Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Students have asked these similar questions
For the beam loaded as shown, use the method of superposition to determine the deflection of the beam at end A. Assume the
following values:
El = 2.8 x 104 kN-m² (constant for entire beam)
L = 15 m
w = 56 kN/m
Answer:
VA=
i
B
W
mm
L
C
If the beam shown is supported by the fixed wall at B and the rod AC. if the rod has a
cross sectional area =
10 x10-4 m2 and is made of the same material of the beam
if the area moment of inertia of the beam's cross section is 9.7 x 10-° m4
if the distributed load w = 8.5 kN, then,
the tension in the rod AC is . ... N
1 m
1 m
2 m
Oa. 27.57
Ob.926.32
Oc 6.38
Od. 63518.95
consider the beam shown in. EI is constant. assume that
EI is in kip * ft2.
determine the expression for the elastic curve using the coordinate x1 for 0 < x1 < 20 ft, where x1 is in feet.
v1 in ft
answer in terms of the variables x1, E and I.
determine the expression for the elastic curve using the coordinate x2 for 0 < x2 < 10 ft where x2 is in feet.
v2 in ft.
answer in terms of the variables x2, E and I.
specify the deflection of the beam at C.
vc in ft.
answer in terms of E and I.
specify the slope at A, measured counterclockwise from the positive x1 axis.
Theta A in rad.
answer in terms of E and I.
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Similar questions
- 1. For a simple supported beam with a bending moment diagram shown, determine the following a. Area moment of inertia of the given cross section b. Maximum tensile flexural stress and its location c. Maximum compressive flexural stresses and its location The beam has the triangular section shown: The beam has the triangular section shown. 200 mm 676 E M (Nm) 300 mm - 1200 - 1560 X-sectionarrow_forwardThe simply supported shaft has a moment of inertia of 2I for region BC and a moment of inertia I for regions AB and CD. Determine the maximum deflection of the shaft due to the load P. The modulus of elasticity is E.arrow_forwardPart B - Moments of inertia of the cross section with respect to the y- and z-axesTo calculate the absolute maximum bending stress in the member using the flexure formula for unsymmetrical bending, the moments of inertia of the cross section must be calculated. Select the correct formulas for these values. Iy=? Part C - Neutral-axis angle due to externally applied momentsThe neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, α, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane.Express your answer to three significant figures and include the appropriate units. α=? Part D - Absolute maximum stress in cross section ABCDDetermine the absolute maximum stress, |σmax|, in cross section ABCD due to the two externally applied moments. |σmax|=?arrow_forward
- Problem 2: The beam is held in equilibrium by a roller at A and a pin at B. The beam supports a uniform distributed load (2 kip/ft) and a concentrated moment (30 kip-ft) at the locations shown. Use the equation method to solve this problem. 2 kip/ft Į 5 ft 5 ft 30 kip-ft 5 ft (a) Derive expressions for V(x) and M(x) in each section of the beam. (b) Use the results from part (a) to draw the shear force (V) and bending moment (M) diagrams for the beam. Clearly label all important values and points on the diagrams.arrow_forwardThe beam is subjected to the load shown. The beam is made of material having an E = 200 GPa and I = 65.0 x 10-6 m4. Using singularity functions, develop an expression for the bending moment M(x) asfunction of position (x) along the beam.arrow_forward3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam shown in the following figure. Also determine the reaction forces and moments. Each element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105 mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for each element, assembly of k matrices to get global stiffness matrix (K) and application of boundary conditions. Then solve the reduced K matrix to get displacements and reactions 3000 N 150 mm 75 mm 125 mmarrow_forward
- 2 - Use double integration to determine the elastic curve of the cantilever beam under lateral loading, where w is the load intensity (per unit length) at the left end. Flexural rigidity is El. Show that the tip displacement is: y w w14 U(L)=-30EIarrow_forwardFor the beam shown, determine in terms of W, L, E, and I: The equation of the elastic curve The rotations at points A and B Deflection of point C The maximum deflection of the beam Check the results of parts b and c using the Area Moment Methodarrow_forwarddetermine the diagram of the shear forces and bending moments in the beam shown below. Data P = 20kN, M = 60kNm, q = 10kN / m, a = 5m, b = 2m, c = 3, alpha = 60.arrow_forward
- The simply supported shaft has a moment of inertia of 2I for region BC and a moment of inertia I for regions AB and CD. Determine the maximum deflection of the shaft due to the load P.arrow_forwardA force tangent to 1.75 feet diameter pulley is 5200 N and is mounted on a 2 inches shaft. Determine the torsional deflection per meter of length if G = 83 x 106 Kpa.arrow_forwardPart A - Free-body diagram of the resolved components of the moments The two externally applied moments can be resolved into their respective y and z components. Determine the moments in each principal direction, My and Mz, and draw the corresponding free-body diagram. Part B - Moments of inertia of the cross section with respect to the y- and z-axes To calculate the absolute maximum bending stress in the member using the flexure formula for unsymmetrical bending, the moments of inertia of the cross section must be calculated. Select the correct formulas for these values. Iy=? Part C - Neutral-axis angle due to externally applied moments The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, αα, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane. |α| =? Part D - Absolute maximum stress in cross section ABCD…arrow_forward
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