A beam with the following cross section is constructed with concrete of compressive strength of 5,000 psi and three fiberglass reinforcing bars that have a cross sectional area of 0.15 in.² The bars are elastic with a modulus of 7,800 ksi until they fail in a brittle manner at a strain of 1.8%. a. Estimate the mode of failure for the beam. Is it desirable? Justify your answer. b. Calculate the nominal moment capacity. c. What strength reduction factor would you use to calculate the factored design moment? 8" 12" 000 10"

A beam with the following cross section is constructed with concrete of compressive strength of 5,000 psi and three fiberglass reinforcing bars that have a cross sectional area of 0.15 in.² The bars are elastic with a modulus of 7,800 ksi until they fail in a brittle manner at a strain of 1.8%. a. Estimate the mode of failure for the beam. Is it desirable? Justify your answer. b. Calculate the nominal moment capacity. c. What strength reduction factor would you use to calculate the factored design moment? 8" 12" 000 10"

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter6: Introduction To Mechanical Properties

Section: Chapter Questions

Problem 6.3P: Compare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2...

See similar textbooks

Similar questions

2. The beam shown in Figure is 150mm wide and 300mm deep. The allowable bending stress on extreme fiber is 8 MPa. If x -2m: Which of the following gives the maximum moment that the beam can resist in Kilonewton-meter. Which of the following gives the maximum value of the uniform load w in Kilonewton per meter? Which of the following gives maximum value of P in Kilonewton? Po Mc 6M I
From the figure shown, fc’ = 18 MPa, fs = 128 MPa, and n = 10. Determine the moment capacity of concrete and steel (Cracked Analysis )
A cylindrical assembly consisting of a brass core and an aluminum collaris compressed by a load P (see figure). The length of the aluminum collarand brass core is 350 mm. the diameter of the core is 25 mm, and theoutside diameter of the collar is 40 mm. Also, the module of elasticity ofthe aluminum and brass are 72 GPa and 100 GPa, respectively.(a) If the length of the assembly decreases by 0.1% when the load Pisapplied, what is the magnitude of the load?(b) What is the maximum permissible load f^ if the allowable stresses inthe aluminum and brass are SO MPa and 120 M Pa, respectively?
A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of the external diameter of 3.6 cm and an internal diameter of 2 cm. The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.5 cm from the neutral axis Solution: (i) The moment of inertia = Answer and unit for part 1 ii) The radius of curvature is Answer and unit for part 2 (iii) The maximum bending stress is Answer and unit for part 3 iv) The bending stress at the point 0.5 cm from the neutral axis is
A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis (i) The moment of inertia in (mm^4)= ii) The radius of curvature in (mm) = (iii) The maximum bending stress in (N/mm^2)= iv) The bending stress at the point 0.6 cm from the neutral axis in (N/mm^2)=
A 2500 lb horizontal bar is supported by three 3/16-inch diameter wires as shown. The wires are symmetrically spaced and 20 feet long. The two outer wires are steel and the middle wire is brass. Calculate: a) Stresses in the wires
A steel pipe of length L = 4.0 ft, outside diameter = 6.0 in., and inside diameter = 4.5 in. is compressed by an axial force P kips. The material has modulus of elasticity E = 30,000 ksi and Poisson’s ratio υ = 0.30. Determine the following quantities for the pipe: (a) the shortening, (b) the lateral strain (c) the increase in the outer diameter and the increase in the inner diameter, and (d) the increase in the wall thickness. (Where P is equal to 51kips)
A steel rod of 15- mm diameter is held snugly (but without any initial stresses) between rigid walls by the arrangement shown in the figure part (a). (For the steel rod, use α = 12 x 10-6/˚C and E = 200 GPa.) Calculate the temperature drop ΔT (degrees Celsius) at which the average shear stress in the 12 – mm diameter bolt becomes 45 MPa. Also, what is the normal stress in the rod? What are the average bearing stresses in the bolt and clevis at A and between the washer (dW = 20mm) and wall (t = 18 mm) at B? If the connection to the wall at B is changed to an end plate with two bolts (see figure part b), what is the required diameter db of each bolt if the temperature drop is ΔT = 38˚C and the allowable bolt stress is 90 MPa?
A rectangular steel block 250 mmx100 mmx80mm is subjected to axial loads as follows. 480 kN (tensile in direction of its length) 900 kN (tensile on 250mm x 80 mm faces) 1000kN (comp. on 250mm x100mm faces) taking E=200 GN/m2 and 1/m=0.25 find a). Change in dimensions (height, width and length) b). Change in volume of the block c). Volumetric Strain c). Values of N and K (Module of Rigidity and Bulk Modulus) for material of the block. d). Determine the volume difference if the temperature of block increased by 20K. (Take alpha steel = 11.7 x 10-6 / 0C ) e). Discuss the behavioral characteristic for given application Comparing the impact from given mechanical loadings and thermal loadings to the block.
A 1 meter long steel rod AB of 15-mm diameter is held snugly (without any initial stresses) between rigid walls by the arrangement shown in the figure. (STEEL ROD : E = 200 GPa , α= 12 x 10-6/°C , and yield strength σY = 250 MPa.) a) If the rod undergoes a temperature drop of 24°C, and the bolt at B is tightened causing the rod to elongate by 0.0566 mm, determine the bearing stress between the washer and the wall. b) Determine the amount of temperature drop that is allowed if the factor of safety against yieldingis 4.
A closed right circular cylinder has radius 2 units and height 17 units A load of an unknown weight is put on top of the cylinder, causing the cylinder to shorten by 1.1 units. Find the new volume of cylinder due to this deformation in the height of the cylinder.
Let’s design a skateboard. The board is 30” long (between the wheels) and 12” wide. It will be composed of a core material with two faces that are not necessarily the same thickness or same material. The face materials will a higher strength, higher stiffness material. Core thickness is 0.5”. When loaded by a center weight of 500 lbs (which accounts for a person plus a safety factor), the bending stresses in the face and in the core must be less than their design values. Also the center deflection y must be less than 0.5”. Note that the center deflection y for a center applied load W is given by y= W x L3 / (48 x E x I) here L is total length and W=500 lbs and the product E x I is the composite (EI)