For the beam in figure 1, find the value and location of the largest tensile and compressive stresses. There may be more than one candidate location for each of these. 3.2. kN/m + 1.9 kN.m im A A 3m Figure 1 2m Figure 2 The cross section shown in Figure 2 is 125x75x8 UA the cross section and material properties are shown below; (Note that in the tables, the horizontal and vertical coordinate n and p, and are right and up respectively. Table 26 Unequal Angles - x-axis and y-axis - Dimensions and Properties Designation Nominal Mass Actual Thickness per Thickness metre Radii Gross Coordinate Area of of Centroid Cross Root Toe (b-t) (b,-t) Section About x-axis About y-axis Torsion Tan Designation Constant Alpha Leg-size b, x b₁₂ t tt mm mm mm ka/m mm mm mm A mm² 125 x 75 x 12 UA 17.7 12.0 10 UA 14.2 9.5 8 UA 11.8 7.8 8.0 5.0 9.42 5.25 2260 8.0 5.0 12.2 6.89 1810 8.0 5.0 15.0 8.62 1500 PB 1 mm mm 10 mm 43.3 18.4 3.91 83.2 42.3 17.5 3.20 83.8 41.5 16.8 2.68 84.2 V₁ mm Z V₁ Ys 10'mm³ mm 10°mm³ mm 47.0 59.7 65.5 34.6 38.2 59.3 53.9 33.9 31.8 58.9 45.5 33.3 Z S₁ X3 Z S₁ J 10 mm² 10°mm³ mm 10 mm mm 10 mm mm 10°mm³ mm 113 81.4 41.6 0.585 19.9 29.3 41.4 14.1 31.9 10 mm² 10'mm³ mm 18.4 29.7 16.1 10 mm 94.4 65.8 42.0 0.476 19.2 24.9 41.6 11.4 30.7 15.5 24.1 16.2 80.4 54.6 42.2 0.399 18.6 21.5 41.8 9.55 29.9 13.3 20.1 16.3 110 56.2 0.360 31.7 0.363 0.356 125 x 75 x 12 UA 10 UA 8 UA Table 27 Unequal Angles - x-axis and y-axis - Properties for Assessing Section Capacity Designation Yield Stress Form Factor About x-axis Load A About y-axis Yield Stress Form Factor About x-axis About y-axis Designation mm mm mm f MPa Za Load C Z Load B Load D Load A Load C Load B Z Z Z Z Load D Z 10³mm³ 10 mm³ 10'mm³ 10³mm³ MPa 10 mm³ 10 mm³ 10³mm³ 10 mm 300PLUS** AS/NZS 3679.1-350 125 x 75 x 12 UA 300 1.00 68.6 70.5 20.6 21.2 340 1.00 67.6 70.5 20.3 212 125 x 75 x 12 UA
For the beam in figure 1, find the value and location of the largest tensile and compressive stresses. There may be more than one candidate location for each of these. 3.2. kN/m + 1.9 kN.m im A A 3m Figure 1 2m Figure 2 The cross section shown in Figure 2 is 125x75x8 UA the cross section and material properties are shown below; (Note that in the tables, the horizontal and vertical coordinate n and p, and are right and up respectively. Table 26 Unequal Angles - x-axis and y-axis - Dimensions and Properties Designation Nominal Mass Actual Thickness per Thickness metre Radii Gross Coordinate Area of of Centroid Cross Root Toe (b-t) (b,-t) Section About x-axis About y-axis Torsion Tan Designation Constant Alpha Leg-size b, x b₁₂ t tt mm mm mm ka/m mm mm mm A mm² 125 x 75 x 12 UA 17.7 12.0 10 UA 14.2 9.5 8 UA 11.8 7.8 8.0 5.0 9.42 5.25 2260 8.0 5.0 12.2 6.89 1810 8.0 5.0 15.0 8.62 1500 PB 1 mm mm 10 mm 43.3 18.4 3.91 83.2 42.3 17.5 3.20 83.8 41.5 16.8 2.68 84.2 V₁ mm Z V₁ Ys 10'mm³ mm 10°mm³ mm 47.0 59.7 65.5 34.6 38.2 59.3 53.9 33.9 31.8 58.9 45.5 33.3 Z S₁ X3 Z S₁ J 10 mm² 10°mm³ mm 10 mm mm 10 mm mm 10°mm³ mm 113 81.4 41.6 0.585 19.9 29.3 41.4 14.1 31.9 10 mm² 10'mm³ mm 18.4 29.7 16.1 10 mm 94.4 65.8 42.0 0.476 19.2 24.9 41.6 11.4 30.7 15.5 24.1 16.2 80.4 54.6 42.2 0.399 18.6 21.5 41.8 9.55 29.9 13.3 20.1 16.3 110 56.2 0.360 31.7 0.363 0.356 125 x 75 x 12 UA 10 UA 8 UA Table 27 Unequal Angles - x-axis and y-axis - Properties for Assessing Section Capacity Designation Yield Stress Form Factor About x-axis Load A About y-axis Yield Stress Form Factor About x-axis About y-axis Designation mm mm mm f MPa Za Load C Z Load B Load D Load A Load C Load B Z Z Z Z Load D Z 10³mm³ 10 mm³ 10'mm³ 10³mm³ MPa 10 mm³ 10 mm³ 10³mm³ 10 mm 300PLUS** AS/NZS 3679.1-350 125 x 75 x 12 UA 300 1.00 68.6 70.5 20.6 21.2 340 1.00 67.6 70.5 20.3 212 125 x 75 x 12 UA
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:For the beam in figure 1, find the value and location of the largest tensile and compressive stresses. There
may be more than one candidate location for each of these.
