Chapter -1- Problems - ISHIK – · PDF fileThe built-up shaft consists of a pipe AB and...

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Ishik University/Sulaimani Civil Eng. Dep. Assistant Lecturer/ Asma Ab. Mustafa 1

Ishik University / Sulaimani

Civil Engineering Department

Mechanics of Materials

CE 211

Problems Chapter 1,2,3


Chapter -1-

Problems

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The 500 kg engine is suspended from the boom crane as shown. Determine

resultant internal loadings acting on the cross section of the boom at point E.

Problem -1-

Ans; NE= -9.81 kN VE= -2.45 kN ME= -2.45 kN.m


Problem -2-

Determine the resultant internal loadings acting on the cross section at G of

the beam shown in Fig. 1–7a. Each joint is pin connected.

Ans; NE= -6200 Ib VE= 3150 Ib ME= 6300 Ib.ft

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Problem -3-

Determine the resultant internal

normal force acting on the cross

section through point A in each

column.

*In (a), segment BC weighs 180

lb/ft and segment CD weighs 250

lb/ft.

*In (b), the column has a mass of

200 kg/m.

Ans; a) FA = 13.8 kip b) FA = 34.9 kN


Problem -4-

Determine the resultant internal loadings in the beam at cross

sections through points D and E. Point E is just to the right of the

3-kip load.

Ans; AY = 3.00 kip, BY = 6.00 kip, ND = 0, VD = 0.750 kip, MD = 13.5 kip.ft, NE = 0, VE = -9.00 kip, ME = -24.0 kip.ft

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Problem -5-

Determine the normal force, shear force, and moment at a section

through point C. Take P = 8 kN.

Ans; NC = -30.0 kN, VC = -8.00 kN MC = 6.00 kN.m


Problem -6-

Determine the resultant internal loadings on the cross section through

point C. Assume the reactions at the supports A and B are vertical.

Ans; AY = 7.50 kN VC = 1.50 kN MC = 4.50 kN.m

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Problem -7-

Determine the resultant internal loadings on the cross section through

point D. Assume the reactions at the supports A and B are vertical.

Ans; ND = 0 VD = -1.875 kN MD = 3.94 kN.m


Problem -8-

Determine the resultant internal loadings acting on the cross section

through point C. Assume the reactions at the supports A and B are

vertical.

Ans; NC = 0 VC = 4.50 kip MC = 31.5 kip.ft

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Problem -9-

Determine the resultant internal loadings acting on the cross section

through point D. Assume the reactions at the supports A and B are

vertical.

Ans; AY = 18.0 kip ND = 0 , VD = 0 MD = 36.0 kip.ft


Problem -10-

Determine the average normal stress developed at points A, B, and C.

The diameter of each segment is indicated in the figure.

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Problem -11-

Determine the average normal stress developed on the cross section.

Sketch the normal stress distribution over the cross section.

Ans;


Problem -12-

The column is subjected to an

axial force of 8 kN, which is

applied through the centroid of

the cross-sectional area.

Determine the average normal

stress acting at section a–a.

Show this distribution of

stress acting over the area’s

cross section.

Ans;

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Problem -13-

The built-up shaft consists of a pipe AB and solid rod BC. The pipe

has an inner diameter of 20 mm and outer diameter of 28 mm. The

rod has a diameter of 12 mm. Determine the average normal stress at

points D and E and represent the stress on a volume element located

at each of these points.

Ans;


Problem -14-

If the block is subjected to the centrally applied force of 600 kN,

determine the average normal stress in the material. Show the stress

acting on a differential volume element of the material.

Ans;

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Problem -15-

Rods AC and BC are used to suspend the 200-kg mass. If each rod is

made of a material for which the average normal stress can not

exceed 150 MPa, determine the minimum required diameter of each

rod to the nearest mm.

Ans;


Problem -16-

The frame supports the loading shown. The pin at A has a diameter of

0.25 in. If it is subjected to double shear, determine the average

shear stress in the pin.

Ans;

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Problem -17-

Ans ;

d = 13.5 mm


Problem -18-

Ans;

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Problem -19-

Ans;


Chapter -2-

Problems

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Problem -20-

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

Ans;


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.

Problem -21-

Ans;

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Problem -22-

The rectangular plate is deformed into the shape of a rhombus shown

by the dashed line. Determine the average shear strain at corner A

with respect to the x and y axes.

Ans;


Problem -23-

The triangular plate is deformed into the shape shown by the dashed

line. Determine the normal strain developed along edge BC and the

average shear strain at corner A with respect to the x and y axes.

