Please check the attachments
l. Given G for aluminium is 26 GPa, and E for aluminium is 70 GPa, find v and the contraction of the diameter of an aluminnun rod with an original length of 200mm and diameter of 30mm and it changed its length by
1.70mm due to the application of a force.
2. While problems in this Engineering Mechanics module can be completed using a scientific calculator, students are encouraged to become familiar with the mathematical capabilities of spreadsheet software (e.g. -Excel-). You will develop skills in creating spreadsheet -calculators- and -look-up tables- that avoid repetitious hand calculations. A working knowledge of -Excel- (or equivalent) spreadsheets is assumed for this subject.Using the built-in Trigonometry functions in your spreadsheet, build a -Sine-, -Cosine- (and -Tangent-) spreadsheet lookup table in Incremental steps of 5 0 from Zero (00) to 1800. Use a scientific calculator to validate and check the spreadsheet table results to ensure your spreadsheet calculator is programmed correctly. (Note: use the spreadsheet -Help- function for correct use of the function -lookup tables-)
3. A 12mm diameter metal bar is subject to 45KN tensile stress when it failed. Calculate the nominal stress and the true stress if the diameter at failure was 10.5mm?
4. A block made of 6MPa concrete with dimensions as shown. What is the maximum load (mass) it can support?
8 Omm
25 Omm
1 1 Omm
5. A tensile test of a specimen of a certain metal had a gauge length of 50mm and an initial diameter of I Omm. When tested it produced the following results:
o Load at proportional limit 28,500N
o Ultimate load 43,000N
o Extension at proportional limit = 0. Imm
A. Calculate the proportional limit stress
B. Calculate the ultimate tensile strength of the metal. If the metal diameter halved what is the maximum tensile force the metal can with stand.
C. Calculate Youngs Modulus
6. Determine if an M16 bolt is suitable for an application if it joins two straps of steel 50mm across and 9 mm thick when the force on the bolt is 25kN and the material properties of the steel (bolt and metal strap from material text books) is allowable shear stress 90MPa, allowable tensile stress = 110MPa and the allowable compressive stress is 220MPa.
7. The tensile force of I l KN acting on 6mm diameter rod. What is the stress? If the UTS of the metal is 500MPa and the Yield Stress of metal is 250MPa, will the rod fail? Comment (consider factor of safety). What if the load was fluctuating and the safety factor of 8 is required to prevent fatigue failure. Is the rod safe from failure?
8. Given a stainless steel rod is subjected to a tensile force of 2.8KN, and the stainless steel has an Ultimate Tensile Strength (UTS) = 700MPa and Factor of Safety of 2.5 based on the UTS- What is minimum diameter of the rod to meet the maximum allowable stress?
9. Bolt Selection: From the diagram below, find the maximum pulling force if the bolt holding the three plates is 24mm diameter, and the bolt is loaded in double shear, with a factor of safety of 3 and the maximum allowable shear stress is 60MPa. Note the -allowable shear stress- has the factor of safety inbuilt.

10.Determine if an M16 bolt is suitable for an application if it joins two straps of steel 60mm across and 6 mm thick when the weight force on the bolt is 2 Tonnes and the material properties of the steel (bolt and metal strap from material text books) is allowable shear stress 90MPa, allowable tensile stress 1 10MPa and the allowable compressive stress is 220MPa?
1 1 -Calculate the torsional shear stress in a 60mm diameter solid cylinder shaft if it is subjected to an 1800N.m Torque.
Nota: Polar cylinder. 32
12.1n the above example, if the power to a drive shaft is 270kW, and the shaft is rotating at 2000RPM, calculate the shear stress in the shaft and from material text books detailing mild steel properties, would a steel shaft made from mild steel be sufficient for this application?
13-Determine the compressive stress m an alununium rod 1.8m long and subject to 55 degree heat from a starting heat of 20 degrees Celsius when the rod ig being FULLY constrained by two unyielding supports.
14.For a 12 mm fillet weld- and electrode strength of 410MPaY find:
a) The Throat Thickness
b) The allowable stress
c) The allowable load per mm of weld length
d) The length of weld required to cany a load of 52.6kN
15-Find the moment of inertia of a square area (hollow) with dimensions across and 4mm thick about a parallel axis 33mm from the centroidal axis
Centroidal axis
refuenee
16-A beam of regular cross section, 350mm deep by 150mm wide is subjected to a bending moment of 77 kN.m. Find the maximum bending stress.
17.Using the charts below, find the maximum bending stress in a bar which has a thickness of 12.5mm, radius of curvature of 7.5mm and is subjected to a bending moment of 900N-m
18-Determine the forces in members B and C given the reaction force of 17kN and an applied load of 12kN as shown for the truss below:
17 KN 4m x 4m x 4m
Average Normal Stress
19.Prob1em
-Ille column is subjected to an axial force of g kN. which is applied through the centroid of the cross-sectional area. Determine the avejagc normal Stress acting at st:ction a—a, Show this distribution of stress acting over the areas ero€g sect ion ,

