Faculty of EMS
Department: ENME
Course : Strength of Materials I
Dr. Amir R. Ali
Tutorial (4)
Subject: Statically Indeterminate Problems
Prob.1: [2.33] Compressive centric
forces of 160 kN are applied at both
ends of the assembly shown by means
of rigid plates. Knowing that Es = 200
GPa and Ea = 70 GPa, determine (a)
the normal stresses in the steel core and
the aluminum shell, (b) the deformation
of the assembly.
(a) σs = -116.3 MPa; σa = -40.7 MPa
(b) δ = -0.145 mm
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Prob.2: [2.35] An axial centric force of
magnitude P = 450 kN is applied to the
composite block shown by means of a
rigid end plate. Knowing that h = 10
mm, determine the normal stress in (a)
the brass core, (b) the aluminum plates.
(a) σb = -140.6 MPa (b) σa = -93.75 MPa
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Prob.3: [2.39] 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 Es = 200 GPa and
Eb = 105 GPa, determine (a) the
reactions at A and E, (b) the
deflection of point C.
(a) RA = 62.8 KN; RE = 37.2 KN
(b) δc = 0.0463 mm (right)
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Prob.4: [2.45] The steel rods BE
and CD each have a diameter of 16
mm (E = 200 GPa). The ends are
threaded with a pitch of 2.5 mm.
knowing that after being snugly fit,
the nut at B is tightened on full turn;
determine (a) the tension in rod CD,
(b) the deflection of point C of the
rigid member ABC.
(a) FCD = 21.17 KN (b) δc = 0.947 mm
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Prob.5: [2.46] The rigid bar AD is
supported by two steel wires of 1.5
mm diameter (E = 200 GPa) and a
pin 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.
(a) TBE = 838.9 N; TCF = 931 N
(b) δD = 1.78 mm (downward)
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