Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 12.5, Problem 12.90P
The beam supports the loading shown. Code restrictions, due to a plaster ceiling, require the maximum deflection not to exceed 1/360 of the span length. Select the lightest-weight A-36 steel wide-flange beam from AppendixB that will satisfy this requirement and safely support the load. The allowable bending stress is σallow = 24 ksi and the allowable shear stress is τallow = 14 ksi. Assume A is a roller and B is a pin.
Prob. 12–90
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AWT305 x 41 standard steel shape is used to support the loads shown on the beam. The dimensions from the top and bottom of the
shape to the centroidal axis are shown in the sketch of the cross section. Assume LAB = 2 m, Lgc = 6 m, LCD = 2 m, PA = 14 kN, WBC= 10
kN/m. Consider the entire 10-m length of the beam and determine:
(a) the maximum tension bending stress o at any location along the beam, and
(b) the maximum compression bending stress oc at any location along the beam.
PA
LAB
Answers:
(a) σT =
(b) oc =
i
B
WBC
N
LBC
WT305 x 41
C
LCD
88.9 mm
211.1 mm
MPa.
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AWT305 x 41 standard steel shape is used to support the loads shown on the beam. The dimensions from the top and bottom of the
shape to the centroidal axis are shown in the sketch of the cross section. Assume LAB = 3 m, LBC= 6 m, LCD= 4 m, PA = 10 kN, WBC = 7
kN/m. Consider the entire 13-m length of the beam and determine:
(a) the maximum tension bending stress or at any location along the beam, and
(b) the maximum compression bending stress oc at any location along the beam.
A
PA
LAB
B
WBC
LBC
T
WT305 x 41
LCD
↑
88.9 mm.
211.1 mm
D
X
AWT305 x 41 standard steel shape is used to support the loads shown on the beam. The dimensions from the top and bottom of the
shape to the centroidal axis are shown in the sketch of the cross section. Assume LAB = 3 m, LBc = 7 m, LCD = 2 m, PA = 17 kN, WBC = 10
kN/m. Consider the entire 12-m length of the beam and determine:
(a) the maximum tension bending stress or at any location along the beam, and
(b) the maximum compression bending stress oc at any location along the beam.
PA
LAB
Answers:
(a) σT =
(b) oc =
i
i
B
WBC
LBC
LCD
Ť
WT305 x 41
88.9 mm
211.1 mm
MPa.
MPa.
D
Chapter 12 Solutions
Mechanics of Materials (10th Edition)
Ch. 12.2 - In each case, determine the internal bending...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope of end A of the cantilevered...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the slope of the simply supported beam...Ch. 12.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 12.2 - The L2 steel blade of the band saw wraps around...Ch. 12.2 - A picture is taken of a man performing a pole...
Ch. 12.2 - El is constant. 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If it is...Ch. 12.3 - Determine the equation of the elastic curve, the...Ch. 12.3 - The beam is subjected to the load shown. Determine...Ch. 12.3 - Determine the equation of the elastic curve, the...Ch. 12.3 - Determine the equation of the elastic curve and...Ch. 12.3 - The shaft supports the two pulley loads. Determine...Ch. 12.3 - Determine the maximum deflection of the...Ch. 12.3 - Determine the slope at A and the deflection of end...Ch. 12.3 - Determine the maximum deflection in region AB of...Ch. 12.3 - Prob. 12.42PCh. 12.3 - Prob. 12.43PCh. 12.3 - Prob. 12.44PCh. 12.3 - Prob. 12.45PCh. 12.3 - Prob. 12.46PCh. 12.3 - Prob. 12.47PCh. 12.3 - Determine the value of a so that the displacement...Ch. 12.3 - Determine the displacement at C and the slope at...Ch. 12.3 - Determine the equations of the slope and elastic...Ch. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection of end A of the...Ch. 12.4 - Determine the slope and deflection at A of the...Ch. 12.4 - Prob. 12.11FPCh. 12.4 - Determine the maximum deflection of the simply...Ch. 12.4 - Determine the slope and deflection at C. El is...Ch. 12.4 - Determine the slope and deflection at C. El is...Ch. 12.4 - Determine the deflection of end B of the...Ch. 12.4 - Prob. 12.54PCh. 12.4 - The composite simply supported steel shaft is...Ch. 12.4 - Prob. 12.56PCh. 12.4 - Prob. 12.57PCh. 12.4 - Determine the deflection at C and the slope of the...Ch. 12.4 - Determine the maximum deflection of the...Ch. 12.4 - Prob. 12.60PCh. 12.4 - Determine the position a of the roller support B...Ch. 12.4 - Prob. 12.62PCh. 12.4 - Determine the slope and the deflection of end B of...Ch. 12.4 - The two A-36 steel bars have a thickness of 1 in....Ch. 12.4 - Determine the slope at A and the displacement at...Ch. 12.4 - Determine the deflection at C and the slopes at...Ch. 12.4 - Determine the maximum deflection within region AB....Ch. 12.4 - Determine the slope at A and the maximum...Ch. 12.4 - Determine the slope at C and the deflection at B....Ch. 12.4 - Determine the slope at A and the maximum...Ch. 12.4 - Determine the displacement of the 20-mm-diameter...Ch. 12.4 - The two force