Ans;

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Problem -24-

The square plate is deformed into the shape shown by the dashed

line. Determine the average normal strain along diagonal AC and the

shear strain of point E with respect to the x and y axes.

Ans;


The rigid beam is supported by a pin at A and wires BD and CE. If the

load P on the beam causes the end C to be displaced 10 mm downward,

determine the normal strain developed in wires CE and BD.

Problem -25-

Ans;

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The two wires are connected together at A. If the force P causes

point A to be displaced horizontally 2 mm, determine the normal

strain developed in each wire

Problem -26-

Ans;


The rigid beam is supported by a pin at A and wires BD and CE. If the

distributed load causes the end C to be displaced 10 mm downward,

determine the normal strain developed in wires CE and BD.

Problem -27-

Ans;

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The corners B and D of the square plate are given the displacements

indicated. Determine the average normal strains along side AB and

diagonal DB.

Problem -28-

Ans;


Problem -29-

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 0.0035 mm/mm,

determine the displacement of point D. Originally the cable is

unstretched.

Ans;

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Chapter -3-

Problems


Problem -30-

Ans;

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Problem -31-

Ans;


Problem -32-

Ans;

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Problem -33-

Ans;


Problem -34-

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Problem -34- Solution;


Problem -35-

Ans;

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Problem -36-

Data taken from a 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 modulus of elasticity and the modulus

of resilience.

Ans;


Problem -37-

The acrylic plastic rod is 200 mm long and 15 mm in diameter. If an

axial load of 300 N is applied to it, determine the change in its length

and the change in its diameter. Ep = 2.70 GPa, vp = 0.4.

Ans;

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Problem -38-

The elastic portion of the stress–strain diagram for a steel alloy is

shown in the figure. The specimen from which it was obtained had an

original diameter of 13 mm and a gauge length of 50 mm. When the

applied load on the specimen is 50 kN, the diameter is 12.99265 mm.

Determine Poisson’s ratio for the material.

Ans;


Problem -39-

The elastic portion of the stress–strain diagram for a steel alloy is

shown in the figure. The specimen from which it was obtained had an

original diameter of 13 mm and a gauge length of 50 mm. If a load of

P=20 kN is applied to the specimen, determine its diameter and gauge

length. Take v (nu)= 0.4.

Ans;

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Problem -40-

The aluminum block has a rectangular cross section and is subjected

to an axial compressive force of 8 kip. If the 1.5-in. side changed its

length to 1.500132 in., determine Poisson’s ratio and the new length

of the 2-in. side. Eal 10(103) ksi.

Ans;


Problem -41-

The block is made of titanium Ti-6A1-4V and is subjected to a

compression of 0.06 in. along the y axis, and its shape is given a tilt of

u = 89.7°. Determine εx, εy, and γxy.

Ans;

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Problem -42-

The shear stress–strain diagram for a steel alloy is shown in the figure.

If a bolt having a diameter of 0.75 in. is made of this material and used

in the double lap joint, determine the modulus of elasticity E and the

force P required to cause the material to yield. Take v (nu) = 0.3.

Ans;


Problem -43-

The elastic portion of the tension stress–strain diagram for an

aluminum alloy is shown in the figure. The specimen used for the test

has a gauge length of 2 in. and a diameter of 0.5 in. When the applied

load is 9 kip, the new diameter of the specimen is 0.49935 in.

Compute the shear modulus Gal for the aluminum.

Ans;

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Problem -44-

The elastic portion of the tension stress–strain diagram for an

aluminum alloy is shown in the figure. The specimen used for the test

has a gauge length of 2 in. and a diameter of 0.5 in. If the applied

load is 10 kip, determine the new diameter of the specimen. The shear

modulus is Gal = 3.811032 ksi.

Ans;

50

Problem -45-

Determine the elongation of the square hollow bar when it is subjected to

the axial force If this axial force is increased to and released, find the

permanent elongation of the bar. The bar is made of a metal alloy having a

stress–strain diagram which can be approximated as shown.

Ans;

Ishik University/Sulaimani Civil Eng. Dep. Assistant Lecturer/ Asma Ab. Mustafa

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Problem -46-

Ans;


Problem -47-

Ans;

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Problem -48-

Ans;


Problem -49-

Ans;

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Problem -50-

Ans;

Chapter -1- Problems - ISHIK – · PDF fileThe built-up shaft consists of a pipe AB and...

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