Statics and Mechanics of Materials (5th Edition)
5th Edition
ISBN: 9780134382593
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 16.2, Problem 12P
To determine
Draw the bending-moment diagram for the shaft.
Draw the deflection or elastic curve for the shaft using the bending moment diagram.
Find the equations of the elastic curve
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3
For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. V
= 9 kN, V2 = 9 kN, V3 = 200 mm, and V4 = 1100 mm.
ATAT-V3
Provide values at all key points shown in the given shear-force and bending-moment diagrams.
X
(mm)
B
A =
B =
C =
D =
E=
F=
P =
Q =
E
* KN
* KN
* KN
× KN
KN
x KN
✩ kN.mm
*kN.mm
D
0.00
Reaction force R₁ (left) =
In the shear-force and bending-moment diagrams given,
+V
0.00
X
(mm)
6.3 kN and reaction force R2 (right) =
P
11.7 kN.
Q
0.00
Draw the bending-moment diagram for the shaft and then, from this diagram, sketch the deflection or elastic curve for the shaft’s centerline. Determine the equations of the elastic curve using the coordinates x1 and x2. Use the method of integration. EI is constant.
The simply supported beam is subjected to the force F = 700 N and the uniform distributed load with
intensity w = 150 N/m. Draw the shear force and bending moment diagrams (in your homework
documentation) and determine the equations for V(r) and M(x). Take a = 0 at point A.
19
F
a
Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.
Variable Value
a
5.2 m
2.6 m
3.12 m
Support Reactions
The reaction at A is
N.
The reaction at D is
N.
Shear Force and Bending Moment Equations
In section AB:
V(x)=
N and M(x)=
N-m.
In section BC:
v(x)-
N and M(x)=
N-m.
In section CD:
V(x)-
N and M(x)=
N-m.
A
Chapter 16 Solutions
Statics and Mechanics of Materials (5th Edition)
Ch. 16.2 - In each ease, determine the internal bending...Ch. 16.2 - Prob. 1FPCh. 16.2 - Determine the slope and deflection of end A of the...Ch. 16.2 - Prob. 3FPCh. 16.2 - Prob. 4FPCh. 16.2 - Determine the maximum deflection of the simply...Ch. 16.2 - Prob. 6FPCh. 16.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 16.2 - The L2 steel blade of the band saw wraps around...Ch. 16.2 - A picture is taken of a man performing a pole...
Ch. 16.2 - Determine the equation of the elastic curve for...Ch. 16.2 - Determine the deflection of end C of the...Ch. 16.2 - Prob. 6PCh. 16.2 - The A-36 steel beam has a depth of 10 in. and is...Ch. 16.2 - Prob. 8PCh. 16.2 - Determine the equations of the elastic curve for...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Prob. 12PCh. 16.2 - Determine the maximum deflection of the beam and...Ch. 16.2 - The simply supported shaft has a moment of inertia...Ch. 16.2 - A torque wrench is used to tighten the nut on a...Ch. 16.2 - The pipe can be assumed roller supported at its...Ch. 16.2 - Determine the equations of the elastic curve for...Ch. 16.2 - The bar is supported by a roller constraint at B,...Ch. 16.2 - The bar is supported by a roller constraint at B,...Ch. 16.2 - Determine the equations of the elastic curve using...Ch. 16.2 - Prob. 21PCh. 16.2 - Determine the elastic curve for the cantilevered...Ch. 16.2 - Prob. 23PCh. 16.2 - Prob. 24PCh. 16.2 - The floor beam of the airplane is subjected to the...Ch. 16.2 - Determine the maximum deflection of the simply...Ch. 16.2 - The beam is made of a material having a specific...Ch. 16.2 - Determine the slope at end B and the maximum...Ch. 16.2 - Prob. 29PCh. 16.2 - Determine the equations of the elastic curve using...Ch. 16.3 - The shaft is supported at A by a journal bearing...Ch. 16.3 - The shaft supports the two pulley loads shown....Ch. 16.3 - Prob. 33PCh. 16.3 - Prob. 34PCh. 16.3 - The beam is subjected to the load shown. Determine...Ch. 16.3 - Prob. 36PCh. 16.3 - Determine the equation of the elastic curve and...Ch. 16.3 - Prob. 38PCh. 16.3 - Prob. 39PCh. 16.3 - Determine the slope at A and the deflection of end...Ch. 16.3 - Determine the maximum deflection in region AB of...Ch. 16.3 - Prob. 42PCh. 16.3 - Prob. 43PCh. 16.3 - Prob. 44PCh. 16.4 - The W10 15 cantilevered beam is made of A-36...Ch. 16.4 - The W10 15 cantilevered beam is made of A-36...Ch. 16.4 - The W14 43 simply supported beam is made of A992...Ch. 16.4 - The W14 43 simply supported beam is made of A992...Ch. 16.4 - The W14 43 simply supported beam is made of A-36...Ch. 16.4 - The W14 43 simply supported beam is made of A-36...Ch. 16.4 - The W8 48 cantilevered beam is made of A-36 steel...Ch. 16.4 - The beam supports the loading shown. Code...Ch. 16.4 - Prob. 53PCh. 16.4 - The W8 48 cantilevered beam is made of A-36 steel...Ch. 16.4 - Prob. 55PCh. 16.4 - Prob. 56PCh. 16.4 - Prob. 57PCh. 16.4 - The assembly consists of a cantilevered beam CB...Ch. 16.4 - Prob. 59PCh. 16.4 - Prob. 60PCh. 16.5 - Determine the reactions at the fixed support A and...Ch. 16.5 - Prob. 8FPCh. 16.5 - Determine the reactions at the fixed support A and...Ch. 16.5 - Prob. 10FPCh. 16.5 - Prob. 11FPCh. 16.5 - Prob. 12FPCh. 16.5 - Prob. 61PCh. 16.5 - Determine the reactions at the supports, then draw...Ch. 16.5 - Determine the reactions at the supports, then draw...Ch. 16.5 - Prob. 64PCh. 16.5 - The beam is used to support the 20-kip load....Ch. 16.5 - Prob. 66PCh. 16.5 - Determine the reactions at the supports A and B....Ch. 16.5 - Before the uniform distributed load is applied to...Ch. 16.5 - Prob. 69PCh. 16.5 - Prob. 70PCh. 16.5 - The beam is supported by the bolted supports at...Ch. 16.5 - Prob. 72PCh. 16.5 - Prob. 73PCh. 16 - Prob. 1RPCh. 16 - Draw the bending-moment diagram for the shaft and...Ch. 16 - Prob. 3RPCh. 16 - Determine the equations of the elastic curve for...Ch. 16 - Determine the maximum deflection between the...Ch. 16 - Prob. 6RPCh. 16 - The framework consists of two A-36 steel...Ch. 16 - Prob. 8RPCh. 16 - Using the method of superposition, determine the...
