■Problem statement Consider a cantilevered quarter-circle curved beam subjected to a uniform stress = σo at the free end as shown. Canvas A Canvas Frame B σο ■What is required? Derive the basic mechanics solutions for the hoop stress (σe) and the shear stress (Ore) as functions of σo, a and b

If the beam in Problem 1 is made of W18 X 65, A992 structural steel, Illustrate the state of stress at point B on an element oriented 30° from horizontal axis and on Mohr's circle for that element. Location of Point B is illustrated in the figure. 1/4 d B d x A В C D | 280 kip.ft 10ft 10ft 10ft

Question 3 Show that the following function o may be used as an Airy stress function $ = Ax? + Ba²y+ Cry Evaluate A, B and C for the rectangle shown in Figure Q3: (1) there are no external loads for any kind applied along KN; (2) along KL there is a uniform normal load p; (3) and along MN there is no normal load; (4) along KL, LM and MN there are shear stresses (but none along KN). Make a neat sketch of the stresses along the boundary KLMN. y N M Thickness=1 b p per unit length a

Find  the stresses in each direction, also find the change in volume of the block of dimension 120 mm x 60 mm x 43 mm, subjected to 3 mutually perpendicular loads.  The load along length, breadth and depth directions are 10 kN (tensile), 25 kN (tensile), 13 kN (compressive) respectively, Take E as 180 GPa, Poisson's ratio as 0.3. The stress along length direction (Unit in kN/m2)= _____________ The stress along width direction (Unit in kN/m2)= _____________ The compressive stress along depth direction (Unit in kN/m2)= _____________ The change in volume of the block is (unit in mm3) = ______________

1. A beam of length L is simply supported shown as follows. A concentrated force F is applied at point A. The cross section of the beam is a rectangular with sides a and b. Please determine: 1) The shear force diagram and the bending moment diagram of the beam. 2) Determine the normal stress distribution on cross section B. Specify the locations and magnitudes of the max. tensile/compressive stress on cross section B. 3) Find the location and the magnitude of the max. bending stress ON THE BEAM. For simplicity, transverse shear stress is neglected. 4) Find the location and magnitude of the max. transverse shear stress on cross section B. F A В

Determine the maximum tensile and compressive stresses developed in the overhanging beam that is loaded and has the cross- sectional properties as shown. 1600 lb 4000 lb 2 in N.A. 6 in 6 ft R I- 90 in 6 ft tensile stress = 3, 840 psi and compressive stress = 7, 680 psi tensile stress = 1, 280 psi and compressive stress = 2,560 psi tensile stress = 7, 680 psi and compressive stress = 3, 840 psi tensile stress = 7, 680 psi and compressive stress = 2, 560 psi

Determine the torsional shear stress in the shaft section AB and BC. There is a fixed support at C that can resist a moment. (Image taken from Statics and Mechanics of Materials by Beer, Johnson, DeWolf and Mazurek) T₁ = 300 N-m 30 mm TB = 400 N-m 46 mm 055 Shear Stress in AB = Shear Stress in BC= B 0.9 m 0.75 m units: units:

Mechanics of Deformable Bodies Please write the complete solutions and Legibly. Thumbs up will given! A W 310 X 52 steel beam is subjected to a point load P = 56 kN and a transverse load V = 15kN at B. The beam has length L = 2 m. See the table for beam properties. (Assume that the structure behaves linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resultant stresses acting at a point. Consider both in-plane and out-of-plane shear stresses unless otherwise specified. (Do not use rounded intermediate values in your calculations) (a) Calculate the principal normal stresses and the maximum shear stress on element D located on the web right below the top flange and near the fixed support. Neglect the weight of the beam. (Enter your answers in MPa. For the normal stresses, use the deformation sign convention. For the shear stress, enter the magnitude.) σ1 =                            MPa σ2 =                            MPa τmax =…

Find the Magnitude of the Maximum Shear Stress in the below beam and cross-section, if: W = = 6 kN/m L = 5 m b = 55 mm h = 144 mm Ensure that your answers are in MPa. Mo W Cross-Section: L b h

Two vertical forces are applied to a simply supported beam, having the cross section shown. Assume LAB=LCD=1.6 m, LBc=5.6 m, P=20 kN, b-205 mm, t-12 mm, tw-8 mm, d=177 mm. Determine the maximum tension (a positive number) and compression (a negative number) bending stresses produced in segment BC of the beam. Answers: OmaxT = Omaxc = LAB IN P B LBC bf T | ktw Cross section MPa MPa P LCD d D X