SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

11. Zadatak
Cilindri�ni stup promjera 4 cm, dužine 120 cm optere�en je u presjecima (1), (2) i (3) na
udaljenostima zi = 0; 40 i 80 cm (i=1,2,3) od slobodnog kraja aksijalnim silamaFi(i=1,2,3) = 15 kN,
10 kN i 5 kN.
Izra�umati naprezanje u pojedinim dijelovima stupa i pomak slobodnog kraja.
E = 2 ⋅10
d = 4cm
L
L = 120cm;
l1
= l2
= l3
= l = = 40cm
3
2 2 −4
d π 4 ⋅10
π
−4
2
A = = = 12,
56 ⋅10
m
4 4
K0
≤ z < 40cm
( 1)
N
σ
( 1)
( 1)
( 2)
N
σ
( 2)
( 2)
( 3)
N
σ
( 3)
( 3)
∆l
= ∆l
k =
∆l
∆l
∆l
N
l
AE
N
N
∆l
= ∆l
= −F
= −15kN
( 1)
A
K40
≤ z
= −F
− F = −25kN
( 2)
A
K80
≤ z
1
2
3
=
=
= −F
− F − F = −30kN
=
1
( 3)
A
= k ⋅ N
+ ∆l
= k ⋅ N
= k ⋅ N
1
5
1
1
1
1
MPa
−15⋅10
=
12,
56 ⋅10
2
−8
3
( 1)
= 0,
159 ⋅10
⋅ ( −15⋅10
)
−8
3
( 2)
= 0,
159 ⋅10
⋅ ( − 25⋅10
)
−8
3
( 3)
= 0,
159 ⋅10
⋅ ( − 30 ⋅10
)
+ ∆l
< 80cm
− 25⋅10
=
12,
56 ⋅10
3
< 120cm
− 30 ⋅10
=
12,
56 ⋅10
2
2
2
2
+ ∆l
+ ∆l
3
3
3
=
3
−4
3
−4
3
−4
l
AE
N
m
2
N
m
2
N
m
2
3
( N ( 1)
+ N ( 2)
+ N ( 3)
) = ∑ k ⋅ N ( i )
i=
1
= −0,
112mm
= −12
⋅10
6
= −24
⋅10
Pa = −12MPa
6
= −20
⋅10
Pa = −20MPa
0,
4
=
= 0,
159 ⋅10
−4
11
12,
56 ⋅10
⋅ 2 ⋅10
6
=
=
=
Pa = −24MPa
−8
m
N
−2,
415⋅10
−4,
00 ⋅10
−4,
80 ⋅10
−5
−5
−5
m = −0,
024mm
m = −0,
04mm
m = −0,
048mm
13