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Question 1A simply supported composite beam 3 m long carnes a uniformly distrbuted load of intensityq 30 kN/m. The beam is constructed of a wood member, 100 mm wide by 150 mm deep,reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide.Find the maximum bending stresses ow and os in the wood and steel, respectvely, dueto the uniform load if the moduli of elasticity are Ew1 110 GPa for the wood and Es =210 GPa for the steelFind the required thickness of the steel plate so that the steel plate and the wood reachtheir allowable stress values, oas = 100 MPa and oaw= 8.5 MPa, sımultaneously12under the maximum moment

Question
Question 1
A simply supported composite beam 3 m long carnes a uniformly distrbuted load of intensity
q 30 kN/m. The beam is constructed of a wood member, 100 mm wide by 150 mm deep,
reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide.
Find the maximum bending stresses ow and os in the wood and steel, respectvely, due
to the uniform load if the moduli of elasticity are Ew
1 1
10 GPa for the wood and Es =
210 GPa for the steel
Find the required thickness of the steel plate so that the steel plate and the wood reach
their allowable stress values, oas = 100 MPa and oaw= 8.5 MPa, sımultaneously
12
under the maximum moment
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Question 1 A simply supported composite beam 3 m long carnes a uniformly distrbuted load of intensity q 30 kN/m. The beam is constructed of a wood member, 100 mm wide by 150 mm deep, reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide. Find the maximum bending stresses ow and os in the wood and steel, respectvely, due to the uniform load if the moduli of elasticity are Ew 1 1 10 GPa for the wood and Es = 210 GPa for the steel Find the required thickness of the steel plate so that the steel plate and the wood reach their allowable stress values, oas = 100 MPa and oaw= 8.5 MPa, sımultaneously 12 under the maximum moment

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check_circleAnswer
Step 1

Calculate the maximum bending moment.

 

max
(30x10 N/m)(3 m)
M.
2
max
8
M 33750 N-m
max
=33750 x10 N mm
max
Calculate the area of part 1.
A bh
4 (100 mm) (150 mm)
A 15000 mm2
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max (30x10 N/m)(3 m) M. 2 max 8 M 33750 N-m max =33750 x10 N mm max Calculate the area of part 1. A bh 4 (100 mm) (150 mm) A 15000 mm2

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Step 2

Calculate the centroidal distance of area 1.

 

2
150 mm
2
h75
Calculate the area of part 2.
A2 bt
A (100 mm (8 mm
A 800 mm
Calculate the centroidal distance of area 2.
8 mm
150 mm
2
J(154-)
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2 150 mm 2 h75 Calculate the area of part 2. A2 bt A (100 mm (8 mm A 800 mm Calculate the centroidal distance of area 2. 8 mm 150 mm 2 J(154-)

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Step 3

Calculate the position of neutral axis f...

Ew A EA = 0
10 MPa
1 GPa
mmk- 75)
15000
10 GPa
=0
10 MPa
)-(154-4)]
210 GPa
800 mm
1 GPa
15000 (h 75) 16800(154-)
h, 116.74 mm
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Ew A EA = 0 10 MPa 1 GPa mmk- 75) 15000 10 GPa =0 10 MPa )-(154-4)] 210 GPa 800 mm 1 GPa 15000 (h 75) 16800(154-) h, 116.74 mm

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