DESIGN 3

3/21/23 7:59 AM

sit A: Imagine that a long steel wire hangs vertically from a

high-altitude hot air balloon. Steel weighs 490
lb/cu.ft. and sea water weighs 63.8 lb/cu.ft.
1. What is the greatest length (feet) it can have without
yielding if the steel yields at 40 ksi?
A. 11,800 B. 13,500
C. 12,600 D. 10,000
2. If the same wire hangs from a ship at sea, what is the
greatest length (feet)?
A. 11,800 B. 13,500
C. 12,600 D. 10,000

sit B: A steel plate 2.5 m x 1.2 m x 100 mm thick is to be

hoisted by a steel cable sling as shown in the figure.
Assume that steel weighs 77.3 kN/cu.m.

3. Determine the vertical displacement of the steel plate

when suspended due if the sling cable is 60 mm^2 in
area.
A. 2.14 mm B. 4.05 mm
C. 2.54 mm D. 5.04 mm
4. Determine the required diameter of the pins through the
clevis if the allowable shear stress is 35 MPa.
A. 12 mm B. 16 mm
C. 20 mm D. 18 mm
5. Determine the required diameter of the pins if the
bearing stress between the pins and plate will not
exceed 7.70 MPa.
A. 12 mm B. 16 mm
C. 20 mm D. 18 mm

sit C: A reinforced concrete slab 2.5 m x 2.5 m x 250 mm

thick is lifted by four steel cables attached to the
corners, as shown in the figure. The cables are
attached to a hook at a point 1.5 m above the top of
the slab. Each cable has an effective cross-sectional
area A = 75 mm^2.

6. Determine the tensile stress (MPa) in the cables due to

the weight of the concrete slab.
A. 125 MPa B. 162.7 MPa
C. 193.2 MPa D. 176.7 MPa

7. Determine the vertical displacement of the concrete

slab when suspended due to the elongation of the
cables.
A. 2.24 mm B. 3.46 mm
C. 1.45 mm D. 2.94 mm
sit D: A joint between two concrete slabs A and B is filled
with a flexible epoxy that bonds securely to the
concrete (see figure). The height of the joint is h =
100 mm., its length is L = 1.0 m, and its thickness is
t = 12 mm. Under the action of shear forces V, the
slabs displace vertically through the distance d =
0.051 mm. relative to each other.

8. What is the magnitude of the forces V if the shear

modulus of elasticity G for the epoxy is 965 MPa?
A. 410 kN B. 523 kN
C. 315 kN D. 761 kN

sit E: A steel rod is held in place between rigid walls by the

12-mm-dia. bolt as shown in the figure below. For the
steel rod, use α = 12μ/oC and E = 200 GPa.

9. Calculate the resulting tensile stress in the 15-mm-

dia. steel rod in MPa?
A. 100 B. 72
C. 145 D. 50
10. If the temperature drops by 30oC, calculate the
resulting shear stress in the 12-mm-dia. Bolt in MPa?
A. 112.50 B. 56.25
C. 143.23 D. 71.62

sit F: A steel bolt is snug in place by a brass sleeve and nut

at temperature of 24oC. The bolt has a diameter of dB
= 25 mm, and the sleeve has inside and outside
diameters of d1 = 26 mm and d2 = 36 mm, respectively.
For the brass sleeve, use α = 21μ/oC and E = 100 GPa.
For the bolt, use α = 10μ/oC and E = 200 GPa.

11. Calculate the resulting compressive stress (MPa) in the

bolt if the temperature rises to 60oC.
A. 24.80 B. 22.16
C. 26.25 D. 28.30
12. Calculate the resulting compressive stress (MPa) in the
sleeve at 60oC.
A. 26.47 B. 24.80
C. 22.38 D. 28.52

13. Calculate the required rise in temperature to produce a

compressive stress of 25 MPa in the brass sleeve.
A. 34oC B. 42oC
C. 66oC D. 58oC
sit G: The fixed-end bar ABCD consists of three prismatic
segments, as shown in the figure. The end segments have
cross-sectional area A1 = 840 mm^2 and length L1 = 200
mm. The middle segment has cross-sectional area A2 =
1260 mm^2 and length L2 = 250 mm. Loads PB and PC are
equal to 25.5 kN and 17.0 kN, respectively.

14. Determine the reaction (kN) at A.

A. 8.5 B. 10.5
C. 7.7 D. 9.5
15. Determine the reaction (kN) at D.
A. 2.0 B. 1.5
C. 3.0 D. 2.5
16. Determine the compressive axial force FBC (kN) in the
middle segment of the bar.
A. 17.0 B. 8.5
C. 25.5 D. 15.0

sit H: When the assembly shown in SI-01 was placed at room

temperature (20°C) a 0.5-mm gap exists between the ends
of the rods shown. At a later time when the temperature
has reached 140°C.

