*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **ameter is 40 mm.
(a) Draw the distribution of the internal torque along the length of the bar from A to D.
(b) Obtain the maximum shear stress, τ max , and the maximum angle of twist, φ max , and indicate
where they occur along the bar. 500 Nm A B
1m 1m 1000 Nm
C Figure 2 1m 40 mm
D Name: Signature:
Student Number: Marks (%)
(25) 3. A simply-supported beam ABCD with overhangs is subjected to a uniformly distributed load
as shown in Figure 3. The cross-section of the beam has a box-shape made up of four
wooden planks with dimensions: h × b nailed together as shown to form a built-up beam.
(a) Draw the shear force and bending moment distribution diagrams for the beam (in terms of q
and L), labeling all critical values including the maximum bending moment and maximum
shear force.
(b) Determine the maximum tensile and compressive bending stresses, σ tmax and σ c and the
max
maximum shear stress, τ max in the beam and indicate the coordinates of the points (i.e. x and
y) where they occur.
(c) Given that q = 2 kN/m , L = 1m , h = 200 mm, b = 20 mm and each nail has an allowable
shear force of 750 N, calculate the maximum permissible longitudinal spacing smax of the
nails. y q A C B L 4L D
L Figure 3 y nail
x z h b
b h b Name: Signature:
Student Number: Marks (%)
(25) 4. A cantilever beam, ABC, has a fully fixed support at A and an elastic spring support at B. A
concentrated force P acts at the free end C. Assume that the beam has a modulus of
elasticity E, cross-sectional second moment of area I, and that the spring stiffness, k = EI /L3.
(a) Using the method of superposition, determine the displacements and angles of rotation at B
and C.
(b)...

View
Full
Document