Technical University „Gheorghe Asachi”, Iasi Student: Lazăr Gheorghe

Facutly of Civil Engineering and Building Services M.Sc. Structural Engineering

Assignment No. 4 WOOD BEAM EXTERNALLY REINFORCED WITH CFRP

Personal Number: No.S=17

It is considered a simple supported wood beam with a length of 4.3 m that is

bended from a uniform distributed load ffq=8-0,05N=8-0,05*17= 7,15 kN/m; L=6-0,1*N=

6-1.7=4.3 m.

Requirements:

a. Determine the necessary beam section so that the deflection that appear from the exterior loading do not exceed the ultimate deformation equal to l / 240;

b. If the initial loading is increased with 10%, determine the width of the CFRP plate bonded underside of the wood beam to increase the capable moment and stiffness.

The characteristics of the composite plate:

t=1.2 mm; Ecfrp=165 GPa; w=5 cm.

It is known the elasticity modulus of wood Ewood=13.1 GPa.

SOLUTION

𝑢𝑚𝑎𝑥 =−5𝑞𝑙4

384𝐸𝐼

𝑢𝑙𝑖𝑚 =𝐿

240= 0.0179 𝑚 = 17.9 𝑚𝑚

𝑢𝑚𝑎𝑥 ≤ 𝑢𝑙𝑖𝑚 = 17.92 𝑚𝑚

𝐼𝑛𝑒𝑐 =5𝑞𝐿4

384 ∗ 𝐸 ∗ 𝑢𝑚𝑎𝑥= 135609506.20229 𝑚𝑚4

𝐼 =𝑏ℎ3

12

ℎ = 1.5 ∗ 𝑏 → 𝑏𝑚𝑖𝑛 = 148.18 𝑚𝑚 𝑎𝑛𝑑 ℎ𝑚𝑖𝑛 = 222.27 𝑚𝑚

It is adopted a beam section with the height h=25 cm

and the width b=15 cm.

𝑞’ = 1.2 ∗ 𝑞 = 7.865 𝐾𝑛/𝑚

𝐸𝐶𝐹𝑅𝑃 = 165 𝐺𝑃𝑎

Technical University „Gheorghe Asachi”, Iasi Student: Lazăr Gheorghe

Facutly of Civil Engineering and Building Services M.Sc. Structural Engineering

THE WOOD SECTION IS TRANSFORMED IN COMPOSITE SECTION

𝑛 =𝐸𝑤𝑜𝑜𝑑

𝐸𝐶𝐹𝑅𝑃= 0.07939

Determine the transformed wood section into CFRP

𝑏𝑤𝑜𝑜𝑑−𝐶𝐹𝑅𝑃 = 𝑏𝑤𝑜𝑜𝑑 ∗ 𝑛 = 11.9091 𝑚𝑚

It is considered 3 strips of CFRP: bcfrp=3*50=150mm

Determine the position of the neutral axis y’

𝑦` =∑ 𝐴𝑖 ∗ 𝑦𝑖

∑ 𝐴𝑖

Awood=CFRP=2977.27 mm2

ACFRP=180 mm2

y1=126.2 mm

y2=0.6 mm

y`=119.039 mm

Determine the inertia moment for the transformed section

Iwood-cfrp= bwood-cfrp*h3/12= 15506628.79 mm4

ywood-cfrp = y1-y'=7,161 mm

Icfrp=150*1.23/12=21.6 mm4

ycfrp = y’-y2=118,44 mm

𝐼 = ∑ (𝑏ℎ3

12+ 𝐴 ∗ 𝑑𝑥) = 18184328𝑚𝑚4 = 18.18 ∗ 106𝑚𝑚4

Determine the maximum deflection

𝑢𝑚𝑎𝑥 =−5𝑞𝑙4

384𝐸𝐼= 11.668 𝑚𝑚 < 𝑢𝑙𝑖𝑚 = 17.92 𝑚𝑚

So that, the width of the composite plate is 150 mm,using 3 strips of CFRP.