5.8 Design of truss members - Verification of members in tension

Steel tension member are probably the most common and efficient member. This is due to the

entire cross section is subjected to almost uniform stress. As the tensile force increases on a

member it will straighten out as the load is increased. For a member that is purely in tension,

we do not need to worry about the section classification since it will not buckle locally. A

tension member fails when it reached the ultimate stress and the failure load is independent of

the length of the member. Tension members are generally designed using rolled section, bars

or flats.

Flats are higher in flexibility and their slenderness should be limited. In general, rolled sections

are preferred and the use of compound sections is reserved for larger loads or to resist bending

moments in addition to tension. In reference to Cl. 6.2.3, EN 1993-1-1:2005, the design value of

tension force, at each cross section shall satisfy;

The tensile resistance is limited by the lesser of:

Design Plastic Resistance Npl,Rd

Design Ultimate Resistance Nu,Rd

Nu,Rd is the design ultimate resistance of the net cross-section, and is concerns with the

ultimate fracture of the net cross-section, which will normally occur at fastener holes.

Partial Factors γM

Net section

A tension member is often connected to main or other member by bolt or welds. For bolts

connection, the members with bolt holes, the net area should be taken into consideration. Holes

in the member will cause stress concentration.

Characteristic Strengths fy and fu

The UK National Annex says you should get the values of fy and fu from the product standards.

For hot-rolled sections you can use the table below.

Anet for Non staggered fasteners

Anet = A – Σd0t

The total area to be deducted should be taken as the greater of:

a) The maximum sum of the sectional areas of the holes on any line perpendicular to the

member axis

b)

where:

t is the thickness of the plate

p is the spacing of the centres of the same two holes measured perpendicular to the member

axis

s is the staggered pitch of the two consecutive holes

n is the number of holes extending in any diagonal or zig-zag line progressively across the

section

d0 is the diameter of the hole

Tension members: Single Angles

For angles connected by 1 leg and other unsyammetrically connected members in tension (i.e.

T or channel sections), the eccentricity in joints and the effects of the spacing and edge

distances of the bolts should be taken into account in determining the design resistance (Cl.

3.10.3, EN 1993-1-8: 2005)

A single angle in tension connected by a single row of bolts in one leg may be treated as

concentrically loaded over an effective net section. The design ultimate resistance should be

determined as follows;

Refer to EN 1993-1-8 (clause 3.10.3)

With 1 bolt

With 2 bolts

With 3 bolts

Values of reduction factors β2 and β3 can be found in Table 3.8 BS EN 1993-1-8

For angle in tension connected through one leg, BS EN 1993-1-1, 6.2.3 (5) refers to BS EN

1003-1-8, 3.10.3. However Eurocode does not cover the case of more than one bolt in the

direction perpendicular to the applied load. Therefore the resistance has been calculated using

expressions from BS 5950-1; the tables apply only to a single row across the angle.

The value of the design resistance to tension has been calculated as follows;

Where

is the equivalent area of the angle

For bolted sections:

For welded sections:

is the number of bolts

is the diameter of the hole

A is the gross area of a single angle

A block tearing check (BS EN 1993-1-8, 3.10.2) is also required for tension members.

Tension Member Design Steps Summary

1. Determine the design axial load NEd

2. Choose a section

3. Find fy and fu from the product standards

4. Get the gross area A and the net area Anet

5. Substitute the values into the equations to work out Npl,Rd and Nu,Rd

For angles connected by a single row of bolts, use the required equation to work out Nu,Rd from

EN 1993-1-8 which will depend on the number of bolts.

The design tensile Resistance is the lesser of the values of Npl,Rd and Nu,Rd

7. Carry out the tension check:

Example 5.3:

Calculate the design tension resistance, Nt,Rd of a plate as shown for steel grade S275.

Solution:

The smaller of;

Therefore, the design tension resistance:

Example 5.4: Tension member

Consider the chord AB of the steel truss, indicated by the figure, assuming it is submitted to a

design tensile axial force of . The cross section consists of two angles of equal

legs, in steel grade S234. Design chord AB assuming two distinct possibilities for the

connection:

a. Welded connections

b. Bolted connections

100 mm

12 mm M20 bolt

S275

plate

Solution

a. Welded connection

The chord is made up by two angles of equal legs, but the connection is made only in

one leg of the angle. Thus, according to Clause 4.13 of EN 1993-1-8: 2005, the effective

area can be considered equal to the gross area. Therefore the following condition must

be satisfied:

Where , and A is the gross area of the section. Considering the design axial

force, then:

Therefore, use

b. In this case, the chord is made up by angles of equal legs, connected by 2 bolts only in

one leg. According to Cl. 3.10.3 of EN 1993-1-8: 2005, the following condition must e

ensured:

30 mm

100 mm A net

Where A is the gross area of the

section and is the reduction factor (Table 3.8)

Based on plastic design of the gross section:

Based on the net area of the cross section:

This will require the evaluation of the net area, Anet and the factor both evaluated

according to Cl. 3.10.3 EN 1993-1-8:2005.

Example 5.5: Tension member

A single unequal angle 125mm 75mm 8mm is connected to 12 mm thick gusset plate at

ends with 6 no 16 mm diameter rivets of Grade 4.6 to transfer tension as shown in figure

below. Determine the tension capacity of an angle section if

a. If longer leg is connected to gusset plate.

b. If shorter leg is connected to gusset plate.

Use

Solution

a. If longer leg is connected to gusset plate.

Design Plastic resistance of gross section, Npl,Rd

Design ultimate resistance of the net cross section at holes for fasteners, Nu,Rd

For angle connected through one leg

Connection with 3 or more rivets

Pitch, p1= 50 mm, 2.5d0 = 2.5 18 = 45 mm thus,

Therefore, the tension capacity

b. If shorter leg is connected to gusset plate.

Design Plastic resistance of gross section, Npl,Rd

Design ultimate resistance of the net cross section at holes for fasteners, Nu,Rd

For angle connected through one leg

Connection with 3 or more rivets

Here

, should be taken as equal to the net sectional area of an equivalent equal leg angle

of length size equal to that of smaller size.

Example 5.6:

Design a single angle tie member to carry the design axial tension of 375 kN, with riveted

connections. Use (Provide rivet preferably in single row).

Solution:

Trial section

Try 125 75 10 with longer leg connected to 12 mm thick gusset plate.

A = 1910

g = 31.9 mm

Tension capacity of section

The smaller of;

For angle connected through one leg

Connection with 3 or more rivets

Pitch, p1= 90 mm, 2.5d0 = 2.5 20 = 50 mm and 5d0 = 5 20 = 100 mm

thus,

Therefore, the tension capacity