Ae211 tutorial sheet no. 3 composite structures and thermal stresses 17.11.2017.. ....................

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Sokoine University of Agriculture
Department of Engineering Sciences and Technology
AE 211: STRENGTH OF MATERIALS
[AGE2/BPE2/IWRE2 – Semester 3]
TUTORIAL SHEET No. 3: [2017/18]
COMPOSITE STRUCTURES & THERMAL STRESSES
Question 1: In a construction site, a concrete column is being erected with its cross-section
area being of 50 cm square and reinforced with four steel rods, each of 2.5 cm diameter
embedded in the concrete near the corners of the square. Estimate the compressive
stresses in the steel and concrete when the total thrust on the column is 1MN. Assume
Young’s Modulus for steel and concrete as being 200 GPa and 14 GPa respectively.
Question 2: A uniform beam weighs 500 N and is maintained in a horizontal position by
three vertical wires, one attached to each end of the beam, and the third one at mid-length.
The outer wires are made of brass of diameter 1.25 mm while the middle wire is made of
steel of diameter 0.625 mm. Assuming that the beam is rigid and the wires are of the same
length and unstressed before the beam is attached, estimate the stresses in the wires. Take
E for brass and steel as being 85 and 200 GPa respectively.
Question 3: Two prismatic bars are rigidly fastened together and support a vertical load
of 45 kN. The upper bar which is fixed to the roof is made of steel having a length of 10m
and cross-sectional area 60 cm2
. The lower bar which is hanging freely at its other end, is
made of brass having a length of 6 m and cross-sectional area 50 cm2
. Determine the
maximum stress in each part of the bar if E for steel and brass are 200 and 100 GPa
respectively and their specific densities are 84 and 77 kN/m3
respectively.
Question 4: A steel tube is tightly surrounding a solid aluminum cylinder. The assembly
is being compressed between two cover plates by a force P = 200 kN. The aluminum
cylinder is 8 cm in diameter and the outside diameter of the steel tube is 9.2 cm. Find the
stresses in the steel and aluminum components given that E for steel and aluminum is
200 and 80 GPa respectively.

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Question 5: A brass rod of 6 mm diameter and 1 m long is joined at one end to a steel rod
of 6 mm diameter and 1.3 m long. The compound rod is then placed in a vertical position
with the steel rod at the top and connected both at the top and bottom to rigid fixings in
such a way that it is carrying a load of 3.5 kN. An attachment is then fixed at the junction
of two rods and to this an axial load of 1.3 kN is applied downwards. Calculate the
stresses in the steel and brass rods given that E for steel and brass are 200 and 85 GPa
respectively.
Question 6:. A steel rod 15 m long is at a temperature of 150
C. Find the free expansion of
the rod when the temperate is raised to 650
C. Also calculate the temperature stress
produced when: (a) the expansion of the rod is prevented and (b) The rod is permitted to
expand by 6 mm. Assume the Coefficient for Thermal Expansion as 12x10-6
per 0
C and
Modulus of Elasticity for steel as 200GPa.
Question 7: An aluminum rod which is 22mm in diameter has screws at its ends, and
passes through a steel tube which is 25mm internal diameter and 3mm wall thickness.
Both are heated to a temperature of 1400
C, when the nuts are screwed lightly on to the
ends of the tube. Estimate the stress in the tube when the common temperature has fallen
to 200
C. Assume E for steel and aluminum is 200 and 70 GPa respectively while coefficient
of linear expansion is 1.2x10-5
and 2.3x10-5
per 0
C respectively.
Question 8: A flat aluminum which is 25 mm wide and 5 mm thick is placed between
two steel bars each 25 mm wide and 10 mm thick to form a composite bar of dimensions
25mm x 25mm. The three bars are fastened together at their ends when the temperature
is 150
C. Find the stress in each of the materials when the temperature of the whole
assembly is raised to 550
C. If at the new temperature a compressive load of 30 KN is
applied to the composite bar determine the final stresses in the steel and aluminum.
Assume E for steel as 200GPa while that of the aluminum is one third that of steel and
the coefficients of linear expansion for steel and aluminum are 1.2x10-5
and 2.3x10-5
per
0
C respectively.
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GCM/lm/AE211 – 15th November 2017