The cross-section of a pretensioned prestressed concrete beam is shown in figure. The reinforcement is place concentrically. If the stress in steel at transfer is 1000 MPa, compute the stress in steel immediately after
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- The concrete at the top of the cross section shown in Figure 4 is formed in a triangle. Calculate the flexural strength, Mn, for the cross scction. The centroid of a triangle is shown for your reference. Assume f. = 4, 000 psi %3D1. Shown is a composite plate joined together by rivets. The components consist of two tension bar plates that is % X 4 inch and riveted together by two splice plates which is 0.8 X 6 inch. Each rivet has a diameter of 25.4 mm. Considering that the allowable stress for the tension bar plates and splice plates is o=20.0 ksi, the allowable shear stress for the rivets is o=25.0 ksi and the allowable bearing stress on the rivets and splice plates is o=25.0 ksi. What will be the maximum permissible load P such that none of the allowable stresses will be exceeded? Splice Plates a-0.75 in Bar Lc =0.80 in. Bar P d = 1.0 in. b=4.0 in. Rivets 'e = 6.0 in.1. Differentiate the permanent and the variable action with suitable examples 2. Analyze the stress-strain relationship of steel. Notes : Internal forces Fcc = 0.567fck(b x 0.8x) = 0.454 fck bx Fst = 0.87 fyk As Moment of resistance with respect to steel, M = Fcc.z Moment of resistance with respect to concrete, M = Fst.z Mbal = Kbal fck bd2 where Kbal = 0.167 As ‘ = (M-Mbal) / 0.87 fyk (d-d’) As = Mbal / 0.87 fyk zbal + As’
- A composite beam is made of two brass [E = 106 GPa] plates bonded to an aluminum [E = 60 GPa] bar, as shown. The beam is subjected to a bending moment of 1720 N-m acting about the z axis. Assume b=45 mm, d₁-53 mm, d₂-13 mm. Determine: (a) the maximum bending stresses Obr, Gal in the brass plates and the aluminum bar. (b) the stress in the brass Obrj at the joints where the two materials are bonded together. Brass (2) Aluminum (1) Brass (2) b ↓ d₂ d₁ d₂A composite beam is made of two brass [E = 97 GPa] plates bonded to an aluminum [E = 72 GPa] bar, as shown. The beam is subjected to a bending moment of 2420 N-m acting about the z axis. Assume b=64 mm, d1=36 mm, d2=13 mm. Determine: (a) the maximum bending stresses opy,Gal in the brass plates and the aluminum bar. (b) the stress in the brass obrj at the joints where the two materials are bonded together. Brass (2) d2 Aluminum (1) Brass (2) dz b Answers: (a) obr = i MPa, oal = i MPа. (b) Obrj MPa.A composite beam is made of two brass [E = 99 GPa] plates bonded to an aluminum [E = 63 GPa] bar, as shown. The beam is subjected to a bending moment of 2210 N-m acting about the z axis. Assume b=44 mm, d1=28 mm, d2=13 mm. Determine:(a) the maximum bending stresses σbr, σal in the brass plates and the aluminum bar.(b) the stress in the brass σbrjσbrj at the joints where the two materials are bonded together.
- Shown is a composite plate joined together by rivets. The components consist of two tension bar plates that is ¾ X 4 inch and riveted together by two splice plates which is 0.8 X 6 inch. Each rivet has a diameter of 25.4 mm. Considering that the allowable stress for the tension bar plates and splice plates is σ=20.0 ksi, the allowable shear stress for the rivets is σ=25.0 ksi and the allowable bearing stress on the rivets and splice plates is σ=25.0 ksi. What will be the maximum permissible load P such that none of the allowable stresses will be exceeded?An axial centric force of magnitude P = 450 kN is applied to the composite block shown by means of a rigid end plate. Knowing that h = 10 mm, determine the normal stress in (a) the brass core, (b) the aluminum plates. Aluminum plates (E = 70 GPa) 300 mm Brass core (E = 105 GPa) 40 mm h Rigid end plate 60 mmA copper strip (Ec= 105 GPa) and an aluminum strip (Ea = 75 GPa) are bonded together to form the composite beam shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 32 N-m, determine the maximum stress in the aluminum strip and in the copper strip. Aluminum Copper 24 mm 6 mm 6 mm The maximum compressive stress in the aluminum strip is -51.22 MPa (include a negative sign). The maximum tensile stress in the copper strip is 60.67 MPa.
- PROBLEM 6/6 F = 520 kN Determine the stress in each aluminum and steel bars after 0.2 mm F = 520 kN is applied. Note that a gap of 0.2 mm exist before the external load is Steel 280 mm applied and bars has equal distance with each other. Neglect the weight at the flat form. A = 1100 mm? E = 200 Gpa Steel Aluminum A = 2500 mm2 %3D E = 70 GPa %3DThe composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each section. The cross-sectional area and modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C. Aluminum Eal = 10(10³) ksi AAB=0.09 in² 2.00 kip -18 in- Copper Steel Ecu=18(10³) ksi Est = 29(10³) ksi ABC = 0.12 in² ACD= 0.06 in² 3.50 kip HK 3.50 kip -12 in.- 1.75 kip 1.75 kip -16 in 1.50 kipThe composite shaft , consisting of aluminium, copper and steel sections, is subjected to the loading shown. The cross-sectional areas of sections AB, BC and CD are AAB=0.08 in2, ABC=0.11 in2, and ACD=0.05 in2, respectively. The modulus of elasticity for each section are shown in the figure. Neglect the size of the collars at B and C. Determine the normal stress in section AB,BC and CD. Also determine the displacment of end A with respect to end D.