Concept explainers
If it supports a cable loading of 800 lb, determine the maximum normal stress at section a–a and sketch the stress distribution acting over the cross section. Use the curved-beam formula to calculate the bending stress.
The maximum tensile stress
The maximum compressive stress
To sketch:
The stress distribution over the cross section.
Answer to Problem 8.1RP
The maximum tensile stress
The maximum compressive stress
Explanation of Solution
Given information:
The force in the cable is 800 lb.
Diameter of the circular is 1.25 in.
Calculation:
Expression to find the location of neutral
Here, R is the location of neutral axis, A is the cross sectional area of the member, r is the arbitrary position, and
Determine the radius
Here, d is the diameter of the circular cross section.
Substitute 1.25 in. for d in Equation (2).
Determine the area
Here, r is the radius of the circular cross section.
Substitute 0.625 in. for r in Equation (3).
Determine the value of
Here, c is the radius of cross section and
Find the distance measured from the center of curvature to the centroid of the cross section
Substitute 0.625 in. for c and 3.125 in. for
Substitute
Sketch the cross section of eye hook as shown in Figure 1.
Let the moment acting at the section be M.
Express to the value of M as shown below:
Here, F is the load and R is the radius.
Determine the bending stress
Here, M is the applied moment and P is the applied load.
Substitute
Determine the maximum tensile stress
Hence, the maximum tensile stress
Determine the maximum compressive stress
Substitute
Hence, the maximum compressive stress
Sketch the stress distribution (tensile and compressive stress) along the cross section as shown in Figure 2.
Want to see more full solutions like this?
Chapter 8 Solutions
Mechanics of Materials (10th Edition)
- Determine the moment M that must be applied to the beam in order to create amaximum stress of 90 MPa. Also sketch the stress distribution acting over the cross section.arrow_forwardThe aluminium machine part shown below is subjected to a moment of M = 75 N.m. Determine the bending stress created at points B and A on the cross section. Sketch the results on a volume element located at each of these points. A- 50mm 50mm 100mm 100mm 20mm B- M=8kN-m 20mmarrow_forwardA member having the dimensions shown is used to resist an internal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown) (b) about the y axis. Sketch the stress distribution for each case. Take: M= 90 kNm A mm A= 200 mm B= 150 mm B mm Solution: The moment of inertia of the cross-section about z and y axes are I;-4 1 - AB³ 12 (10) m* I BA = (10) m*arrow_forward
- Below 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_forwardDetermine the normal force, shear force, and moment at point C. Take that P = 8 kN and M = 33 kN m. (Figure 1) Figure M B . 1 of 1 -1.5 m 1.5 m 1.5 m-1.5 m-arrow_forwardThe wooden section of the beam is reinforced with two steel plates as shown. If the beam is subjected to a moment of M = 30 kN # m, determine the maximum bending stresses in the steel and wood. Sketch the stress distribution over the cross section. Take Ew = 10 GPa and Est = 200 GPa.arrow_forward
- If the beam is subjected to an internal moment of M = 100 kN*m, determine the bending stress developed at points A, B, and C. Sketch the bending stress distribution on the cross section. Construct the stress distribution in 2D similar to in-class examples, rather than isometrically similar to the textbook examples for clarity. 30 mm A B 300 mm M 150 mm 150 mm 30 mmarrow_forwardDetermine the maximum positive normal bending stress that occurs in member ABC of the engine crane given the following information: Engine weight = 1500 lb Member ABC height (vertical cross sectional dimension) = 7 in Member ABC width (horizontal cross sectional dimension) = 1 in Express your answer to the nearest whole psi value. In your work, draw the shear and moment diagram for member ABC. For the question above, determine the maximum shear stress in member ABC that occurs between points A and B. Express your answer using the nearest whole psi value.arrow_forwardIf the internal moment acting on the cross-section is 800 N.m, determine the maximum tensile and compressive bending stresses acting in the beam. Sketch the stress-distribution acting on the cross-section.arrow_forward
- 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 0.00arrow_forwardThe beam is supported by a pin at point A and a roller at kN point B. A distributed load of W₁ = 8 - and an applied m force of F₁ = 12 kN are applied to the beam. The beam has an allowable bending stress of allow = 6 MPa. Neglect the weight and thickness of the beam. Take the origin for all functions to be at A., i.e. start at the left and go right. Must use positive sign convention for V and M. d3 1 d3 d1 W1 d1 B O h d2 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Dimensions for the whole beam Variable Value d₁ 4 m d₂ 2 marrow_forward4arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning