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Q1:The steel beam W18x46 is subjected to loading as shown below. Derive the equation of the deflection curve, and then determine the maximum deflection and rotation in the beam. I=700 in4. E=29.000 ksi. 5 kip/ft RA - .9 ft 9 ftSee Answer
Q2:12-19. Determine the maximum deflection of the beam. El is constant. Problems 12-18/19 Wo A B LSee Answer
Q3:*12-32. The shaft supports the two pulley loads. If the bearings only exert vertical reactions on the shaft, determine the equation of the elastic curve. El is constant. Problem 12-32 1 B x- 20 in. 1 20 in. - 20 in .- 40 1b 60 lbSee Answer
Q4:*12-20. Determine the equations of the elastic curve using the x1 and x2 coordinates. What is the slope at A and the displacement at C? El is constant. Problem 12-20 8 kip B C A 20 kip·ft x1 20 ft 10 ftSee Answer
Q5:12-15. A torque wrench is used to tighten the nut on a bolt. If the dial indicates that a torque of 60 lb - ft is applied when the bolt is fully tightened, determine the force P acting at the handle and the distance s the needle moves along the scale. Assume only the portion AB of the wrench distorts. The cross section is square having dimensions of 0.5 in. by 0.5 in. Take E = 29(103) ksi. Problem 12-15 A 12 in. 0.5 in. S 0.5 in. B 18 in. PSee Answer
Q6:12-6. Determine the displacement of end C of the 100-mm-diameter solid circular shaft. The shaft is made of steel having a modulus of elasticity of E = 200 GPa. Problem 12-6 A B x1 · X2 -2 m -1 m 6 kNSee Answer
Q7:*12-4. Determine the equation of the elastic curve and the maximum deflection of the cantilever beam. Problem 12-4 Wo A x-+ LSee Answer
Q8:Problem Set 6 CE 4400 1-Use microsoft excel to draw elastic settlement-based bearing capacity (in ksf) versus a square foundation width (ranging from 2 to 20 ft) curves for two limit settlements of 0.5 and 1.0 in. (Please upload your excel file on Canvas). (use FHWA equation for settlement-based bearing capacity) Given: Soil Poisson's ratio=0.30 Soil average elastic modulus=300 ksf 2-An eccentrically loaded foundation is shown below. Use FS of 4 and calculate the maximum allowable load that the foundation can carry. Use Meyerhof's effective area method. (Eccentricity in one direction only) e = 0.15 m y = 17 kN/m3 c' =0 1.0 m ₲' = 36° 1.5 m × 1.5 m CenterlineSee Answer
Q9:7. Due to a loading, the plate is deformed into the dashed shape shown in the figure below. Determine (a) the average normal strain along the side AB, and (b) the average shear strain in the plate at A relative to the x and y axes. (16 pts) 1.4 mm B - 1 0.8mm 125 mm x C 150 mmSee Answer
Q10:6. The center portion of the rubber balloon has a diameter of d = 93 mm. If the air pressure within it causes the balloon's diameter to become d' = 111 mm, determine the average normal strain in the rubber. (10 pts)See Answer
Q11:5. The control arm is subjected to the loading shown in the figure below. Determine the required diameters of the steel pins at A and C (show the calculated diameters, and then round up to the nearest 1/4 in) if the factor of safety for shear is F.S .= 1.75, and the failure shear stress is 12 ksi. (20 pts) A B 9 in. Single shear c Double shear - 3 in. - 2 in. - 4,840 lb 2.825 lbSee Answer
Q12:4. Find the stresses in members BC, BD, and CF for the truss shown below. Indicate tension or compression. The cross- sectional area of each member of the truss is 1735 mm2. (20 pts) B 3 m A 3 m 4 m E C D 60 kN Y 90 kN V 4 m FSee Answer
Q13:2 Axial loads are applied to the compound rod that is composed of an aluminum segment rigidly connected between steel and bronze segments. What is the stress in each material given that P = 3150 lb? (18 pts) Bronze A =0.85 in.2 Aluminum A = 1.0 in.2 Steel A = 0.5 in.2 3P 2P P 4P 3 ft -* 5 ft 4 ft-See Answer
Q14:1. Determine the reactions at the supports. Neglect the thickness of the beam, and the weight of the beam. (17 pts) 475 N/m B A 3.3 m 3.3 mSee Answer
Q15:The rectangular plate is subjected to the deformation shown by the dashed line. Assume a = 600 mm, Ax = 1.1 mm, and Ay = 1.7 mm. Determine the shear strains Yxy and Yx'y' at point A. y Ax Ay 7 1 a * -x A a 1 1 Ay x - a Answers: Yxy = i µrad Yx'y' = i µrad Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. A rigid steel bar is supported by three rods as shown. There is no strain in the rods before the load P is applied. After load P is applied, the normal strain in rods (1) is 3890 um/m. Assume initial rod lengths of L1 = 1,250 mm and L2 = 2,000 mm. Determine the normal strain in rod (2). (2) L2 (1) (1) L1 A B C Rigid bar P O 2596 µm/m 3068 µm/m 2016 µm/m 2431 µm/m 3305 µm/m Two solid cylindrical rods support a load of P = 17 kN as shown. Determine the axial load in rod (1). 3.8 m 4.6 m A (1) C 5.6 m (2) 3.3 m B P O 13.82 kN 15.17 kN 9.85 kN 11.75 kN 8.57 kNSee Answer
