Prob. 3.4-16. A uniform circular cylinder of diameter d and length L is made of material with modulus of elasticity E. It is fixed to a rigid wall at end A and subjected to distributed external axial loading of magnitude p(x) per unit length, as shown in Fig. P3.4-16a. The axial stress, (x), varies linearly with x as shown in Fig. P3.4-16b. (a) Determine an expression for the distributed loading, p(x). (Hint: Draw a free-body diagram of the bar from section x to section (x + Ax).) (b) Using Eq. 3.12, determine an expression for the axial displacement, u(x), of the cross section at distance x from end A. A (a) * u(x) p(x) B P3.4-16 08 (b)

Prob. 3.4-16. A uniform circular cylinder of diameter d and length L is made of material with modulus of elasticity E. It is fixed to a rigid wall at end A and subjected to distributed external axial loading of magnitude p(x) per unit length, as shown in Fig. P3.4-16a. The axial stress, (x), varies linearly with x as shown in Fig. P3.4-16b. (a) Determine an expression for the distributed loading, p(x). (Hint: Draw a free-body diagram of the bar from section x to section (x + Ax).) (b) Using Eq. 3.12, determine an expression for the axial displacement, u(x), of the cross section at distance x from end A. A (a) * u(x) p(x) B P3.4-16 08 (b)

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Determine the magnitude of the maximum vertical force P (in kN) that can be applied to the bell crank so that the average normal stress developed in the 10-mm diameter rod CD, and the average shear stress developed in the 6-mm diameter double sheared pin B not exceed 175 MPa and 75 MPa, respectively
For the beam in figure: 1. Compute the maximum shearing stress devloped in the beam. 2. Determine the shear stress in a fiber located at y1 = 26 mm , from the bottom for section 2 m from the left end of the beam.
The cantilever beam is subjected to a concentrated load of P=20kips. The cross-sectional dimensions of the rectangular tube shapre are b=5.2in , d=8.10in , and t=0.400in. Determine:a) The magnitude of the maximum horizontal shear stress in the rectangular tube shape. Answer in ksi, rounded-off to 2 decimal places.b) The magnitude of the shear stress at point K, which is loacted to the left of the vertical centroidal axis zK=1.1in. Answer in ksi, rounded off to 2 decimal places.
A column with a wide-flange section has a flange width b = 200 mm , height h = 200 mm , web thickness tw = 8 mm , and flange thickness tf = 12 mm (Figure 1). Calculate the stresses at a point 75 mm above the neutral axis if the section supports a tensile normal force N = 2.9 kN at the centroid, shear force V = 4.6 kN , and bending moment M = 4.8 kN⋅m as shown (Figure 2). Calculate the magnitude of the shear stress at the point due to the internal shear on the section. τ =?
Determine the distribution of the shear stress over the cross section of the beam shown in Fig.a
a horizontal single force P of 150 lb magnitude is applied to the end D of lever ABD. 1. what is the normal and shear stresses at point H having sides parallel to the x and y axes? 2. determine the principal planes and pricipal stress at the point H
Given the system below. It is pinned at B as shown in Fig. P-119. The pin diameter is 20 mm Determine the shear force developed at B Determine the shearing stress developed at pin B
A compound shaft consists of two pipe segments. Segment (1) has an outside diameter of 236 mm and a wall thickness of 8 mm. Segment (2) has an outside diameter of 120 mm and a wall thickness of 16 mm. The shaft is subjected to torques TB = 44 kN-m and TC = 16 kN-m, which act in the directions shown. Determine the maximum shear stress magnitude in segment (2).
A beam with the cross-section shown in Figure Q2 is exposed to a transverse load (Q) of magnitude 5 kN acting vertically downward through its centroid. (i) Develop the general expression for the distribution of transverse shear stresses in the web of a transversely loaded beam with the I cross-section shown in Figure Q2. (ii) Use the developed expression in (i) above to determine the stresses in the web at the horizontal centroidal axis of the cross-section, and at the intersections of the web and flanges. (iii) Develop the general expression for the distribution of transverse shear stresses in the flanges of a transversely loaded beam with the I cross-section shown in Figure Q2.
A. Determine the maximum bearing stress in MPa if P = 115 kN. B. Determine the maximum shear stress in MPa if P = 115kN. C. Determine the maximum tensile stress in MPa if P = 11 kN.
g. What is the moment of inertia (I) about the neutral axis of the section? (in in^4) h. What is the first moment of an area (Q) about the neutral axis of the section? (in in^3) i. What is the maximum shearing stress (fv) of the beam? (in psi) j. What is the maximum flexural stress (fb) of the beam? (in psi)
A compound shaft consists of two pipe segments. Segment (1) has an outside diameter of 10.75 in. and a wall thickness of 0.365 in. Segment (2) has an outside diameter of 7.25 in. and a wall thickness of 0.280 in. The shaft is subjected to torques TB = 56 kip-ft and TC = 14 kip-ft, which act in the directions shown. Determine the maximum shear stress magnitude in segment (1).