Strength of Material-1 G-1 worksheet 1

1) Two solid cylindrical rods AB and BC are welded together at B and loaded as shown.
Knowing that the average normal stress must not exceed 150 MPa in either rod,
determine the smallest allowable values of the diameters d1 and d2.
Ans: d1=22.6mm, d2=40.2mm

2) Two loads are applied to the bracket BCD as shown. (a) Knowing that the control rod
AB is to be made of a steel having an ultimate normal stress of 600 MPa, determine
the diameter of the rod for which the factor of safety with respect to failure will be
3.3. (b) The pin at C is to be made of steel having an ultimate shearing stress of 350
MPa. Determine the diameter of the pin C for which the factor of safety with respect
to shear will also be 3.3. (c) Determine the required thickness of the bracket supports
at C, knowing that the allowable bearing stress of the steel used is 300 MPa.
ANS a) dab = 16.74 mm b) dC = 21.4 mm c) t = 5.78 mm

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3) In the hanger shown, the upper portion of link ABC is 10mm thick and the lower
portions are each 6mm thick. Epoxy resin is used to bond the upper and lower
portions together at B. The pin at A has 10mm diameter, while a 6mm diameter pin is
used at C. Determine (a) the shearing stress in pin A, (b) the shearing stress in pin C,
(c) the largest normal stress in link ABC, (d) the average shearing stress on the
bonded surfaces at B, and (e) the bearing stress in the link at C
ANS a) 38.2MPa b) 53.1MPa c) 15MPa d)1.1MPa e) 41.7MPa

4) Knowing that the central portion of the link BD has a uniform cross sectional area of
800 mm2, determine the magnitude of the load P for which the normal stress in that
portion of BD is 50 MPa.
ANS P=62.7kN

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5) The hydraulic cylinder CF, which partially controls the position of rod DE, has been
locked in the position shown. Member BD is 15 mm thick and is connected at C to the
vertical rod by a 9-mm-diameter bolt. Knowing that P = 2 kN and θ = 75°, determine
(a) the average shearing stress in the bolt, (b) the bearing stress at C in member BD.

6) A 6-mm-diameter pin is used at connection C of the pedal shown. Knowing that P =

500 N, determine (a) the average shearing stress in the pin, (b) the nominal bearing
stress in the pedal at C, (c) the nominal bearing stress in each support bracket at C.
ANS a) 23 MPa b) 24.1 MPa c) 21.7 MPa

7) Knowing that a force P of magnitude 750 N is applied to the pedal shown, determine
(a) the diameter of the pin at C for which the average shearing stress in the pin is 40
MPa, (b) the corresponding bearing stress in the pedal at C, (c) the corresponding
bearing stress in each support bracket at C.
ANS a) 5.57 mm b) 38.9MPa c) 35MPa

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Fig for Q 5&6

Fig For Q 7&8

8) The rod ABC is made of an aluminum for which E = 70 GPa. Knowing that P = 6 kN
and Q = 42 kN, determine the deflection of (a) point A, (b) point B.
ANS a) 0.01819mm b) -0.0919mm

9) In Q.7 Both portions of the rod ABC are made of an aluminum for which E = 70 GPa.
Knowing that the magnitude of P is 4 kN, determine (a) the value of Q so that the
deflection at A is zero, (b) the corresponding deflection of B.
ANS a) Q=32.8KN b) -0.0728mm

10) Each of the links AB and CD is made of aluminum (E = 75 GPa) and has a cross-
sectional area of 125 mm2• Knowing th~t they support the rigid member BC,
determine the deflection of point E.
ANS 0.1095mm

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11) Two cylindrical rods, one of steel and the other of brass, are joined at C and
restrained by rigid supports at A and E. For the loading shown and knowing that E, =
200 GPa and El> = 105 GPa, determine (a) the reactions at A and E, (b) the deflection
of point C.
ANS a) 62.8 KN & 37.2 KN b) 46.3 x 10-6

12) The rigid bar AD is supported by two steel wires of 1.5 mm diameter (E = 200 GPa)
and a pin and bracket at D. Knowing that the wires were initially taut, determine (a)
the additional tension in each wire when a 900 N load P is applied at D, (b) the
corresponding deflection of point D.

