Example Problems for Tension Members 1) A tension member made of an angle L160x100x12mm is connected at end by two rows of 12mm diameter bolts in the 160mm leg and one row of 12mm diameter bolts in the 100mm leg as shown below. Assume bolt holes are made by drilling. 1
2
100 mm 60 mm 108 mm
70 mm
T
T
60 mm
248 mm
160 mm
70 mm
2
s
s?
s
1
s
a) Determine the pitch distance between the adjacent bolts ‘s’ for the same net -area of an angle section . -diameter of bolt holes, d b 1.5mm12 1.5 13.5mm -Gross area of an angle section, A g 160 100 12 12 2976 mm2 -Net area of critical section through bolt holes is determined using An A g n . d . t t .
si2 4 g i
and, AISC also requires, An 0.85 A g 0.85 2976 2529.6 mm2 Section 1-1:
An1 2976 2 13.5 12 2652mm2 2529.6 mm2 2
An1 2529.6mm
Section 2-2:
An 2 2976 3 13.5 12 12
s 2 4 70
12
s 2 4 108
2490 0.0706 s
2
By equating An1 with An 2 , 2
2490 0.0706 s 2529.6 2
2
s 560.9 m m
s 23.68 mm
take
s 25 mm
b) Determine the net area of an angle section if the pitch distance between the adjacent bolts ‘s’ is ‘s’ is 40mm. Section 1-1: An1 2976 2 13.5 12 2652mm2 2
Section 2-2:
An 2 2976 3 13.5 12 12
40
2
12
40
4 70 4 108 and, AISC also requires, An 0.85 A g 0.85 2976 2529.6 mm2 2
An 2529.6mm
2
2603mm
--take the smallest value
1
2) Determine the maximum allowable tensile load that can be carried by tension member made of an angle section L160x100x12mm connected at the end to gusset plate by two rows of 22mm diameter bolts as shown below. Angle section is made of A50 steel F y 345 MPa & F u 485 MPa . 100 mm
2
1
60 mm
T a ?
50 mm 160 mm 1 2
50 50 50
50 mm
50 -diameter of bolt holes, d b 1.5mm 22 1.5 23.5mm -Gross area of an angle section, A g 160 100 12 12 2976 mm2 -Net area of critical section through bolt holes, An1 2976 1 23.5 12 2694mm2 Section 1-1: Section 2-2:
An 2 2976 2 23.5 12 12
502
2
2562mm
4 50 and, AISC also requires, An 0.85 A g 0.85 2976 2529.6 mm2 2
An 2529.6mm
--take the smallest value
-Net effective area of critical section, --since connection is made through one leg only Ane 0.9 An
2
Ane 0.9 2529.6 2276.64mm
then, allowable tension load capacity is obtained as, For yield failure through gross area, T a 0.6 F y A g 0.6 345 2976 616.032 103 N or, For fracture failure through bolt holes, T a 0.5 F u Ane 0.5 485 2276.64 552.085 103 N Ta 552.085kN
2
3) Select the lightest single angle section for a tension member supporting a service design axial tension load of 210 kN. The member is to be connected at the end to gusset plate by two rows of 22mm diameter bolts in a pattern as shown below. The length of member is 1.9m. Assume the member as main tension member with limiting slenderness ratio of l r 240 where r I A . Angle sections are made of A36 steel F y 250 MPa & F u 400MPa . Select among a) Equal leg angles, and b) Unequal leg angles
1
2
T 210 kN
g
2
1
s
s
-diameter of bolt holes, d b 1.5mm 22 1.5 23.5mm -From minimum stiffness criteria of main tension members, l 1900 l r 240 r min 7.92mm 240 240 -Trial gross area of section from yield failure criteria, 3 T 210 10 1400mm A g 0.6 F y 0.6 250 2
-select a trail angle section from table with A g 1400mm2 a) If selected among equal leg angles, 1st trail: L64x64x12.7 2
A g 1452mm , t=12.7mm, & r min r z 12.4 mm 7.92 mm
ok !
-Net area of trial section through bolt holes, An1 1452 2 23.5 12.7 855.1mm2 Section 1-1: An 2 1452 2 23.5 12.7 12.7
Section 2-2:
s 2 4 g
2
855.1mm 12.7
s 2 4 g
2
and, AISC also requires, An 0.85 A g 0.85 1452 1234.2 mm 2
An 855.1 mm
--take the smallest value
-Net effective area of critical section, Ane
0.9 An
--since connection is made through one leg only
Ane 0.9855.1 769.59mm then, checking adequacy of trial section for fracture failure, T a 0.5 F u Ane 0.5 400 769.59 153.918 103 N 2
T a 153.918 kN T ( given) 210kN therefore, first trial is not adequate!
3
2nd trail: L102x102x7.9 2
A g 1548mm , t=7.9mm, & r min r z 20.1mm 7.92 mm
ok !
-Net area of trial section through bolt holes, Section 1-1: An1 1548 2 23.5 7 .9 1176.7 mm2 An 2 1548 2 23.5 7.9 7.9
Section 2-2:
s 2 4 g
2
1176.7 mm 7.9
s 2 4 g
and, AISC also requires, An 0.85 A g 0.85 1548 1315.8 mm2 2
An 1176.7 mm
--take the smallest value
-Net effective area of critical section, Ane
0.9 An
--since connection is made through one leg only
Ane 0.9 1176.7 1059.03mm then, checking adequacy of trial section for fracture failure, T a 0.5 F u Ane 0.5 400 1059.03 211.806 103 N 2
T a 211.806 kN T ( given) 210 kN therefore, L102x102x7.9 can be selected as lightest angle section.
ok !
b) If selected among unequal leg angles, Ans: L102x89x9.5 can be selected as lightest angle section.
4
Exercise Problems 1) Select the lightest double angles section placed back to back for a tension member supporting a service design axial tension load of 400 kN. The member is to be connected at the end to 12mm thick gusset plate between back of the angles by one row of 22mm diameter bolts in a pattern as shown below. The length of member is 3.2m. Assume the member as main tension member with limiting slenderness ratio of l r 240 where r I A . Angle sections are made of A50 steel F y 345 MPa & F u 485MPa . Select among a) Equal leg angles, and b) Unequal leg angles (for unequal leg angles, connection is made through longer leg of angles) t gus set 12 mm plate
T 400 kN
2)
Design a tension member of bridge truss subjected to a service design tensile force of 1130kN made of W-310 section connected at end to two gusset-plates of 16mm thick by two lines of 22mm diameter bolts on each flange of W-section (total four lines of bolts on two flanges). Connection is made through flanges of W-section. The length of the member is 8.5m. There will be at least three bolts in each line. Check selected section for minimum stiffness criteria assuming as main tension member. Select among W-310 sections. W-section and gusset-plates are made of A-36 steel ( F y 250MPa & F u 400 MPa ).
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