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- Determine the ff: •Internal bending moment at point c •internal shear force at point c •internal normal force at point c Asap please.arrow_forwardconsider the beam shown in. EI is constant. assume that EI is in kip * ft2. determine the expression for the elastic curve using the coordinate x1 for 0 < x1 < 20 ft, where x1 is in feet. v1 in ft answer in terms of the variables x1, E and I. determine the expression for the elastic curve using the coordinate x2 for 0 < x2 < 10 ft where x2 is in feet. v2 in ft. answer in terms of the variables x2, E and I. specify the deflection of the beam at C. vc in ft. answer in terms of E and I. specify the slope at A, measured counterclockwise from the positive x1 axis. Theta A in rad. answer in terms of E and I.arrow_forwarddetermine the diagram of the shear forces and bending moments in the beam shown below. Data P = 20kN, M = 60kNm, q = 10kN / m, a = 5m, b = 2m, c = 3, alpha = 60.arrow_forward
- If the simply supported beam is subjected to the load shown below, determine the following: c- c - The internal bending moment acting on the cross-section through point C. d- d- The shear stress at section C.arrow_forwardDetermine the internal normal force and shear force, and the bending moment in the beam at points C and D. Assume the support at B is a roller. Point C is located just to the right of the 8-kip load. For your explanation section, complete a FBD of the other side of the beam from the version you did to solve the problem. 8 kip 40 kip · ft A to to D B- 8 ft 8 ft- -8 ftarrow_forwardDraw the bending-moment diagram for the shaft and then, from this diagram, sketch the deflection or elastic curve for the shaft’s centerline. Determine the equations of the elastic curve using the coordinates x1 and x2. EI is constantarrow_forward
- Part B - Moments of inertia of the cross section with respect to the y- and z-axesTo calculate the absolute maximum bending stress in the member using the flexure formula for unsymmetrical bending, the moments of inertia of the cross section must be calculated. Select the correct formulas for these values. Iy=? Part C - Neutral-axis angle due to externally applied momentsThe neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, α, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane.Express your answer to three significant figures and include the appropriate units. α=? Part D - Absolute maximum stress in cross section ABCDDetermine the absolute maximum stress, |σmax|, in cross section ABCD due to the two externally applied moments. |σmax|=?arrow_forwardA leaf spring 75 cm long is required to carry a central load of 8 kN. If the central deflection is not to exceed 2 cm and bending stress no greater than 200 MPa, determine the thickness, width and number of plates. Also compute the radius to which plates should be curved. As- sume width of plate to be 12 times its thickness and E = 200 GPa.arrow_forwardBelow Figure shows the section of an angle purlin. A bending moment of 5 kN.m is applied to the purlin in a plane at an angle of 30 deg to the vertical y axis. If the sense of the bending moment is such that both its components Mx and My produce tension in the positive xy quadrant, calculate the maximum direct stress in the purlin, stating clearly the point at which it acts. * 100 mm E 10mm 30 C D -10mm 57 MPa. 89 MPa. Non Above O 72 MPa. 125mmarrow_forward
- Give the expression for the shear force, V = V(x), and the bending moment,M = M(x), as a function of the distance, x, measured from point A.Hint: Find the expressions of shear force and bending moment in each section:AB (0< x <4), BC (4 <x <7) and CD (7< x <10)arrow_forward2 - Use double integration to determine the elastic curve of the cantilever beam under lateral loading, where w is the load intensity (per unit length) at the left end. Flexural rigidity is El. Show that the tip displacement is: y w w14 U(L)=-30EIarrow_forward1. Calculate reactions at the external supports. 2. Draw the free body diagram. 3. Build the diagrams if shear force and bending moment. (use the section method) 4. Find the diameter of section of the beam. 5. Calculate the maximum Tangential Stress and show the corresponding section. 6. Draw the stress distribution diagram in the most dangerous section of the beam. a (m) 4 b (m) | P (kN) q (kN/m) 1 80 8 A D-? [G] - 100 MPa a q B b Parrow_forward
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Bending Stress; Author: moodlemech;https://www.youtube.com/watch?v=9QIqewkE6xM;License: Standard Youtube License