Design of Tension Members
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Basic Concept
The stress in an axially loaded member is
The stress in a tension member is uniform throughout the cross-section except (1) near the point of application of load, and (2) at the cross-section with holes for bolts or other discontinuities.
The unreduced area of the member at section a-a is called its gross area and will be denoted as Ag.
The reduced area of the member at section b-b is called its net area, and will be denoted as An. This area will be subjected to a higher stress.
Tension member can fail by reaching one of two limit states:
1. Excessive deformation
This can occur due to yielding of the gross section (section a-a) along the length of the member
2. Fracture
Fracture of the net section can occur if the stress at the net section (section b-b) reaches the ultimate stress Fu.
504.1 Slenderness Limitation
There is no maximum slenderness limit for design of members in tension.
User Note: For members designed on the basis of tension, the slenderness ratio L/r preferably should not exceed 300. This suggestion does not apply to rods or hangers in tension.
504.2 Tensile Strength
The design tensile strength φPn and the allowable tensile strength Pn/Ω of tension members, shall be the lower value obtained according to the limit states of tensile yielding in the gross section and tensile rupture in the net section.
Tensile Yielding in the Gross Section
Tensile Rapture in the Net Section
When members without holes are fully connected by as defined in Section 504.3. When holes are present in a member with welded end connections, or at the welded connection in the case of plug or slot welds, the effective net area through the holes shall be used in Equation 504.2-2.
504.3 Area Determination
504.3.1 Gross Area
The gross area, Ag, of a member is the total cross-sectional area.
504.3.2 Net Area
The net area, An, of a member is the sum of the products of the thickness and the net width of each element computed as follows:
In computing net area for tension and shear, the width of a bolt hole shall be taken 2 mm greater than the nominal dimension of the hole.
For a chain of holes extending across a part in any diagonal or zigzag line, the net width of the part shall be obtained by deducting from the gross width the sum of the diameters or slot dimensions as provided in Section 510.3.2, of all holes in the chain, and adding, for each gage space in the chain, the quantity.
For angles, the gage for holes in opposite adjacent legs shall be the sum of the gages from the back of the angles less the thickness.
For slotted HSS welded to a gusset plate, the net area, An , is the gross area minus the product of the thickness and the total width of material that is removed to form the slot. In determining the net area across plug or slot welds, the weld metal shall not be considered as adding to the net area.
User Note: Section 510.4. l .(2) limits An to a maximum of 0.85Ag connection design for splice plates with holes.
504.3.3 Effective Net Area
The effective area of tension members shall be determined as follows:
where U, the shear lag factor, is determined as shown in Table 504.3. l.
Members such as single angles, double angles and WT sections shall have connections proportioned such that U is equal to or greater than 0.60. Alternatively, a lesser value of U is permitted if these tension members are designed for the effect of eccentricity in accordance with Section 508.1.2 or Section 508.2.
Shear Lag
Shear lag occurs when the tension force is not transferred simultaneously to all elements of the cross-section. This will occur when some elements of the cross-section are not connected.
For example, in the figure above, where only one leg of an angle is bolted to the gusset plate. A consequence of this partial connection is that the connected element becomes overloaded and the unconnected part is not fully stressed. Lengthening the connection region will reduce this effect
Shear lag can be accounted for by using a reduced or effective net area Ae.
Shear lag affects both bolted and welded connections. Therefore, the effective net area concept applied to both types of connections.
For bolted connection, the effective net area is Ae = U An
For welded connection, the effective net area is Ae = U Ag
Where, the reduction factor U is given by
Section Examples
Example
Given the following data of the figure shown:
Gross width = 300 mm
Plate thickness = 12 mm
Bolt diameter = 16 mm
Hole diameter = 17 mm
Plate yield strength, Fy = 248 MPa
Plate tensile strength, Fu = 400 MPa
Determine the design tensile strength of the plate.
A. 874.8 kN
B. 803.5 kN
C. 745.2 kN
D. 926.5 kN
Determine the allowable tensile strength of the plate
A. 583.2 kN
B. 658.7 kN
C. 534.4 kN
D. 475.1 kN
Example
For the two lines of bolt holes shown , determine the pitch x that will give a net area abcd equal to the one along efg. The holes are punched for 16 mm bolts (standard hole = 18 mm). Given, y1 = 50 mm.
