SKRIPTA RIJEÅ ENIH ZADATAKA IZ OTPORNOSTI MATERIJALA

49. Zadatak
Za zadani nosa� i optere�enje odrediti mjerodavan koeficijent sigurnosti prema teoriji najve�ih
normalnih naprezanja u to�kama 1 i 2 presjeka I-I ako je zadano kriti�no naprezanje materijala
�K.
P = 30kN
H = 25kN
q = 15kN
/ m
σ
ΣF
R
ΣM
1 1,
5
− q ⋅1⋅
+ q ⋅
2 2
ΣF
= 0 :
R
x
Ax
Ay
y
− H = 0 ⇒ R
A
=
0 :
=
+ R
0 :
B
Presjek I – I :
N = −25kN
T = −18,
125kN
2
Ax
M = 27,
1875kNm
I
I
= H = 25kN
+ P ⋅1,
5 − R ⋅3
= 0 ⇒ R
− q ⋅ 2,
5 − P = 0 ⇒ R
3
70 ⋅10
= + 70 ⋅10
⋅
12
6 4
= 5,
83⋅10
mm
B
Ay
B
= 49,
375kN
10 ⋅100
12
3
= 18,
125kN
10 ⋅ 70 ⋅5
+ 10 ⋅100
⋅ 60 + 20 ⋅ 40 ⋅120
159500
yT
=
= ⇒ y
10 ⋅ 70 + 10 ⋅100
+ 20 ⋅ 40 2500
2
A = 2500mm
S
y
y
W
K
y max
y max
= 320MPa
=
z
I
y
max
= 40 ⋅ 20 ⋅
5,
83⋅10
=
66,
2
T
= 63,
8mm
40 ⋅ 20
12
2
2
( 63,
8 − 5)
+ + 10 ⋅100
⋅ ( 63,
8 − 60)
+ + 40 ⋅ 20 ⋅ ( 66,
2 −10)
6
⇒ W
y max
3
= 88,
1⋅10
mm
3 3
( 66,
2 −10)
+ ( 66,
2 − 20)
⋅10
⋅ ⇒ S = 55,
6 ⋅10
mm
3
66,
2 − 20
2
y
y max
T
40
2
1
30 10 30
70 mm
z
3
20
100
10
130
2
78