3.2 kN/m
2
1.9 kN.m
Im A
3m
2m
Figure 1
Figure 2
The cross section shown in Figure 2 is 125x75x8 UA the cross section and material properties
are shown below; (Note that in the tables, the horizontal and vertical coordinate n and p, and
are right and up respectively.
Table 26 Unequal Angles - x-axis and y-axis - Dimensions and Properties
Designation Nominal Mass Actual Radii
Thickness per Thickness
About x-axis
About y-axis
Torsion Tan Designation
Constant Alpha
Gross Coordinate
metre
Area of of Centroid
Cross
Leg-size
Root Toe (b,-t) (b,-t) Section
b, x b,
t
r 5,
t
A
Рап
y
Z
V₁
mm mm mm
ka/m
mm
mm mm
mm²
mm mm 10 mm
mm
10 mm
mm
125 x 75 x 12 UA
17.7
12.0
10 UA
14.2
9.5
8 UA
11.8
7.8
8.0 5.0 9.42 5.25 2260
8.0 5.0 12.2 6.89 1810
8.0 5.0 15.0 8.62 1500
43.3 18.4
42.3 17.5 3.20
41.5 16.8 2.68
3.91
83.2
83.8
84.2
59.7
31.8
Z Y₁ Z S r
10-mm³ mm 10 mm 10mm³
47.0
65.5 34.6 113 81.4 41.6
38.2 59.3 53.9 33.9 94.4 65.8
58.9 45.5 33.3 80.4 54.6
V
x,
Z
2日 X
mm 10 mm mm
0.585 19.9
42.0 0.476 19.2
42.2 0.399 18.6
10 mm³
mm
29.3 414
24.9
41.6
21.5
Z
10-mm³ mm 10 mm² 10mm
14.1 31.9 18.4 29.7
11.4 30.7 15.5 24.1 16.2
9.55 29.9 13.3 20.1 16.3
S
r
J
mm
10 mm
16.1
110 0.356 125 x 75 x 12 UA
56.2 0.360
31.7 0.363
10 UA
8 UA
Form Factor
Table 27 Unequal Angles - x-axis and y-axis - Properties for Assessing Section Capacity
Designation Yield Stress
About x-axis
About y-axis
Yield Stress
Form Factor
About x-axis
About y-axis
Designation
Load A
Load C
Load B
Load D
Load A
f
k₁
Z
Z
Z
Z
f
k
Z
Load C
Z
Load B
Z
Load D
Z
mm mm mm
MPa
10mm
10 mm
10'mm³
10 mm
MPa
10 mm
10 mm
10/mm³
10-mm³
300PLUS
AS/NZS 3679.1-350
125 x 75 x 12 UA
300
1.00
68.6
70.5
20.6
21.2
340
1,00
67.6
70.5
20.3
21.2
125 x 75 x 12 UA
10 UA
320
1.00
51.6
572
15.5
17.2
360
1.00
50.6
57.2
15.2
17.2
10 UA
8 UA
320
0.964
39.8
46.0
119
14.3
360
0.931
38.8
44.7
11.6
14.3
8 UA
Table 28 Unequal Angles - n-axis and p-axis - Dimensions and Properties
Designation
About n-axis
About p-axis
Product of 2nd
Moment of Area
Designation
P
Z
P.
Z
S
Z
n₂
6
mm mm mm
10 mm
mm
10°mm³
mm
10 mm
10 mm
mm
10 mm
mm
10°mm³
mm
10'mm³
10 mm
mm
10 mm²
125 x 75 x 12 UA
3.54
43.3
818
81.7
43.3
77.3
39.6
0.958
18.4
52.0
56.6
16.9
31.4
20.6
-105
125 x 75 x 12 UA
10 UA
2.88
42.3
68.2
827
34.9
62.5
39.9
0.789
17.5
45.2
575
13.7
25.1
20.9
-0.867
10 UA
8 UA
2.41
415
58.1
83.5
28.9
52.0
40.1
0.664
16.8
39.6
58.2
114
20.7
21.0
-0.731
8 UA
Value (MPa)
Does this stress exceed the
yield stress of the
member?
Location on beam
(draw sketch)
Location on Cross section
(draw sketch)
Largest tensile stress
Largest compressive stress
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