(Solved): A gabled-roof portal frame, shown in Fig. 1, is constructed from 150UB18.0 grade 300MPa structural ...

A gabled-roof portal frame, shown in Fig. 1, is constructed from 150UB18.0 grade 300MPa structural steel cross section to resist uniformly distributed wind pressure of Wp=2.4kN/m. If the height of the frame (H) is 3.2m and the roof angle (a) is 17 degrees, what would be the longest span length (L) for this frame to satisfy the flexural, shear and deflection design criteria? we we Coordinates of nodes 1 to 5 4 1 (0,0) 2 (0, H) we We 3 (0.5Lmax, H+0.5L maxxtana) 4 (Lmax, H) 6 (Lmax, 0) Lmax=? Fig. 1 Gabled-roof portal frame Flexural Design Criterion (My). Flexural design criterion is to ensure that the yielding moment (My) of a cross section is within the allowable values. My of a cross section is defined as the bending moment corresponding to the onset of yielding at the outermost fibre of the section. It is calculated by My = oy x I/C, where Oy is the yield normal stress (300 MPa), / is the moment of inertia of the section, and c is the distance from the neutral axis to the outermost fibre of the section. Shear Design Criterion (Vn). Shear design criterion is to ensure that the design shear force (Vn) does not cause stress in excess of the yield shear stress (Ty). The design shear force is calculated by Vn = TyxIxtw/Q, where ty= 0.60y, Q is the first moment of area of half cross section about the neutral axis, and tw is the web thickness of the cross section. Note that an approximate formula for calculating Vn of an I-shape steel section having a web thickness of tw and a web depth dw is Vn = Ty X dwX tw. Deflection Design Criteria (47 and 4H). To satisfy the serviceability requirement of a structure, its maximum deformation must not exceed an allowable value, even if all the other design criteria are met. AS4100-1998 specifies the maximum allowable vertical deflection Av to be L/250 and the lateral drift Ay to be H/150. a) Important Note: To obtain an accurate value of Lmax, you should continue the trials until the difference between each calculated/obtained criterion and the corresponding design criterion is within +/-1%. To achieve this you can use smaller increments than 0.2m. Task 1: What is the value of the moment of inertia for the specified section? (This value can be taken from STRAND7 section property tab; Provide two decimal places) = x 106mm4 What is the distance from the neutral axis to the outermost fibre for the specified section? (This value can be taken from STRAND7 geometry property tab; Provide one decimal place) c= mm What is the My value for the specified section? (Provide two decimal places) My= kNm What is the Lmax value based on My design criterion? (Provide two decimal places) Lmax= m Task 2: What is the value of the web depth for the specified section? (This value can be taken from STRAND7 geometry property tab; Provide an integer) dw= mm What is the thickness of the web for the specified section? (This value can be taken from STRAND7 geometry property tab; Provide an integer) tw= mm What is the Vn value for the specified section? (Provide two decimal places) Vn= KN What is the Lmax value based on Vn design criterion? (Provide two decimal places) Lmax= m Task 3: Important Note: Please note that the design criterion Ay is a function of Lmax, therefore, more trials should be expected to obtain an accurate max- What is the maximum allowable vertical deflection that can satisfy AS4100-1998? (Provide two decimal places) Ay= mm What is the Lmax value based on the Av design criterion? (Provide two decimal places) Lmax= m What is the maximum allowable horizontal deflection that can satisfy AS4100-1998? (Provide two decimal places) Ah= mm What is the max value based on the Ah design criterion? (Provide two decimal places) Lmax= m Task 4: What is the Lmax value satisfying ALL design criteria? (Provide two decimal places) Lmax= b) Task 1: Based on the maximum span length obtained from Task 4 of Part a, determine MMax and (I/C)original of the frame. (Provide two decimal places) [Note: 1/c=MMaxoy]. MMax= kNm (1/C)original = x103 mm Task 2: If your maximum span length in Task 1 of Part b is doubled whilst other parameters remain the same, detremine the correspoding MMax, and percentage change in the elastic section modulus (I/C) to ensure a safe design? (Provide two decimal places) [Note:Percentage change (%)=[(1/C)new-(I/C)original]/(1/C)new X 100). Mmax= kNm (1/C)new = x103 mm3 Percentage change= % c) Task 1: If the column members are changed to 180UB18 while the roof section remains the same (150UB18), how would the Mmax of the final portal frame (with respect to your answer to Task 1 Part b) change? o It will decrease. o It will increase. o It will remain the same. d) Task 1: The maximum span length calculated based on the shear criterion Vn (i.e. your answer to Task 2 of Part a) is obviously much longer than those according to the other three criteria (i.e., flexure My, vertical deflection Av and lateral drift AH). If a span length is to be determined based on the shear criterion, which of the following two options would you suggest to strengthen the original cross section so that the other three criteria can also be satisfied simultaneously? Why? (a) Option 1 (b) Option 2 WARTY I I o Option 1, beacuse strengthening the web would considerably increase the moment of intertia of the section, which helps to reduce the bending stresses and deflection. o Option 1, beacuse strengthening the web would considerably decrease the moment of intertia of the section, which helps to reduce the bending stresses and deflection. o Option 2, beacuse strengthening the flanges would considerably decrease the moment of intertia of the section, which helps to reduce the bending stresses and deflection. o Option 2, beacuse strengthening the flanges would considerably increase the moment of intertia of the section, which helps to reduce the bending stresses and deflection. QUESTION 1 Please upload the frame deformed shape image (including the un-deformed shape; scale factor 10%). Attach File Browse Local Files Browse Content Collection QUESTION 2 Please upload the frame bending moment diagram image (the moment values must be clearly seen). Attach File Browse Local Files Browse Content Collection QUESTION 3 Please upload the frame axial force diagram image (the axial force values must be clearly seen). Attach File Browse Local Files Browse Content Collection QUESTION 4 Please upload the frame shear force diagram image (the shear force values must be clearly seen). Attach File Browse Local Files Browse Content Collection