17. Determine the normal stress in the aluminum rod.

A. 369.574 kN B. 396.574 kN
C. 232.389 kN D. 223.389 kN
18. Determine the deformation in the Aluminum rod.
A. 0.381 mm B. 0.363 mm
C. 0.035 mm D. 0.089 mm

sit I: A stepped shaft ACB having solid circular cross

sections with two different diameters is held against
rotation at the ends.

19. If the applied torque is To = 150 N·m, determine the

shear stress (MPa) on segment AC?
A. 26.87 B. 43.00
C. 47.74 D. 24.45
20. What is the shear stress on segment CB?
A. 26.87 B. 43.00
C. 47.74 D. 24.45
21. What is the maximum value of To if the shear stresses
will not exceed 50 MPa?
A. 183.11 B. 157.11
C. 174.41 D. 143.22

sit J: A solid steel bar of diameter d1 = 25.0 mm is enclosed

by a steel tube of outer diameter d3 = 37.5 mm and
inner diameter d2 = 30.0 mm. Both bar and tube are
held rigidly by a support at end A and joined securely
to a rigid plate at end B. The composite bar, which has
a length L = 550 mm, is twisted by a torque T = 400 N·m
acting on the end plate.

22. Determine the maximum shear stresses in the tube.

A. 32.7 MPa B. 40.7 MPa
C. 49.0 MPa D. 36.2 MPa
23. Determine the maximum shear stresses in the bar.
A. 32.7 MPa B. 40.7 MPa
C. 49.0 MPa D. 36.2 MPa
24. Determine the angle of rotation (in degrees) of the end
plate, assuming that the shear modulus of the steel is
80 GPa.
A. 1.03 B. 2.06
C. 2.25 D. 1.75
sit K: A copper tube 55 mm in outside diameter and wall
thickness 5 mm fits loosely over a solid steel circular
bar 40 mm in diameter. The two members are fastened
together by two metal pins each 8 mm in diameter and
passing transversely through both members, one pin
being near each end of the assembly. At room
temperature the assembly is stress free when the pins
are in position. The temperature of the entire
assembly is then raised by 40°C. For copper E = 90
GPa, α = 18μ/°C; for steel E = 200 GPa, α = 12μ/°C.
25. Calculate the average shear stress in the pins.
A. 132 MPa B. 145 MPa
C. 128 MPa D. 156 MPa
26. Calculate the normal stress on the copper tube.
A. 10.54 MPa B. 16.86 MPa
C. 33.72 MPa D. 21.08 MPa
27. Calculate the normal stress on the steel bar.
A. 10.54 MPa B. 16.86 MPa
C.
` 12.32 MPa D. 14.11 MPa

sit A: A retaining wall 5 ft high is constructed of horizontal wood

planks 3 in. thick (actual dimension) that are supported by
vertical wood piles of 12 in. diameter (actual dimension),
as shown in the figure.

1. Calculate the maximum bending stress in each pile in psi if

the piles are spaced 60” on centers.
A. 1000 B. 885
C. 1136 D. 972
2. Calculate the maximum bending stress in the horizontal wood
planks in psi.
A. 684 B. 745
C. 833 D. 972
3. Calculate the maximum permissible spacing s of the piles if
the allowable bending stress in the wood is 1200 psi.
A. 68” B. 85”
C. 72” D. 100”

sit B: A built-up, laminated plastic beam of square cross section

fabricated by gluing together three pieces of 10 mm x 30 mm
strips as shown below. The beam is simply supported over a
span of 320 mm and weighs 10 N/m.

4. Calculate the maximum concentrated load P (N) that may be

placed at the midspan if the allowable shear stress in the
glued joint is 0.3 MPa.
A. 401.8 B. 405.0
C. 536.8 D. 356.8
5. Calculate the maximum shear stress (MPa) in the plastic if P
= 375 N.
A. 0.375 B. 0.315
C. 0.225 D. 0.405
6. Calculate the maximum concentrated load P that may be placed
at the midspan if the allowable bending stress in the
plastic is 7.5 MPa.
A. 440.8 B. 420.2
C. 392.1 D. 375.6

sit A:
sit B:
sit C:
sit D:
sit E:
sit F:
sit G:
sit H:
sit I:
sit J:
sit K:
sit L:
sit M:
sit N:
sit O:
sit P:
sit Q:
sit R:
sit S: An angle bar 100x100x11 mm tension member is connected with
20-mm-diameter bolts with nominal hole diameter of 22 mm as
shown in the figure. Both legs of the angles are connected.
Use Fy = 248 MPa and Fu = 400 MPa.

