lvl hip rafter design

7/28/2019 LVL Hip Rafter Design

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Timber Design Knowledge

for Professionals of the Future

Page 1 of 4

WORKED EXAMPLE

LVL hip rafter subject to combined axialcompression and bending

References

Notes : The design approach follows the general principles of prEN 1995-1-1 and associated documents.The references on the right hand side of the pages are to prEN 1995-1-1 unless otherwise stated

Prerequisites

Home \ Core teaching material \ Introduction to timber engineering \ Timber design to limit states.Home \ Core teaching material \ Introduction to timber engineering \ Ultimate limit states design.Home \ Core teaching material \ Prerequisite STEP Lectures \ Limit state design and safety format.Home \ Core teaching material \ Prerequisite STEP Lectures \ Columns.Home \ Core teaching material \ Prerequisite STEP Lectures \ Buckling lengths.

Aim

To check the stability under combined bending and compression of a double LVL hip rafter.

Problem

Figure 1

Figure 1 shows a pyramidal roof structure comprising four LVL hip rafters which thrust against an LVLring beam fixed to the top of the walls. Each rafter is made of a pair of 75 mm x 650 mm sectionsfastened together to form a single 150 mm x 650 mm member 11610 mm long. It is assumed thattongue-and-groove boarding provides effective restraint against buckling of the hip rafters in the planeof the roof.

Pair of 75 mm 650 mmLVL hip rafters

LVL ring beam

LVL purlins

Offsiteprefabricatedroof panels


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Page 2 of 4

WORKED EXAMPLE


References

Service class 1 is assumed

The hip rafter resists a short-term design bending moment about the y-y axis ofMd= 186 x 10

6Nmm

and a short-term design axial compressive force of

Nd= 132 kN

Clause 2.3.1.3


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Page 3 of 4

WORKED EXAMPLE


References

Solution

Geometrical properties

Breadth: b = 150 mm

Depth of hip rafter: h = 650 mm

Length of hip rafter: L = 11610 mm

Area of cross section: A = 97.5 x 103

mm2

Section modulus about y-y axis: Wy =6

650150 2 = 1.056 x 107

mm3

Second moment of area about y-y axis: Iy =12

650150 3 = 3.433 x 109

mm4

Characteristic values of mechanical properties of a typical european softwoodstructural LVL

Bending strength parallel to grain: f m,y,k= 51 N/mm2

Compression parallel to grain: f c,0,k = 42 N/mm2

Minimum MOE parallel to grain: E0,05 = 12400 N/mm2

Strength modification factor

Partial safety factor for LVL: M= 1.2LVL, Service Class 1 or 2 and Short-Term loading: kmod= 0.9

Dimension factor for timber members in bending: kh = 1.0(assumes manufacturers declared data for parameters are not available)

Design buckling resistance

Effective length assuming pinned ends: Lef,y = 1.0 L = 11610 mm

Gyration radius: iy=12

h

A

Iy= = 187.60 mm

Slenderness ratio: y=60.187

11610

i

l

y

y,ef= = 61.89

Relative slenderness ratio: rel,y =0,05

kc,0,y

E

f

= 1.15

rel,y 0.3, therefore combined flexural and compressive buckling will influence the resistance.

Instability factors, ky and kc,y

Ky= 0.5 (1+ c (rel, y 0.3) + rel, y2)

Clause 6.3.2 (

Clause 6.3.2 (

Table 2.3Table 3.1Clause 3.4 (3)

TRADA StructTimber CompoDesign Guide Table 8

Expression (6

Clause 6.1.1


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Page 4 of 4

WORKED EXAMPLE


References

With c= 0.1 for LVL

ky= 1.20

kc,y=2

y,rel2

yy kk

1

+

kc,y= 0.65

Applied stresses

Design compressive stress along the grain: c, 0, d= 4

3

d

109.75

10132

A

N

= = 1.35 N/mm

2

Design bending stress about y-y axis: m, y, d=7

6

y

d

101.056

10186

W

M

= = 17.61 N/mm

2

Design values of strength properties

Design compressive strength along the grain: fc, 0, d=2.1

429.0fk

M

kc,0,mod =

= 31.5 N/mm2

Design bending strength parallel to grain about y-y axis:

1.2

510.19.0fkkfM

ky,m,hmoddy,m,

==

= 38.25 N/mm2

Completion of stability check

Note: as stated on Page 1, adequately attached diaphragms are assumed to prevent buckling inweaker direction.

25.38

61.17

5.3165.0

35.1

ffk dy,m,

dy,m,

dc,0,yc,

dc,0,+

=

+

= 0.07 + 0.46 = 0.53

1f

fk dm,y,

dm,y,

dc,0,c,y

dc,0,+

Therefore the hip rafter stability is satisfactory. Further action combinations and otherstructural checks would be likely in a complete design.

Clause 6.3.2 (andExpression (6

Clause 2.4.1 (

Expression (6


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Page 5 of 4

WORKED EXAMPLE


References

This document was produced as part of a collaborative project part-sponsored by the TimberResearch and Development Association (TRADA) and the Department of Trade and Industry (DTI).

TRADA Technology wishes to acknowledge and thank these organisations, and the partners whoselogos are shown below, for their support.Users are advised to check the current versions of all referenced codes at the time of use. Whilstevery effort is made to ensure the accuracy of the advice given, the company cannot accept liabilityfor loss or damage arising from the use of the information supplied. TRADA Technology 2003

lvl hip rafter design

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