design of truss roof

Prof Dr Z. A. Siddiqi 1

DESIGN OF TRUSS ROOF

Chapter 7

University of Engineering & Technology, Taxila


TABLE OF FORCES

There are three important points to be considered while

calculating the member forces:

1. Panel load multiplied with unit load forces gives the

member forces by the principle of superposition.

According to this principle, which is applicable for

elastic structures, if a unit load is applied on a truss

and the force in any member is calculated as F; then if

we apply another unit load simultaneously at the same

point, the force in the member will be 2F.


Similarly, this member force will be 3F for three unit

loads or P x F if P times unit loads are applied.

2. Effects of various types of loads are to be added while

calculating member forces.

Vertical and inclined loads on the truss cannot be added

directly because of different lines of action of each.

However, separate member forces due to vertical and

inclined loads have the same direction (along the

member longitudinal axis) and hence can be

algebraically added together.


3. Probability of occurrence of various loads in a load combination and corresponding load factors (factor of safety) are also applied during these calculations.

In case only dead, live and wind loads are acting on a truss, following combinations may be investigated:

1. 1.2D + 1.6Lr + 0.65W

(Wind effect is small and may be ignored especially suction is present throughout)


2. 1.2D + 0.5Lr + 1.3W

Wind towards the Right Wind towards the left

3. 0.9D + 1.3WWind towards the Right Wind towards the Left

For the roof design, the first (gravity) or second (wind)

load combination is critical. It is to be noted that the

downward wind load is to be considered in the second

combination.


The third combination is critical for reversal of forces

and hence is evaluated for upward wind pressures.

In case the wind load has two values, one downward

and one upward, the downward value should be used

for the second combination and the upward value

should be used for the third combination.

It would be unreasonable to include full wind and full

snow (or live load) stresses together in a single

combination.


Similarly, when the wind is blowing at its full strength,

the live load intensity may be reduced.

The second combination reflects the condition when

most severe windstorm is blowing and hence the live

load intensity may be reduced to 0.5/ 1.6 or 0.31 times

its maximum intensity, showing less probability of

occurrence of full live load together with wind.

The third combination represents an unoccupied

building subjected to the heaviest wind.


The negative sign with the wind forces only indicates

that the combination is critical when the wind is

producing member forces opposite in sense to that

produced by the dead loads.

The design forces may be calculated by entering the

values into a Table of Forces as in Table 7.2.

The first four columns of this table are directly taken

from the unit load analysis of the truss while columns 5

to 9 are calculated using the first four columns and the

algebraic values of the panel loads, already determined.


Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member

force due to unit wind load on roller side

(1.2PD

+1.6PL

) x Col.2

(1.2 PD

+ 0.5 PL) x Col.2+ 1.3 Pww x Col.3+ 1.3 PwL x Col.4

(1.2 PD

+ 0.5 PL) x Col.2

+ 1.3 P ww x

Col.4+ 1.3 PwL x Col.3

(0.9 PD) x Col.2+ 1.3 P

ww x Col.3+ 1.3 PwL x Col.4

(0.9 PD) x Col.2+1.3 P

ww x Col.4+1.3 PwL x Col.3

Maximum

factored tension(Tu)

Maximum

factoredCompression (Pu)

Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Sample Table of Forces


After getting the values in these columns, the maximum

factored tension and compression may be found out and

entered in the next two columns.

Usually tension is represented by positive sign and

compression by a negative sign in columns 2 to 4 and

hence maximum tension is defined as the maximum

positive value and maximum compression as the

minimum value (maximum negative answer) in

columns 5 to 9.


The remarks column is used to describe the type of the

member for design such as pure tension member, pure

compression member, member under reversal of

stresses and zero force member.

A computer spreadsheet may conveniently be used to

construct such a table.

The truss members may now be selected by using the

procedure given in earlier chapters and connections

may be designed by the methods outlined in the coming

chapters.

Unit Gravity Loads


Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member


(1.2PD

+1.6PL

) x Col.2

Maximum


Maximum


Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)


Unit Wind Load on Hinge Side

Unit Wind Load on Roller Side

If Panel wind load is negative = Suction

Pww

Pww= +ve (1.2PD+0.5PL) X COL. 2+ 1.3 PWW X COL. 3

PwwPwl

Pww= +ve (1.2PD+0.5PL) X COL. 2+ 1.3 PWW X COL. 3Pwl = -ve

PwwPwl

Pww= +vePwl = -ve

(1.2PD+0.5PL) X COL. 2+ 1.3 PWW X COL. 3+ 1.3 PWL X COL. 4

Load Combination in Column No 6

PwwPwl

Pww= +vePwl = -ve



Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member


(1.2PD

+1.6PL

) x Col.2

(1.2 PD


Maximum


Maximum


Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)


Pww= +vePwl = -ve


PwwPwl



Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member


(1.2PD

+1.6PL

) x Col.2

(1.2 PD


(1.2 PD

+ 0.5 PL) x Col.2

+ 1.3 P ww x


Maximum


Maximum


Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)


PwwPwl

Pww= -vePwl = -ve

(0.9PD) X COL. 2+ 1.3 PWW X COL. 3+ 1.3 PWL X COL. 4



Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member


(1.2PD

+1.6PL

) x Col.2

(1.2 PD


(1.2 PD

+ 0.5 PL) x Col.2

+ 1.3 P ww x


(0.9 PD) x Col.2+ 1.3 P


Maximum


Maximum


Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)


Pww= -vePwl = -ve

(0.9PD) X COL. 2+ 1.3 PWW X COL. 4+ 1.3 PWL X COL. 3

PwwPwl



Member No.

Unit

gravity load member

force

Membe

r forc

e due to

unit Win

d load on

hinge

side

Member


(1.2PD

+1.6PL

) x Col.2

(1.2 PD


(1.2 PD

+ 0.5 PL) x Col.2

+ 1.3 P ww x


(0.9 PD) x Col.2+ 1.3 P


(0.9 PD) x Col.2+1.3 P

ww x Col.4+1.3 PwL x Col.3

Maximum


Maximum


Remarks

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)


Assignment:

Draw the Table of Forces for Your Data & find the Truss Member Forces.

Time Allowed: 1 week

design of truss roof

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