1. Determine the gross area of member.

A. 2,200 mm2 B. 2,126 mm2
C. 1,900 mm2 D. 2,079 mm2
2. Determine the effective net area of member.
A. 1,573 mm2 B. 1,610 mm2
C. 1,627 mm2 D. 1,815 mm2
3. Determine the allowable tensile strength according to the
limit state of tensile yielding in the gross section.
A. 318.14 kN B. 257.80 kN
C. 308.73 kN D. 234.06 kN
4. Determine the design tensile strength according to the limit
state of tensile rupture in the net section.
A. 547 kN B. 483 kN
C. 488 kN D. 471 kN

sit B: An angle bar 150x90x8 mm tension member is connected with

20-mm-diameter bolts as shown in the figure. Both legs of
the angles are connected. Use Fy = 248 MPa and Fu = 400 MPa.
The member is designed to sustain a tensile dead load of 138
kN and tensile live load of 138 kN.

5. Determine the effective net area of member in mm^2.

A. 1,472 B. 1,312
C. 1,284 D. 1,380
6. Determine the ratio of the factored load to the design
tensile strength based on gross yielding.
A. 0.933 B. 0.982
C. 0.902 D. 1.003
7. Determine the ratio of the factored load to the design
tensile strength based on tensile rupture.
A. 0.933 B. 0.982
C. 0.902 D. 1.003

sit C: The tension member shown in the figure is C12x20.7 of A572

Grade 50 steel, Fy = 345 MPa, Fu = 446 MPa. Properties of
the section are: A = 3,929 mm2, bf = 75 mm, d = 305 mm, tf =
12.7 mm, tw = 7.2 mm, 𝑥̅ = 17.73 𝑚𝑚

8. Determine the allowable tensile strength (kN) according to

the limit state of tensile yielding in the gross section.
A. 1,016.6 B. 677.7
C. 1,219.9 D. 811.7

9. Determine the design tensile strength (kN) according to the

limit state of tensile rupture in the net section.
A. 1,020.7 B. 765.6
C. 1,167.3 D. 875.5

10. Determine the design block shear strength in kN.

A. 890.8 B. 1,045.6
C. 784.2 D. 1,187.7

sit D: Two plates, each 11 mm thick, are bolted together form a

lapped tension member as shown in the figure below.
Diameter of bolts are 16 mm and the plate material is A36
steel with Fy = 248 MPa and Fu = 400 MPa. Assume the
fasteners are adequate and do not control the tensile
capacity.

11. Determine the allowable tensile strength based on tensile

rupture in kN.
A. 651 B. 791
C. 664 D. 638

12. Determine the allowable block shear strength in kN.

A. 825.0 B. 648.4
C. 768.9 D. 577.8

sit E: A W12x79 A36 (Fy = 248 MPa) steel is used as a compression

member. It is 7 m long, fixed at the top and bottom, and
has additional support in the weak direction 3 m from the
top. Properties of the section are: A = 14,500 mm2, Ix =
258.6 x 106 mm4, Iy = 84.375 x 106 mm4
13. Calculate the critical slenderness ratio of the given
column.
A. 26.208 B. 21.882
C. 36.706 D. 41.680
14. Calculate the elastic critical buckling stress.
A. 2,873 MPa B. 1,465 MPa
C. 1,879 MPa D. 1,136 MPa
15. Calculate the nominal axial strength of the column.
A. 3 350 kN B. 3 392 kN
C. 4 810 kN D. 5 098 kN
16. Calculate the service axial live load if the service dead
load is 800 kN based on design axial strength according to
LRFD.
A. 2 068 kN B. 1 270 kN
C. 1 284 kN D. 2 230 kN

sit F: Four angle bars 100 mm x 90 mm x 10 mm of material A36 steel

(Fy = 248 MPa) are welded at the tip of the legs to form a
box section. Column height is 4 m and effective length
factor K = 1.0 for both axes. The properties of each angle
is given:
A= 1,800 mm2
Ix = 1.22 x 106 mm4
Iy = 0.767 x 106 mm4
x= 19.8 mm
y= 32.33 mm

17. Calculate the critical slenderness ratio of the built-up

section.
A. 55.16 B. 193.78
C. 54.67 D. 153.64
18. Calculate the limiting flexural buckling stress, Fcr in MPa.
A. 148.80 B. 211.32
C. 568.79 D. 648.56
19. Calculate the service axial live load if the service dead
load is 500 kN based on allowable axial strength by ASD.
A. 1,952 kN B. 480 kN
C. 641 kN D. 411 kN

sit G: A built-up tee-shape consists of a 22-mm flange and 25-mm

web. The yield strength is 345 MPa.

20. Determine the distance from the top of the shape to the
horizontal plastic neutral axis in mm.
A. 62 B. 103
C. 40 D. 125
21. Determine the plastic moment strength for the horizontal
plastic neutral axis in kN‧m.
A. 497.7 B. 395.2
C. 259.3 D. 318.9
22. Compute the plastic section modulus x10^3 mm^3 with respect
to the minor principal axis.
A. 282.359 B. 290.364
C. 118.550 D. 195.312