13) Rod ABC consists of two cylindrical portions AB and BC; it is made of a mild steel
that is assumed to be elastoplastic with E = 200 GPa and σY = 250 MPa. A force P is
applied to the rod and then removed to give it a permanent set δP = 2 mm. Determine
the maximum value of the force P and the maximum amount δm by which the rod
should be stretched to give it the desired permanent set. Ans: a) 176.7 kN b)3.84mm

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14. In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins
are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the
ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is
desired, determine the largest load P that can be applied at A. Note that link BD is not
reinforced around the pin holes.

15. In the structure shown, an 8-mm-diameter pin is used at A, and 12-mmdiameter pins are
used at B and D. Knowing that the ultimate shearing stress is 100 MPa at all connections
and that the ultimate normal stress is 250 MPa in each of the two links joining B and D,
determine the allowable load P if an overall factor of safety of 3.0 is desired.
Ans:3.97kN

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16. Link BC is 6 mm thick and is made of a steel with a 450-MPa ultimate strength in
tension. What should be its width w if the structure shown is being designed to support a
20-kN load P with a factor of safety of 3?

17. The rod ABCD is made of an aluminum for which E = 70 GPa. For the loading shown,
determine the deflection of (a) point B, (b) point D.

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18. The device shown in Figure below consists of a horizontal beam ABC supported by two
vertical bars BD and CE. Bar CE is pinned at both ends but bar BD is fixed to the
foundation at its lower end. The distance from A to B is 450 mm and from B to C is 225
mm. Bars BD and CE have lengths of 480 mm and 600 mm, respectively, and their cross-
sectional areas are 1020 mm2 and 520 mm2, respectively. The bars are made of steel
having a modulus of elasticity is 205 GPa. Assuming that beam ABC is rigid, find the
maximum allowable load Pmax if the displacement of point A is limited to 1.0 mm.
Ans P=23.2 kN

19. The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum
(E = 70 GPa) and has a cross-sectional area of 500 mm2. Link CD is made of steel (E =
200 GPa) and has a cross-sectional area of 600 mm2. For the 30-kN force shown,
determine the deflection (a) of B, (b) of D, (c) of E
Ans: δB = 0.514 mm, δD = 0.300 mm, δE = 1.928 mm

20. The 4-mm-diameter cable BC is made of a steel with E = 200 GPa. Knowing that the
maximum stress in the cable must not exceed 190 MPa and that the elongation of the
cable must not exceed 6 mm,find the maximum load P that can be applied as shown.
Ans:1.988kN

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21. Link BD is made of brass (E = 105 GPa) and has a cross-sectional area of 240 mm2. Link
CE is made of aluminum (E = 72 GPa) and has a cross-sectional area of 300 mm2.
Knowing that they support rigid member ABC, determine the maximum force P that can
be applied vertically at point A if the deflection of A is not to exceed 0.35 mm.

22. When force P is applied to the rigid lever arm ABC in Fig. 2–5a, the arm rotates
counterclockwise about pin A through an angle of 0.05°. Determine the normal strain
developed in wire BD.
Ans 0.00116

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23. When force P is applied to the rigid arm ABC, point B displaces vertically downward
through a distance of 0.2 mm. Determine the normal strain developed in wire CD.

24. If the applied force P causes the rigid arm ABC to rotate clockwise about pin A through
an angle of 0.02°,determine the normal strain developed in wires BD and CE.

25. Part of a control linkage for an airplane consists of a rigid member CBD and a flexible
cable AB. If a force is applied to the end D of the member and causes a normal strain in
the cable of , determine the displacement of point D. Originally the cable is unstretched.
Ans: 0.00251

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26. The force applied to the handle of the rigid lever arm causes the arm to rotate clockwise
through an angle of 3° about pin A. Determine the average normal strain developed in the
wire. Originally, the wire is unstretched. Ans: 0.0258

27. Rigid beam AB rests on the two short posts shown in Figure below. AC is made of steel
and has a diameter of 20 mm, and BD is made of aluminum and has a diameter of 40 mm.
Determine the displacement of point F on AB if a vertical load of 90 kN is applied over
this point.Take Est = 200 GPa, Eal = 70 GPa.
Ans:δA=-0.286 mm , δB= -0.102 mm δF=-0.225 mm

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