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Unformatted text preview: CEE108 Introduction to Mechanics of Deformable Solids Dr. Yuan
HW7 (Due on 08/11/10) Summer 2010 Problem 1 130/301: (lVIohr’s circle —— plane stress)
Draw Mohr’s circle to solve the Problem 96 on Page 484. (30 points) Problem 2 130/301: (Shear stress in beam) Please solve the Problem 7~5 on Page 399. (30 points)
E  Hint: See Example 7.2 on Page 396. Problem 3 (40/401: (Shear stress in beam) Please solve the Problem 7—16 on Page 401. (40 points) E
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1! E 484 CHAPTER 9 STRESS TRANSFORMATEON 96. The state of stress at a point in a member is showu on 941. Determine the equivalent state of stress On an
the element. Determine the stress components acting on element if the element is oriented 60° clockwise from the
the inclined plane AB. Solve the problem using the method element shown. of equilibrium described in Sec. 9.1. . 1f —> 120 psi 300 psi
90 MPa
r 35 War
_ *9—12. Solve Prob. 9M6 using the stresstransformation
50 MP3 equations. 9—13. The state of stress at a point is showu on the element,
Determine (a) the principal stresses and (b) the maximum
in—plane shear stress and average normal stress at the point.
Specify the orientation of the element in each case. 9—7. Solve Prob. 9—2 using the stresstransformation
equations developed in Sec. 9.2. 60 MPa *9—8. Solve Prob. 9—4 using the stress—transformation
equations developed in Sec. 9.2. 45 MPa
9—9. Solve Prob. 9—6 using the stress~transformation equations deveioped in Sec. 9.2. Show the result on a sketch. 9—10. Determine the equivalent state of stress on an
element if the element is oriented 30° counterclockwise Horn th 9.13
the element shown. Use the stresstransformation equations. 9—14. The state of stress at a point is Shown on the
element. Determine (a) the principal stresses and (b) the
300 psi maximum inplane shear stress and average normal stress
at the point. Specify the orientation of the element in
each case. 180 MPa ;H_,. 156‘ {lea Prob. 9—10 Prob. 9—14 1. If the beam is subjected to a shear of V = 15 kN,
termine the web's shear stress at A and B. Indicate the
.ear_5tress components on a volume element located
these points. Set w = 125 mm. Show that the neutral S is located at y = 0.1747m from the bottom and
NA = 0.2182(10’3) m4. am for the _
. learinthe ‘2. If the wideflange beam is subjected to a shear of
3 s 30 kN. determine the maximum shear stress in the
( ' ,Set w 2" 200 mm.
a1 axis wﬂl earn _
om of the ,3. If the Wideﬂange beam is subjected to a shear of
, We have = 30 kN, determine the shear force resisted by the web
7 fthe beam. Set w = 200 mm.
200 mm
= 0.120 m
g. 7—12a, is 5
0.075 my]
0.120 my]
Probs. 7—1313
'd (web) by _
insequently . 7—4. If the wideﬂange beam is subjected to a shear of
ave ' 3 Y = 25 kip, determine the maximum shear stress in the
1150 m) beam. ear formula APa Ans. _ I is shown in metal shear .
_e support C . " Prob. 7—4 PROBLEMS 399 7~—5. If the wide~ﬂange beam is subjected to a shear of
V : 25 kip, determine the shear force resisted by the web
of the beam. Prob. 75 7—6. The beam has a rectangular cross section and is made
of wood having an allowable shear stress of Tallow = 1.6 ksi.
If it is subjected to a shear of V = 4 kip, determine the
smallest dimension :1 of its bottom and 1.5:; of its sides. 7—7. The beam has a rectangular cross section and is made
of wood. If it is subjected to a shear of V : 4kip, and
a = 10 in, determine the maximum shear stress and plot
the shearistress variation over the cross section. Sketch the
result in three dimensions. Probe. 7617 ' 4. If the T~beam is subjected to a vertical shear of
12 kip, determine the maximum shear stress in the
2331 Also, compute the shearstress jump at the
gageWeb junction AB. Sketch the variation of the shear~
tress jntensity over the entire cross section. 15_ If the T—beam is subjected to a vertical shear of
; 12 kip, determine the vertical shear force resisted by e ﬂange Probs. 7—14115 j ..__t'7—16. The T—beam is subjected to the loading shown.
'.Determine the maximum transverse shear stress in the
; beam at the critical section. _ is subjected to
51' n shear stress. 20 RN 5 kip Prob. 7—16 PROBLEMS 401 7—17. Determine the largest end forces Pthat the member
can support if the allowable shear stress is Tallow = 10 ksi. The supports at A and B only exert vertical reactions on the
beam. 748. If the force P = 8001b, determine the maximum
shear stress in the beam at the critical section. The supports
at A and B only exert vertical reactions on the beam. 200 lb ,Irt 1.5 in. Probs. 7—17118 7—19. Plot the shearstress distribution over the cross
section of a rod that has a radius (2. By what factor is the maximum shear stress greater than the average shear stress
acting over the cross section? Prob. 7—19 ...
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 Fall '09
 YANASE

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