20.Prob1em
The anchor shackle supports a cable force of 30 kÑ. It tho pin has diameteJ of 6 mm. determine the average shear stre$$ in the pin,

3.0kN
21 Problem
While running the foot of a 75 kg man is momentarily subjected to a force which is 5 times his weight.
Determine the average normal stress developed in the Tibia T of his leg at the midsection a-a. The cross section can be assumed as circular, having an outer diameter of 45 mm and an inner diameter of 25 mm. Assume the fibula F does not support a load

22-Probl em
The 250-N lamp is supported by thrcc stccl rods

connected by a Ting at Determine which is subjected to the greater average normal stress and compute its value. Take 0 = 300. The diameter of each rod K given in the figure.
23-Prob1em
The 250ëN lamp is supported by three steel rods connected hy a ring at A. Determine the anglc of orientation O of AC such that the average normal stres in rod AC is twice the average normal stress in rod AD. What is thc magnitude of stress in each rod? Thc diameter of cach rod is given in the figure,

Allowable Stress
24Problem
The joint is fastened together using two bolts. Determine the required diameter of the bolts if the failure shear stress for the bolts is = 350 MPa. Use a factor of safety for shear of F,S.
40
25.Problem
The fillet weld size a is determined by computing the average shear stress along the shaded plane* which hag the smallest cross section. Detcrmine the smallest size a of thc two welds if the force applied to the plate is T 100 kN.The allowable shear stress for the weld material i$ TaUow - 100 MPa.

26-Prob1em
The eye bolt is used to support the load of 25 kN Determine its diameter d to the nearest multiples of 5 mm and the required thickness h to the nearest multiples of 5 mm of the support so that the washer will not penetrate or shear through it, The allowable normal stress for the bolt is 150 MPa and the allowable shear stress for the supporting matcrial is = 35 MPa.

Strain & Deformation
27Prob1em
An air-filled rubber ball has a diameter of 150 mm. If the air pressure within it is increased until the balls diameter becomes 175 rnrn, determine the average normal strain in thc rubber.
28.Prob1em
The rigid beam is supported by a pin at A and wires BD and CE. If the load P On thc bcam causes thc cnd C to be displaced 10 mm downward, determine the normal strain developed in wireg CE and BD.
29-Prob1em
The rigid beam is supported by a pm at A and wire BD and CE
If the maximum allowable normal strain in each wire is
= 0.002 mm/mm
Determine the maximum vertical displacement of the load P.

30. Problem

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 it to rotate by 0 0.3 0 , determine the normal strain in the cable. Originally the cable is unslretched.

Stress Strain Diagram
31 -Problem
concrete cylindcr having a diameter of 150 mm and gauge length of 300 mm is tested in comprc$ion. Thc rcsulgs of the test are reported in the table as load versus contraction* Draw the stress-strain diagram using scales of 10 mm = 2 MPa and 10 mm 0.1(11) 2) mm/mmv From the diagram, determine approximately the modulus al
elasticity.
Contraction (mm)
0.0
250
4715
825
1025
1275
150,0
172.5
1925
2325
250,0
2610 0.0000 0.0150 omm 0.0500
0.0650
0.080 0.1000
o. 1125 0.1250
(1.1550 0.1750
c.i675
32-Prob1em
Data taken from stress—strain test for a ceramic are given in the table. The curve is linear between the origin and the first point. Plot the diagram, and determine the rfioclulus of elasticity and the modulus of resilience,
(mm/mm)
ovo 232.4
218.5
345 k
360.5
373 A 040000
00010
0.0018
00012
33 -Problem
A tension test was performed on a steel specimen having an original diameter of 13mm and a gauge length of 50 mm The data is listed in the table -Plot the stress- strain diagram and determine approximately the modules of elasticity the yield stress the ultimate stress and the rupture stress -use a scale of 10mm=209 MPA and 10 mm = 0.05 mm/mm- Redraw the elastic region using the same stress scale but a strain scale of 10 mm = 0.001 mm/mm.
Load (kN) ElOngation (mm)
0.0
7.5
23.0
40.0
55.0
59.0
59.0
60.0
83.0
1000
107.5
97.5
025 0.0000
0.0125
0.0375
0.0625
0.0875
0.1250
02000
0.5000
1.0000
2.5000