components act on the tire of the...Ch. 12.4 - Prob. 12.73PCh. 12.4 - The rod is constructed from two shafts for which...Ch. 12.4 - Prob. 12.75PCh. 12.4 - Determine the slope at point A and the maximum...Ch. 12.4 - Determine the position a of roller support B in...Ch. 12.4 - Determine the slope at B and deflection at C. El...Ch. 12.4 - Prob. 12.79PCh. 12.4 - Prob. 12.80PCh. 12.4 - Prob. 12.81PCh. 12.4 - Determine the maximum deflection of the beam. El...Ch. 12.5 - The W10 15 cantilevered beam is made of A-36...Ch. 12.5 - The W10 15 cantilevered beam is made of A-36...Ch. 12.5 - The W14 43 simply supported beam is made of A992...Ch. 12.5 - The W14 43 simply supported beam is made of A992...Ch. 12.5 - The W14 43 simply supported beam is made of A-36...Ch. 12.5 - The W14 43 simply supported beam is made of A-36...Ch. 12.5 - The W8 48 cantilevered beam is made of A-36 steel...Ch. 12.5 - The beam supports the loading shown. 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EI...Ch. 12.7 - Determine the reactions at roller support A and...Ch. 12.7 - Determine the moment reactions at the supports A...Ch. 12.7 - The beam has a constant E1I1 and is supported by...Ch. 12.7 - The beam is supported by a pin at A, a roller at...Ch. 12.8 - Determine the moment reactions at the supports A...Ch. 12.8 - Determine the reaction at the supports, then draw...Ch. 12.8 - Determine the vertical reaction at the journal...Ch. 12.8 - Determine the reactions at the supports A and B,...Ch. 12.8 - Determine the reactions at the supports. EI is...Ch. 12.8 - Determine the vertical reaction at the journal...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reactions at the fixed support A and...Ch. 12.9 - Determine the reaction at the roller B. EI is...Ch. 12.9 - Determine the reaction at the roller B. 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Use...Ch. 12 - Draw the bending-moment diagram for the shaft and...Ch. 12 - Determine the moment reactions at the supports A...Ch. 12 - Specify the slope at A and the maximum deflection....Ch. 12 - Determine the maximum deflection between the...Ch. 12 - Determine the slope at B and the deflection at C....Ch. 12 - Determine the reactions, then draw the shear and...Ch. 12 - El is constant.Ch. 12 - Using the method of superposition, determine the...
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- AWT305 x 41 standard steel shape is used to support the loads shown on the beam. The dimensions from the top and bottom of the shape to the centroidal axis are shown in the sketch of the cross section. Assume LAB = 3 m, LBc = 7 m, LcD = 1 m, PA = 9 kN, WBC = 11 kN/m. Consider the entire 11-m length of the beam and determine: (a) the maximum tension bending stress or at any location along the beam, and (b) the maximum compression bending stress oc at any location along the beam. A PA LAB B WBC LBC C Z + WT305 x 41 LCD 88.9 mm 211.1 mm Xarrow_forwardSelect the lightest-weight wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is sallow = 22 ksi and the allowable shear stress is tallow = 12 ksi.arrow_forwardDetermine the value of the applied torque, M if the beam's midspan deflection is to be zero. Assume El=const. Sketch SHEAR / MOMENT / DISPLACEMENT diagrams. P = 100 lb 2 ft M w=10 lb/ft 3 ft 5 ft Barrow_forward
- The T-beam is made from two plates welded together as shown. Determine the maximum uniform distributed load w that can be safely supported on the beam if the allowable bending stress is allow = 159 MPa and the allowable average shear stress is Tallow = 71 MPa. [w = 11.4 kN/m] A -1.5 m -1.5 m- 200 mm T 20 mm 200 mm 20 mmarrow_forwarda. the maximum tension bending stress at any location along the beam b. Determine the maximum compression bending stress at any location along the beamarrow_forwardA simply supported beam of dimension 12 m x 45 mm x 65 mm. It carries a uniformly distributed load of 450 kN/m for entire span. Determine (a) Maximum stress due to bending and (b) Young's modulus of the material used for the beam, if it deflects 150 mm maximum at the mid of the span. Also find the maximum slope in the beam. (Enter only the values by referring the units given, Also upload your hand written answers in the link provided) Moment of inertia of the cross section of the beam in m4 : Young's modulus of the beam material in MPa is = Maximum bending stress due to bending in MPa is = The slope at the supports of beam in radians isarrow_forward
- a. the maximum tension bending stress at any location along the beam b. Determine the maximum compression bending stress at any location along the beamarrow_forwardanswer item 4 only.arrow_forward1. For the same beam used in IC-13, determine the jump in shear stress at the web-flange junction (at point A). V = 20KN. A 200 mm 20 mm B 200 mm 20 mm 300 mm 2. Now cut off the bottom flange and recalculate the maximum shear stress. (Remove the bottom flange so that the beam has a T-shaped cross-section.)arrow_forward
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