SHEET 1
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 175 MPa in rod AB and 150 MPa in
rod BC, determine the smallest allowable values of d1 and d2.
1.2 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown.
Knowing that d1 = 50 mm and d2 = 30 mm, find the average normal stress at the
midsection of (a) rod AB, (b) rod BC.
1.3 Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Determine
the magnitude of the force P for which the tensile stress in rod AB has the same magnitude as the
compressive stress in rod BC.
1.4 In Prob. 1.3, knowing that P = 160 KN, determine the average normal stress at the midsection of
(a) rod AB, (b) rod BC.
1.5 Two steel plates are to be held together by means of 16-mm-diameter high-strength steel bolts
fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not
exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the outer diameter of the
spacers that yields the most economical and safe design.
17
1.6 Two brass rods AB and BC, each of uniform diameter, will be brazed together at B to form a non-
uniform rod of total length 100 m which will be suspended from a support at A as shown. Knowing
that the density of brass is 8470 kg/m3, determine (a) the length of rod AB for which the maximum
normal stress in ABC is minimum, (b) the corresponding value of the maximum normal stress.
1.7 Each of the four vertical links has an 8 x 36-mm uniform rectangular cross section and each of the
four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in
the links connecting (a) points B and D, (b) points C and E.
1.8 A couple M of magnitude 1500 N. m is applied to the crank of an engine. For the position shown,
determine (a) the force P required to hold the engine system in equilibrium, (b) the average normal
stress in the connecting rod BC, which has a 450-mm2 uniform cross section.
1.9 When the force P reached 8 kN, the wooden specimen shown failed in shear along the surface
indicated by the dashed line. Determine the average shearing stress along that surface at the time
of failure .
18
1.10 The wooden members A and B are to be joined by plywood splice plates that will be fully
glued on the surfaces in contact. As part of the design of the joint, and knowing that the clearance
between the ends of the members is to be 6 mm. determine the smallest allowable length L if the
average shearing stress in the glue is not to exceed 700 kPa.
1.11 A load P is applied to a steel rod supported as shown by an aluminum plate into which a 12
mm.-diameter hole has been drilled. Knowing that the shearing stress must not exceed 180 MPa
in the steel rod and 700 kPa in the aluminum plate, determine the largest load P that can be applied
to the rod.
1.12 Two wooden planks, each 22 mm thick and 160 mm wide, are joined by the glued mortise
joint shown. Knowing that the joint will fail when the average shearing stress in the glue reaches
820 kPa, determine the smallest allowable length d of the cuts if the joint is to withstand an axial
load of magnitude P = 7.6 kN.
1.13 A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing
resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing,
(b) the size of the footing for which the average bearing stress in the soil is 145 kPa
19
(Ans. 8.52 ksi)
Prob. 1.15
(Ans. 8.8 MPa, 127 MPa, 203 MPa)
Prob. 1.16
(Ans. 3.35, d=1.35)