10.0000
11.5000
34.Prob1em
-Ihc strcss—strain diagram for a stccl bar is shown in the figure. Determine approximatcly thc modulus of elasticity, the proportional limit, the ultimate stress and the modulus of resilience. If the bar is loaded until it is stressed to 450 MPa, determine the amount of elastic strain recovery and the permanent set or strain in the bar when it is unloaded.
cr (MPa)
(ntm/mm)
0.10 0120 0.30
Stress Concentrations
35.Problem
The allowable stress for the bar is aallow= 175 NIPA - Determine the maximum moment M that can be applied to the bar.
30 mm

Shear Modulus of Elasticitv
36-Prob1em
Thc elastic portion Of the tension stress—strain diagram for an aluminum alloy is shown in the figure, The specimen used for the test bas a gauge length of SO mm and a diameter Of 12.5 mm, When thc applicd load is 45 kN, the new diameter of the spccimcn is 12.48375 mm. Compute the shear modulus Gat for the aluminum$
(mm/mm)
0.00614
Equilibrium
37.Problem
Determine the resultant internal normal force acting on the cros section through point in each COILInj11. In (a), scgmcnt BC weighs 300 kg/m and segment CD weighs
400 In the column has a mass of 200 kg/m,

Determine the resultant internal torque acting on the cross sections through points B and C.

39Prob1em
A force Of 80 N is supported by the bracket as shown. Determine the resultant internal loadings acting on the sectGon through point A.
80 N
1-6. *Ihc beam AB is pin supported at and supported by a cable BC Determine the resultant internal loadings acting on the cross section at point D.
Solve Prob. 1—6 for the resultant internal loadings acting at point
41 Problem
The beam supports the distributed load shown, Determine the resultant internal loadings on the cros sections through points D and E. Assume the reactions at the supports A and 8 are verticalv

Determine the resultant internal loadings acting on lhe cross scction at point B. .
c
43.Prob1em
Determine the resultant internal loadings acting on the cross section through point D in Prob. 1—18
44_prob1em
Determine Ille resultant internal loadings acting on the cross section through paint B of the signpost. post is fixed to the ground and a uniform presstue al 500 acts pcrpondicular to the face of the gign.

Shear and -Moment Diagrams
45.Prob1em
Draw the shear and moment diagrams for the shaft. The bearings at and B exert only vertical reactions on the shaft.

46.Prob1em
The load binder is used to support a load. If the force applied to the handle is 250 N, determine the tensioms TI and Tt in each end of the chain and then draw the shear and moment diagrams for the arm ABC

Draw the shear and moment diagrams for the shaft.The bearings at A and D exert only vertical rcactions on the shaft. The loading is applied to the pulleys at D and Cand EE
--350 mm 500 mm mm
300 mm

400 N
175
N
550 N
48. Problem
The engine crane is used to support the engine. which has a weight of 6 kN, Draw the shear and moment diagrams of the boom ABC when it is in the horizontal positi{-i) shown,

The 75 kg man sits in the center of the boat which has a uniform width and a weight per linear meter of 50 N/m - determine the maxnnum bending moment exerted on the boat. Assume that the water exerts a uniform distributed load upward on the bottom of the boat .

BENDING STRESS
50.Problem
The slab of marble, Which can be assumed a linear elastic brittle material, has a specific weight of 24 kN/m3. If it is supported on its edges as shown in determine the minimum thickness it should have without causing it to break.The fracture stress is MPau
The member has a cross section with the dimensions shown. Determine the largest internal M that can be applied without exceeding allowable tensile and compressive stresses of (at) allow 150 MPA and (ac)allow = 100 MPA respectively.
10 mm
I—SO mm r