STRUCTURAL ANALYSIS (LL)
6th Edition
ISBN: 9780357030967
Author: KASSIMALI
Publisher: CENGAGE L
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Textbook Question
Chapter 5, Problem 54P
For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.
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There is a statically indeterminate beam in which the horizontal force
at the left and right ends (points A and D) is zero, and the vertical
force is shown in the figure below,
The flexural stiffness of the beam section is constant El:
(a) Find the (bending moment) reaction forces at points A and D.
B.2.
Elementary beam theory predicts that the axial bending stress ox in a
prismatic beam is given by:
σ, X
(M.1, M,1,)y+ (M, I. - M.1,-) z
(1,1.-1²-)
where My and M₂ are bending moments applied to a cross-section, and
where ly, Iz and lyz are second moments of area in the usual notation
(Oxyz is a Cartesian coordinate system in which the x axis corresponds
to the centroidal axis of the beam).
(i) What assumptions have been made in the derivation of the
above expression?
(ii) Indicate by means of a sketch the directions in which positive
values of the bending moments My and M₂ act on a cut plane
facing in the positive x direction.
The bending moment diagram is constant for an interval of a beam then the crossponding shear force diagram
is an inclined straight line.
A curved line.
A line parallel to the axis.
A zero line
Chapter 5 Solutions
STRUCTURAL ANALYSIS (LL)
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - Determine the equations for shear and bending...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.12 through 5.28 Determine the equations for...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - 5.29 through 5.51 Draw the shear and bending...Ch. 5 - Draw the shear and bending moment diagrams for the...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - For the beam shown: (a) determine the distance a...Ch. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Similar questions
- Start with the shear diagram. To use a segment of the left end of the beam to develop the expression for the shear, the vertical reaction at A must be known. Calculate the vertical reaction at A. Let a positive force act up. Write an expression for the internal shear for an arbitrary point between A and B. Write an expression for the internal shear for an arbitrary point between B and C. Draw the shear diagram for the beam. Write an expression for the bending moment at an arbitrary point between A and B. Use the standard sign convention for the internal moment for a beam. Write an expression for the bending moment at an arbitrary point between B and C. Draw the moment diagram for the beam.arrow_forwardIn the structures shown below all members have the same Young's Modulus, E, second moment of area, I, and cross sectional area, A. (a) Calculate the vertical deflection of the point load in the structure shown below. L A L (b) Using the principle of virtual work, calculate the internal forces in all the members in the structure shown below L A в (c) State all the assumptions. Barrow_forwardNonearrow_forward
- A simply supported beam of length L is subjected to a varying distributed load sin (3x/L) Nm-¹, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support isarrow_forwardFigure Q2(a) shows a cantilever beam that is subjected to a pure bending moment M = 3kN.m about the neutral axis (N.A) and the cross-section of a beam is shown in Figure Q2(b). Determine: (a) The moment of inertia about the neutral axis, InA. (b) The bending stress acting at point B and state whether it is in tension or compression. (c) The bending stress acting at point C (d) The maximum bending stress in the beam. M Figure Q2 (a) 20 mm B 150 mm C N 20 mm 150 mm 20 mm 250 mm Figure Q2 (b)arrow_forwardFor the beam shown, how does the shear change as you move from A to B? L- Select the correct response: There is not enough information to tell. It stays constant. It decreases linearly. It increases linearlyarrow_forward
- Plz solve A simply supported beam is subjected to series of point load moving from right to left as shown in the figure calculate maximum positive Siya present maximum bending moment at 10 m on the left supportarrow_forwardDetermine all the reactions at the support of the three-span continuous beam shown in the figure. Take flexural rigidity EI as constant. Horizontal Reaction at fixed support A, Ax, is zero. Draw the shear force and bending moment diagrams. Using the Method of Consistent Deformations. Solve the moment reaction at A (MA in kN-m), vertical reaction at A (Ay), B (By), C (Cy), D (Dy) (in kN)arrow_forwardFor certain values of w and P, the maximum positive bending moment in the beam is +7044 lb-ft, and the maximum negative bending moment is -8873 lb-ft. The cross section of the beam is shown. The pertinent section properties of the cross section are e = 2.90 in., f = 1.30 in., and I,= 18.3990 in.4. Calculate (a) the maximum tensile bending stress and (b) the maximum compressive bending stress that is produced in the beam. Enter your answers with the appropriate sign. B D b d yarrow_forward
- Determine/derive the Shear and Moment Equations of each segment of the beam (kindly include the FBD). Compute the Reactions and Draw the detailed Shear and Moment Diagram indicating values.arrow_forwardpls ans soonarrow_forwardThe rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm; link CD is-made of steet E = 200 GPa) and has a cross-sectional area 600 mm. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. 0.4 m 0.3 m 30 kN E T0.4 m 0.2 marrow_forward
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