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Name \/ {l A, sTE‘EV Seat Number Use the following properties for steel, unless otherwise stated in the problem: E = 29,000 ksi, G =
11,200 ksi, thermal coefficient of expansion = 6.5x10—6 in/in per degrtilgoisson’s ratio = 0.29.
8 1) Determine the maximum normal tensile stress induced in 6 0t long 1/2” diameter bar. A 10 kip
tensile axial load is directed along the centroid of the bar. 2) Determine the maximum shear stress induced in the bar of problem 1. 3) Determine the maximum normal compressive stress induced in the bar of problem 1. 4) Determine the maximum normal tensile stress induced in the bar of problem 1 if the centroidal
axial load is moved from the centroid of the bar to the edge of the bar. The load is still directed
along the longitudinal axis of the bar. 5) Determine the maximum bending stress in the bar in Problem 4. 6) Determine the required thickness of a thin—walled spherical pressure vessel with 80 psi internal
pressure. The tank is 40 inches in diameter, and 120 inches long. The maximum allowed tensile
stress in 30 ksi, the maximum allowed compressive stress is 20 ksi, and the maximum allowed
shear stress is 15 ksi. 7) Determine the maximum bending moment in a simply supported beam 12 m long, uniformly
loaded along its entire length with 200kN/m. The simple supports are on the ends of the beam. 8) Determine the maximum shear in a simply supported beam 12 m long, uniformly loaded along its
entire length with 200kN/m. The simple supports are on the ends of the beam. 9) The maximum moment induced in a rectangular beam is 5 kip ft. Determine the required height of
the beam (like a 2x4) if the width of the beam is given to be 2 inches. The maximum allowed
stresses permitted in the beam are: tension = 2000 psi, comgr; . 'on = 1500 psi. 10) The maximum shear force induced in a rectangular beam 1;” . 1‘ Determine the required width
of the beam if its height is specified to be 10 inches. The max ‘" allowed shear stress permitted
in the beam is 300 psi. 11) A steel wide ﬂange is composed of a 1”x12” web, and two 1/2”x6” ﬂanges. Determine the strong
axis moment of inertia of this beam. 12) Determine the strong axis section modulus for the beam of problem 11. 13) A wooden wide ﬂange is composed of a l”x12” web, and two 1/2”x6” ﬂanges. Determine its
strong axis moment of inertia. 14) A square concrete column is 10 inches x 10 inches. It is reinforced with ten 1/2” diameter steel
bars. The ratio of the modulus of elasticity of the steel to that of the concrete is 10. What
percentage of any load placed on the column will the steel bars carry? Econcrete = 2900 ksi. 15) Determine the maximum normal stresses and maximum shear stresses in a piece of steel subjected
to the following conditions: Sigmax = 40 ksi compressive, Sigmay = 20 ksi compressive, Tauxy =
5 ksi directed downwards on the left face of the stress block. 16) A steel wide ﬂange has the following properties: Area = 14.7 in"2, Depth 2 12.19 in, Width =
8.08 in, Web thickness = 0.37 in, Flange thickness = 0.640 in, Ixx = 394 in"4, Iyy = 56.3 in"4.
How much shear force can the beam carry if the allowed shear stress of the steel is 30 ksi? 17) A 12 foot long simply supported beam carries a uniformly distributed beam of 2 k/ft along the left
onehalf of its length (from O to 6 feet.) A concentrated load of 10 kips is applied 9 feet from the
left end of the beam and a concentrated counterclockwise moment of 300 kip ft is applied on the
beam over the right reaction. Determine the right reaction on this beam. The reactions are located
at the ends of the beam. 18) A 6” wide plate is 1/2” thick and is bolted to a second plate with ten 3/4” diameter bolts. If a load
of 200 kips is applied to the plate, determine the maximum bearing stress in the plate. 19) A 10” long circular steel bar elongates 0.01” under the application of a 20 kip tensile load. Before
the bar was loaded, determine its diameter. 20) Determine how much smaller the diameter of the bar in the previous problem got after the bar was
loaded. 21) A 2” diameter bar 20 inches long is welded to the walls at each end of the bar. A centric axial load
is applied to the bar 5 inches from one of the walls. Determine the maximum normal stress
induced in the bar. 22) A 2” diameter bar 20.000” long is slipped between two rigid walls, and is to be welded to the
walls. At 70 degrees F there is a 0.05” gap between the bar and one wall, i.e. the distance between
the two walls is 20.05”. After the left end of the bar was welded to the wall, the welder heated the
bar until it expanded and touched the right wall. While the bar was still hot he welded the right
end of the bar to the right hand wall and went home. After the bar cooled back down to 70
degrees, what stress was induced in the bar? 23) Determine the required diameter of a 10 foot long circular steel bar, used to transmit a torque of
525.5 ft#. The maximum allowed shear stress in the steel is 15 ksi. 24) Determine the maximum permitted length of a column made of a solid circular steel bar, with a
diameter of 2 inches, carrying an axial load of 5,000 pounds. The bar looks like a ﬂagpole and a factor of safety of 2 is required.
