5) + 퐹 ∙ 푥 −173

+ 푀 = 0

⇒ 푀 = −10 ∙ 푥 + 100

푀 √ =2

27137√70 − 694 ≈ 33.498[푘푁 ∙ 푚]

푀 = 30[푘푁 ∙ 푚]

푀 = 0[푘푁 ∙ 푚]

푥 = 10.0[푚]

-16

-12

-8

-4

0

4

8

12

16

20

24

28

32

36

0 1 2 3 4 5 6 7 8 9 10

V [kN]

M [kN·m]

2 1 4 3

F

Q1

Q2

x[m]