Question

A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an effective modulus of elasticity 140 GPa. a) If the cable is 14 m long, how much will it stretch when the load is picked up? (ans: 12.5 mm) If the cable is rated for a maximum load of 70 kN, what is the safety with respect to failure of the cable? (ans: 5.8) b) 3. A flexible connection consisting of rubber pads (thickness -9 mm) bonded to steel plates as shown below. The pads are 160 mm long and 80 mm wide a) Find the average shear strain in the rubber if the force P 16 kN and the shear modulus for rubber is 1250 kPa. (ans: 0.50) What is the horizontal displacement between the interior plate and the outer plate? (ans: 4.92 mm) b) 160 mm Rubber pad pad 80 mm r 9 mm Section X-X 4. A torque To is transmitted between two flanged shafts by means of ten 20 mmm bolts. The pitch circle diameter of the bolts is d = 250 mm. What is the maximum permissible torque if the allowable shear stress in the bolts is 85 MPa? (ans: 33.4 kNm) 5. Rigid bar ACB is supported by an elastic circular steel struct DC having an outer diameter of 380 mm and inner diameter of 365 mm. The elastic modulus of steel is 200 GPa. If P is 22 kN, calculate the change in length of the circular struct DC. What is the vertical displacement of the rigid bar at point B? (ans: 7.05x10 mm, 0.264 mm) 15 m 1.2 m 0.9 m 6. A safety valve on the top of a tank contain steam under pressure p has a discharge to release the steam when pressure reached p If the natural length of the spring is L and its stiffness is k, what should be the value of h of the valve? (Express your result as a formula for h.) (ans: h = 1-Thad, 4k 7. The three-bar truss ABC has a span L- 3m and is constructed of steel pipes of cross- sectional area A 3900 mm, and E-200 GPa. Identical loads fact both vertically and horizontally at joint C a) If P 475 kN, what is the horizontal displacement of joint B? (ans: 1.827 mm) b) What is the maximum permissible load value Pmr if the displacement of joint B is limited to 1.5 mm? (ans: 390 kN) 45° 45° 8. A slightly tapered bar BA of solid circular cross section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameter of the bar at ends A and B are ds and ds respectively. Determine the length of the bar if the elongation of the bar due to the load F-200 kN is 0.5 mm. Assume E# 72 GPa. (ans: 2.827 m) dg 200 mm da = 100 mm 9 Three steel cables jointly support a load of 60 kN. The diameter of the middle cable is 20 mm and the diameter of each outer cable is 12 mm. The tension in the cables are adjusted so that each cable carries one-third of the load (i.e. 20 kN). Later, the load is increased by 40 kN to a total load of 100 kN. Determine (a) what percent of the total load is now carried by the middle cable? And (b) What are the stresses in the middle and the outer cables respectively. (ans: 41.2%, 238 MPa, 383 MPa) Nominal Diameter Approximate Weight Effective Area Ultimate Load 0119 7672300 075 0.95 481 14400041 0745 1.75 25000 120 230 37200 6 192 10. The fixed-end bar ABCD consists of three segments. The end segments have a cross- sectional area A- 840 mm2 and length L- 200 mm. The middle segment has a cross- sectional area A:-1260 mm2 and length L-250 mm. Loads Ps and Pc are equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reaction at the fixed supports at A and D. (b) Determine the compressive axial force in the middle segment of the bar BC (ans: 10.5 kN, 2.0 kN, 15.0 kN) A2 11. A bar AB of length L is held between rigid supports and heated non-uniformly in such a manner increase AT at a distancex from end A is given by the expression where ΔTB is the increase in temperature at end B of the bar. Derive a formula for the compressive stress in the bar. (Assume the material has modulus of elasticity E and the coefficient of thermal expansion α). (ans: ATB AT 0 12. The bar ABC is loaded by a force P at the end C and by a force Q acting at the midpoint B. The bar has a constant axial rigidity EA. (a) Determine the strain energy of the bar when the force P acts alone (i.e. -0). (b) Determine the strain energy when the force O acts alone(i.e. P 0. (c) Determine the strain energy when the forces P and Q act simultaneously upon the bar. (an: 274 471 264201474 2EA 4EA 2EA 2EA 4EA

Answer 1

인ver Fable 40a AE (b) Factor of s R,LT =1104kN (From Talle) 70 non FBD → thickness t Rubbes pad Rubbex pods tm bmn

(a) SHEAR STRESS STRAIN TN THE RUBBER PADS avs (b Hori zontal Displacument h= heert ,of vale ( ompreued length of spring) d = diameter of dischame Hole ppress uwr n tank. Par pressw wohen valve opens し= natural length of.sping (L7h) k= stiffness"。 Fove in ompre.red pring Pressiuu Fora on spiny

)one degree stat mun use supexpos adon R as the Redundant non unifom tamperaltne chage Bar with AT AT at distanax ort at the end 'B" on Removing the supp of the Bar consider an element dx at a distana from end A d8-Elongation of element d ㄥ 0 comprenive Fora p g uiyed to shorter the ban by the amount δ

Compretive tre in Ba