25) Write a moment singularity function for the beam loaded as shown. W1 = 6 k/ft, W2 = 9 k/ft, L1 = 6 ft, L2 = 8 ft, L3 = 9 ft, R1 = 39.45k, R2 = 76.04 k. W1 W2 Rl‘ L1 L2 L3 f2 26) State the boundary conditions for the beam shown below. The distance between each of the
supports is 18 feet. Xivvvvviiiiii
”A. MAN 27) Use the method of superposition to solve for the reaction at the center support on the beam loaded
as shown.
M a
fit R3 28) Determine the theoretical critical buckling load for a pinned—fixed 1 3A” x 3 1/2” piece of timber.
The column is 16 feet long and has an E = 1000 ksi. 29) How much torque is in a shaft, which is transmitting 500 HP at 5000 RPM? 30) How long can a 2” diameter steel shaft be if it is to carry 500 ft# of torque at 6000 RPM, and
cannot twist more that 2 degrees over its entire length? Name Seat Number Exam B Use the following properties for steel, unless otherwise stated in the problem: E = 29,000 ksi, G =
11,200 ksi, thermal coefficient of expansion = 6.5x106 in/in per degree F, Poisson’s ratio = 0.29. 1) Determine the maximum normal tensile stress induced in an 8 foot long 1/2” diameter bar. A 10
kip tensile axial load is directed along the centroid of the bar. 2) Determine the maximum normal compressive stress induced in the bar of problem 1. 3) Determine the maximum shear stress induced in the bar of problem 1. 4) Determine the maximum normal tensile stress induced in the bar of problem 1 if the centroidal
axial load is moved from the centroid of the bar to the edge of the bar. The load is still directed
along the longitudinal axis of the bar. 5) Determine the maximum bending stress in the bar in Problem 4. 6) Determine the required thickness of a thinwalled spherical pressure vessel with 80 psi internal
pressure. The tank is 40 inches in diameter, and 120 inches long. The maximum allowed tensile
stress in 30 ksi, the maximum allowed compressive stress is 20 ksi, and the maximum allowed
shear stress is 15 ksi. 7) Determine the maximum bending moment in a simply supported beam 12 m long, uniformly
loaded along its entire length with 200kN/m. The simple supports are on the ends of the beam. 8) Determine the maximum shear in a simply supported beam 12 m long, uniformly loaded along its
entire length with 200kN/m. The simple supports are on the ends of the beam. 9) The maximum moment induced in a rectangular beam is 5 kip ft. Determine the required height of
the beam (like a 2x4) if the width of the beam is given to be 2 inches. The maximum allowed
stresses permitted in the beam are: tension = 2000 psi, compression = 1500 psi. 10) The maximum shear force induced in a rectangular beam is 6 kips. Determine the required width
of the beam if its height is specified to be 10 inches. The maximum allowed shear stress permitted
in the beam is 300 psi. 11) A steel wide ﬂange is composed of a l”x12” web, and two 1/ ”x6” ﬂanges. Determine the strong
axis moment of inertia of this beam. 12) Determine the strong axis section modulus for the beam of problem 11. 13) A wooden wide flange is composed of a l”x12” web, and two 1/ ”x6” ﬂanges. Determine its
strong axis moment of inertia. 14) A square concrete column is 10 inches x 10 inches. It is reinforced with ten 1/2” diameter steel
bars. The ratio of the modulus of elasticity of the steel to that of the concrete is 10. What
percentage of any load placed on the column will the steel bars carry? Econcrete = 2900 ksi. 15) Determine the maximum normal stresses and maximum shear stresses in a piece of steel subjected
to the following conditions: Sigmax = 40 ksi compressive, Sigmay = 20 ksi compressive, Tauxy =
5 ksi directed downwards on the left face of the stress block. 16) A steel wide ﬂange has the following properties: Area = 14.7 in"2, Depth = 12.19 in, Width =
8.08 in, Web thickness = 0.37 in, Flange thickness = 0.640 in, Ixx = 394 in"4, Iyy = 56.3 inA4.
