The state of strain at the point on the leaf of the caster assembly has components of Ex = -400(10-6), y = 860(10-6), and Yxy = 375(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 0 = 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane.

The state of strain at the point on the leaf of the caster assembly has components of Ex = -400(10-6), y = 860(10-6), and Yxy = 375(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of 0 = 30° counterclockwise from the original position. Sketch the deformed element due to these strains within the x-y plane.

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

The state of strain at the point on the member has components of Px = 180(10-6), P y = -120(10-6), and gxy = -100(10-6). Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. Ineach case specify the orientation of the element and show how the strains deform the element within the x–y plane.
Rigid bar ABC is supported by bronze rod and aluminum rod as shown in the figure. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod has an elastic modulus of 15,000ksi and a diameter of 0.65in. Aluminum rod (2) has an elastic modulus of 10,000ksi and a diameter of 0.85in. Aluminum rod (3) has a diameter of 1.20in. The yield strength of the bronze is 52ksi, and the yield strength of the aluminum is 42ksi.a. Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 1.70 is required.b. Determine the deflection of point D for the load determined in question (a).c. The pin used at B has an ultimate shear strength of 56ksi. If a factor of safety of 3.0 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B.
The beam shown below is suspended from two steel rods as shown and is initially horizontal. The midpoint B of the beam is deflected 15 mm downward by force Q. The steel used for the rods has properties E = 200 GPa and σ = 275 MPa, determinea. the required maximum value of Q.b. the deformation of rod AD.c. the deformation of rod CE.
The state of plane strain on the element is P x = -300(10-6), P y = 0, and gxy = 150(10-6). Determine the equivalent state of strain which represents (a) theprincipal strains, and (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element.
The beam shown below is suspended from two steelrods as shown and is initially horizontal. The midpointB of the beam is deflected 15 mm downward byforce Q. The steel used for the rods has properties E= 200 GPa and  = 275 MPa, determinea. the required maximum value of Q.b. the deformation of rod AD.c. the deformation of rod CE.
a uniform bar 1 is connected to a tapered rod 2. both are subjected to axial loads as shown. if P=7 kN, determine the axial deformation of tapered rod 2 (in mm). indicate negative sign if compression
The strain components for a point in a body subjected to plane strain are Ex - 930 JE, Ey - -112Que and Wxy - -583 urad. Using Mohr'scircle. determine the principal strains (6p1 > p2), the maximum inplane shear strain yip, and the absolute maximum shear strain Ymax atthe point. Show the angle , (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximumin-plane shear strain distortion in a sketch.
A uniform bar 1 is connected to a tapered rod 2. Both are subjected to axial loads as shown . If P = 7kN Determine the total axial deformation (in mm) Indicate negative sign if compression. Complete solution no rounding off.
A hollow aluminum tube used in a roof structure has an outside diameter d2= 112mm and an inside diameter d1= 80mm. The tube is 2.80m long, and the aluminum has a shear modulus of G= 28GPa.a. If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist, in degrees,when the maximum shear stress is 52MPa?b. What diameter d, in mm, is required for a solid shaft, as shown, to resists the same torque with the same maximum stress?c. What is the ratio of the weight of the hollow tube to the weight of the solid shaft?
Provide and explain the reactions involved in the Wrinkler Method
Pin-connected rigid bars AB, BC, and CD are initially held in the positions shown by taut wires (1) and (2). The bar lengths are a = 28 ft and b = 21 ft. Joint C is given a horizontal displacement of 3.0 in. to the right. (Note that this displacement causes both joints B and C to move to the right and slightly downward.) What is the change in the average normal strain in wire (1) after the displacement?
The stress strain diagramfor an unknown material is shown. Determine tha strain at point Y. (Unitless) Do not round off and complete solution. Thanks.