A wooden log from a molave tree is to be used as a footbridge to span 3-m gap. The log is required to support a concentrated load of 9 kN at a point 1m from the left support. The diameter of the log is 200mm, the unit weight is 940 kg/m³ and it is simply supported at both ends. Assume the log is very nearly circular. 1. What is the maximum flexural stress of the footbridge? Is it safe? 2. What is the maximum shearing stress of the footbridge? Is it safe? 3. What is the maximum deflection of the footbridge? If the allowable deflection is L/180, is the design of the footbridge satisfactory?
A wooden log from a molave tree is to be used as a footbridge to span 3-m gap. The log is required to support a concentrated load of 9 kN at a point 1m from the left support. The diameter of the log is 200mm, the unit weight is 940 kg/m³ and it is simply supported at both ends. Assume the log is very nearly circular. 1. What is the maximum flexural stress of the footbridge? Is it safe? 2. What is the maximum shearing stress of the footbridge? Is it safe? 3. What is the maximum deflection of the footbridge? If the allowable deflection is L/180, is the design of the footbridge satisfactory?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Answer number #3
Transcribed Image Text:A wooden log from a molave tree is to be used as a footbridge to span 3-m gap. The log is required to
support a concentrated load of 9 kN at a point 1m from the left support. The diameter of the log is
200mm, the unit weight is 940 kg/m³ and it is simply supported at both ends. Assume the log is very
nearly circular.
1. What is the maximum flexural stress of the footbridge? Is it safe?
2. What is the maximum shearing stress the footbridge? Is it safe?
3. What is the maximum deflection of the footbridge? If the allowable deflection is L/180, is the
design of the footbridge satisfactory?
Species
I. High Strength Group
Agoho
Liusin
Malabayabas
Manggachapui
Molave
Narig
Sasalit
Yakal
Table TMBR-3: Properties of Philippine Woods at 80% Grade
Bending and
Compression
Modulus of
Elasticity in
Parallel to
Tension Parallel
to Grain
Bending
Grain
1/2
MPa
26.30
25.00
28.10
25.80
24.00
21.80
31.30
24.50
GPa
9.36
8.30
9.63
6.54
8.33
9.72
9.18
Simply-supported beam deflection formulas
Beam and load cases
1/2
8.22
Smax
=
8max =
Smax
MPa
14.50
15.60
15.80
16.00
15.40
13.70
21.60
15.80
=
Maximum Beam Deflection
PL3
48EI
Compression
Perpendicular
to Grain
MPa
5wL4
384EI
5.91
4.31
8.70
6.03
6.34
4.91
10.20
6.27
Pb(3L²-46²)
48EI
Shear Parallel
to Grain
MPa
2.95
2.64
3.02
2.78
2.88
2.61
3-38
2.49
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