How much shear force can the beam carry if the allowed shear stress of the steel is 30 ksi? 17) A 12 foot long simply supported beam carries a uniformly distributed beam of 2 k/ft along the left
one—half of its length (from 0 to 6 feet.) A concentrated load of 10 kips is applied 9 feet from the
left end of the beam and a concentrated counter—clockwise moment of 300 kip ft is applied on the
beam over the right reaction. Determine the right reaction on this beam. The reactions are located
at the ends of the beam. 18) A 6” wide plate is 1/2” thick and is bolted to a second plate with ten 3/4” diameter bolts. If a load
of 200 kips is applied to the plate, determine the maximum bearing stress in the plate. 19) A 10” long circular steel bar elongates 0.01” under the application of a 20 kip tensile load. Before
the bar was loaded, determine its diameter. 20) Determine how much smaller the diameter of the bar in the previous problem got after the bar was
loaded. 21) A 2” diameter bar 20 inches long is welded to the walls at each end of the bar. A centric axial load
is applied to the bar 5 inches from one of the walls. Determine the maximum normal stress
induced in the bar. 22) A 2” diameter bar 20.000” long is slipped between two rigid walls, and is to be welded to the
walls. At 70 degrees F there is a 0.05” gap between the bar and one wall, i.e. the distance between
the two walls is 20.05”. After the left end of the bar was welded to the wall, the welder heated the
bar until it expanded and touched the right wall. While the bar was still hot he welded the right
end of the bar to the right hand wall and went home. After the bar cooled back down to 70
degrees, what stress was induced in the bar? 23) Determine the required diameter of a 10 foot long circular steel bar, used to transmit a torque of
525.5 ft#. The maximum allowed shear stress in the steel is 15 ksi. 24) Determine the maximum permitted length of a column made of a solid circular steel bar, with a
diameter of 2 inches, carrying an axial load of 5,000 pounds. The bar looks like a ﬂagpole and a
factor of safety of 2 is required. 25) Write a moment singularity function for the beam loaded as shown. W1 = 6 k/ft, W2 = 9 k/ft, L1
= 6 ft, L2 = 8 ft, L3 = 9 ft, R1 = 39.45k, R2 = 76.04 k. Wl W2 ml Ll L2 L3 1R2 26) State the boundary conditions for the beam shown below. The distance between each of the
supports is 18 feet. tittttttttttt
”A. ”A... 27) Use the method of superposition to solve for the reaction at the center support on the beam loaded
as shown.
M Cir
ll. 28) Determine the theoretical critical buckling load for a pinnedfixed l 3A” x 3 1/2” piece of timber.
The column is 16 feet long and has an E = 1000 ksi. 29) How much torque is in a shaft, which is transmitting 500 HP at 5000 RPM? 30) How long can a 2” diameter steel shaft be if it is to carry 500 ft# of torque at 6000 RPM, and
cannot twist more that 2 degrees over its entire length? \ Loading Shear Bending Moment
=__ k _ _ n+1 ___j_;; _. n+2
V05) n+1<x [11> M(x)— (n+1)(n+2)<x 54> ‘ Fig. 5.19 Basic loadings and corresponding shears and bending moments expressed
I in terms of singularity functions. ?
\ After a given beam loading has been broken down into the basic
: ——————————————— loadings of Fig. 5.19, the functions V(x) and M(x) representing the shear
and bending moment at any point of the beam can be obtained by adding
the corresponding functions associated with each of the basic loadings
and reactions. Since all the distributed loadings shownin Fig. 5.19 are 346 E 762 1m and Loading Elastic Curve _ PL3
48E] For a > b:
Pb(L2 — 2253/2 9\/§EIL
L2 — b2 atx _ 5wL4
384E] ML2
9\/§E1 Appendix. D. Beam Deflections and Slopes Maximum
Deflection Slope at End Equation of Elastic Curve
PL2 P
—— = — x3 — 31262
251 y 6EI( )
wL3 w 4
—— = ——  41x3 + 6L2
6E1 y 243106 x2)
ML M
__ = __ x2
E] y 2E1
For x S %L:
PL2 P
: = —— 4 ~ 3L2
16E] y 48EI( ”‘3 x)
For x < a:
Pb(L2 — b2) Pb
6 — — — x3 L2 ~ 192
A 6EIL y 6EIL[ ( )x]
0 _ Pa(L2 — 612) F __ . _ _Pa2b2
B 6EIL or x a‘ y 3EIL
'wL3 w
i = — 4  2Lx3 + L3
24E] y 24E] (x x)
6 — +ML
A _ _
M
6E1 y:__(x3_L2x)
0 _ ML 6EIL
B _ ummaowwmximmc.‘ ,, my." The welder didn’t notice this, and could have cared less had he noticed it. While the bar was still
hot he welded the right end of the bar to the right hand wall and went home. After the bar cooled
back down to 70 degrees, what stress was in the bar? 23) Determine the required diameter of a 10 foot long circular steel bar, used to transmit 500 HP at
5000 RPM. The maximum allowed shear stress in the steel is 15 ksi, andtthemnaximum permitted
angle of twist is 2 degrees. E for steel = 30,000 ksi and G = 1h,000 ksi. 24) Determine the maximum allowed length of a circular steel bar with a diameter of 2 inches and
carrying an axial load of 5000 pounds. The bar looks like a ﬂagpole. A factor of safety of 2 is
required. 25) Write a moment singularity function for the beam loaded as shown. 26) State the boundary conditions for the beam shown below. 27) Use the method of superposition to solve for the reaction at the roller support on the beam loaded
as shown. 28) Determine the theoretical critical buckling load for a l %” x 3 1/2” piece of timber. The column is
16 feet long and has an E = 1000 ksi. \zgﬂ m yr?” V 32 M w w V \ J a j/ x /
Vw M ,T G L
Kw , \j ...
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 Spring '08
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