Q16:3. Carry out the following two set of calculations and bring your neat solution sheets to the lab session. These will be kept by your demonstrator - please print your name and student number on each sheet, assume that the concrete average strength f. = 40MPa and characteristic strength fe'=30MPa: a. Predict the loading capacity for the under-reinforced beam (Fig. 2a) and the shear capacity (Fig. 2b) using the equations on Page 9 in "RC beam bending Lab.pdf". Hint: calculate the moment and shear capacities first using the equations, then draw the SFD and BMD to find the relationship between the failure moment/shear force and the applied load; b. Repeat the same calculations by using the average material strength without any partial safety factors, i.e. the concrete compressive force Fc =0.8xbfc and steel tensile force F₁ = f A.See Answer
Q17:Q3: Stress Relaxation in Elevated Temperature Flange Bolts A flange in a high temperature pipeline is sealed by tightening 6 steel bolts with Young's modulus is E = 172E3 MPa. The flange is required to operate for 10,000 hours without leakage, which is known to occur when the stress in the bolts is 30 MPa or lower. a) Assuming steady state creep occurs in the bolts according to the Norton power law Esc with Norton's law parameters: = Bon B = 40.0x10-16, n = 3.6 determine the minimum initial preload stress required in the bolts to ensure that the stress does not relax to below 36 MPa (i.e. the 30MPa seal preload multiplied by a design factor of 1.2) after 10,000 hours in service conditions. 1 (MPa)"h [7 Marks] b) Assuming sealing condition of 30 MPa bolt stress applies, determine the maximum time at which the bolts must be re-tightened to prevent leakage./nNOTE: Part b(i), calculating c. Part b(i) requires you to determine c. This involves solving a cubic equation. You may do thi by any suitable method you choose, including use of mathematical software. For students not familiar with such software, the simplest way is probably to use a graphical method in Excel. All the values in the moment equation are known except c. In Excel, calculate and plot M for an appropriate range of values of c. From the plot, determine the value of c that gives M = 14kNm. Moment kNm CSee Answer
Q18:Part 2: Limit Collapse of a Cracked Beam a) A long solid rectangular section beam, length L=1.4m, width b=40mm and depth 2h=100mm, is subject to uniform distributed loading W per unit length, as shown. The beam is made from alloy steel with yield strength oy = 665 MPa. W po x Wy L/2 16bh²oy 3L² L/2 Show that first yield will occur simultaneously on the top and bottom surfaces at the middle of the beam when the load W = Wy, where: 2h [2 marks]/n[2 Marks] b) The beam material is elastic perfectly plastic, with yield stress dy. Sketch the following stress distributions through the depth of the beam -h ≤ y ≤ h) at the mid-span: • Elastic • Partially plastic • Limit state From equilibrium (i.e. lower bound limit load approach), show that the limit load W₁ is: WL 8bh²oy L² Calculate the numerical value of W₁./nc) Visual inspection of the beam identifies a crack of undefined length a across the full section width b located mid-span at the bottom surface of the beam, as shown. a 9m 2hSee Answer
Q19:5. During the assembly of an aircraft wing, oversized fasteners are pressed into holes to fasten the skin and spars together. The stress field that develops in the skin takes on the form (in polar coordinates) = 0 = 0 = 0 = 0, where A = 0.001" is the amount of interference, Ore θz -AaE ΔαΕ ee = 4r² 472, ZZ rz Orr = a = 0.5" is the hole diameter, E = 10,000 ksi is the Young's modulus and r is the distance from the center of the hole. Take the Poisson's ratio of the material to be v = 0.33 and the yield strength to be Oy = 45 ksi. During operation, the wing bends and there is an additional far field axial stress in the skin of ax = 20 ksi. Note: when a press fit fastener is inserted, the stress concentration in a hole is greatly reduced. Take the fastener stress concentration factor to be K = 1 here. a. What and where are the greatest principal stresses around the hole without a fastener? (5 points) b. What and where are the greatest principal stresses around the hole with a fastener? (10 points) c. Does the material yield under a von Mises yield criterion in either case. (10 points) d. Why might it be advantageous to include press fit rivets (vs loose fasteners)? (10 points) Upper surface of sleeve Clearance-fit A2aA Lower surface of bolt head 6 Interference-fit Bolt Sleeve 6 a 6 axSee Answer
Q20:3.) (3 pts) What is the shear stress on the bolt (Diameter provided in the quiz description on the course space) that fastens the two steel plates together, which is subjected to a 2000 lb load acting as shown.See Answer

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