Question 7 (Required knowledge: Stresses 2, 6 and 7 lecture material) A 125*38mm piece of F8 unseasoned Jarrah, spanning 0.8 metres, is intended to be subjected to a point load of 20 kN, 200mm from the left hand end. The shear force and bending moment diagrams for this arrangement are shown. a) Using the BMD and SFD given, calculate the normal stress at the extreme fibres at the location of the point load and the average shear stress in the timber to the immediate left of the point load (ie: using the maximum bending moment and shear force). b) Using Mohr's circle, determine the principal normal stresses and the maximum shear stress in the timber at the bottom of the beam, just to the left of the point load. c) It has been noticed that the grain of this particular piece of timber is not parallel to the longitudinal axis of the beam. The capacity of timber changes relative to the direction of the grain. It is therefore useful to know the shear and normal stresses relative to the direction of the grain in order to assess the suitability of the piece of timber in this circumstance. The angle of the grain is 10° from the longitudinal axis. Assuming that the grain slopes down to the right as shown in the diagram (clockwise from the longitudinal axis), determine the stress normal to the grain (ie stress of
Question 7 (Required knowledge: Stresses 2, 6 and 7 lecture material) A 125*38mm piece of F8 unseasoned Jarrah, spanning 0.8 metres, is intended to be subjected to a point load of 20 kN, 200mm from the left hand end. The shear force and bending moment diagrams for this arrangement are shown. a) Using the BMD and SFD given, calculate the normal stress at the extreme fibres at the location of the point load and the average shear stress in the timber to the immediate left of the point load (ie: using the maximum bending moment and shear force). b) Using Mohr's circle, determine the principal normal stresses and the maximum shear stress in the timber at the bottom of the beam, just to the left of the point load. c) It has been noticed that the grain of this particular piece of timber is not parallel to the longitudinal axis of the beam. The capacity of timber changes relative to the direction of the grain. It is therefore useful to know the shear and normal stresses relative to the direction of the grain in order to assess the suitability of the piece of timber in this circumstance. The angle of the grain is 10° from the longitudinal axis. Assuming that the grain slopes down to the right as shown in the diagram (clockwise from the longitudinal axis), determine the stress normal to the grain (ie stress of
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 7
(Required knowledge: Stresses 2, 6 and 7 lecture material)
A 125*38mm piece of F8 unseasoned Jarrah, spanning 0.8 metres, is intended to be
subjected to a point load of 20 kN, 200mm from the left hand end. The shear force and
bending moment diagrams for this arrangement are shown.
a) Using the BMD and SFD given, calculate the normal stress at the extreme fibres at the
location of the point load and the average shear stress in the timber to the immediate
left of the point load (ie: using the maximum bending moment and shear force).
b) Using Mohr's circle, determine the principal normal stresses and the maximum shear
stress in the timber at the bottom of the beam, just to the left of the point load.
c) It has been noticed that the grain of this particular piece of timber is not parallel to
the longitudinal axis of the beam. The capacity of timber changes relative to the
direction of the grain. It is therefore useful to know the shear and normal stresses
relative to the direction of the grain in order to assess the suitability of the piece of
timber in this circumstance. The angle of the grain is 10° from the longitudinal axis.
Assuming that the grain slopes down to the right as shown in the diagram (clockwise
from the longitudinal axis), determine the stress normal to the grain (ie stress
perpendicular to the grain) and the shear stress along the grain (using Mohr's circle of
stress drawn earlier), at the bottom of the beam, just to the left of the point load.
d) If the beam is flipped, so that the grain now slopes down to the left, determine the
tensile stress across the grain, and the shear stress along the grain, at the bottom of
the beam, just to the left of the point load.
20kN
200mm
600mm
38mm
125mm
15 kN
Shear Force Diagram
5 kN
Bending Moment Diagram
(drawn on tension side)
3.0 kNm
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