A. 48.98 mm
B. 52.47 mm
C. 75.89 mm
D. 63.25 mm
Example
Given the following data of the connection shown:
Plate thickness = 10 mm
Bolt diameter = 12 mm
Hole diameter = 14 mm
x1 = 40 mm; y1 = 50 mm; y2 = 80 mm
Plate yield strength, Fy = 248 MPa
Plate tensile strength, Fu = 400 MPa
Determine the design tensile strength of the plate.
A. 666 kN
B. 724 kN
C. 580 kN
D. 510 kN
Determine the allowable tensile strength of the plate
A. 386 kN
B. 410 kN
C. 444 kN
D. 360 kN
Example
Determine the critical net and effective area of the L200 x 150 x 12 shown.
Given:
S1 = 75 mm S2 = 75 mm
S3 = 60 mm S4 = 65 mm
S5 = 40 mm
Bolt diameter, db = 22 mm
Hole diameter, dh = 24 mm
Angle section
Area, A = 4320 mm²
Thickness, t = 12 mm
A. 3496 mm²
B. 3842 mm²
C. 3248 mm²
D. 3058 mm²
Example
Refer to the splice connection shown.
Given:
x1 = 50 mm; y1 = 60 mm; y2 = 80 mm
Plate thickness, t = 16 mm
Bolt diameter, db = 20 mm
Hole diameter, dh = 22 mm
Plate yield strength, Fy = 248 MPa
Plate tensile strength, Fu = 400 MPa
Service dead load, PD = 950 kN
Determine the maximum safe service live load PL using LRFD.
A. 1360 kN
B. 1250 kN
C. 1450 kN
D. 1120 kN
Determine the maximum safe service live load PL using ASD.
A. 1360 kN
B. 1210 kN
C. 1590 kN
D. 1140 kN
Example
The angle shown is L 127 x 76 x 11, with short leg outstanding.
Given:
s = 75 mm
Bolt diameter = 16 mm
Hole diameter = 18 mm
Fy = 248 MPa
Fu = 400 MPa
Properties of L 127 x 76 x 11
A = 2130 mm²
x = 18.5 mm
y = 43.9 mm
Determine the design tensile strength of the single angle.
A. 325 kN
B. 475 kN
C. 475 kN
D. 525 kN
Determine the allowable tensile strength of the single angle.
A. 316 kN
B. 387 kN
C. 284 kN
D. 350 kN
Example
The 25 mm x 150 mm plate is connected to a 25 mm x 250 mm plate with longitudinal fillet welds to transfer a tensile load.
Given:
L = 200 mm
Fy = 345 MPa
Fu = 448 MPa
Determine the design tensile strength of the plate.
A. 875 kN
B. 1248 kN
C. 1164 kN
D. 945 kN
Determine the allowable tensile strength of the plate.
A. 630 kN
B. 775 kN
C. 863 kN
D. 520 kN
Example
The W360 x 64 tension member is spliced as shown in the figure.
Given:
S1 = 75 mm S3 = 50 mm
S3 = 50 mm S4 = 100 mm
Thickness of splice plate, tp = 25 mm
Bolt diameter, db = 22 mm
Hole diameter, dh = 24 mm
Material Properties:
Fy = 345 MPa
Fu = 448 MPa
Properties of W360 x 64
Area, A = 8130 mm2
Depth, d = 348 mm
Flange width, bf = 203 mm
Flange thickness, tf = 13.5 mm
Web thickness, tw = 7.75 mm
Determine the design tensile strength of the wide-flange section.
A. 2524 kN
B. 1920 kN
C. 1762 kN
D. 2804 kN
Determine the allowable tensile strength of the wide-flange section.
A. 1679 kN
B. 2561 kN
C. 1560 kN
D. 1280 kN
The two 20-mm-thick plates shown connects the W 250 x 58 tension member to the column as shown. Given, l = 200 mm.
Properties of W250 x 58
A = 7420 mm²
bf = 203 mm
tf = 13.5 mm
d = 252 mm
tw = 8 mm
Determine the effective net area of the wide flange section at the connection..
A. 6530 mm²
B. 6154 mm²
C. 6875 mm²
D. 6236 mm²
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